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How to Check Math Homework

Last Updated: May 10, 2021 References

This article was co-authored by Sean Alexander, MS . Sean Alexander is an Academic Tutor specializing in teaching mathematics and physics. Sean is the Owner of Alexander Tutoring, an academic tutoring business that provides personalized studying sessions focused on mathematics and physics. With over 15 years of experience, Sean has worked as a physics and math instructor and tutor for Stanford University, San Francisco State University, and Stanbridge Academy. He holds a BS in Physics from the University of California, Santa Barbara and an MS in Theoretical Physics from San Francisco State University. There are 9 references cited in this article, which can be found at the bottom of the page. This article has been viewed 14,721 times.

Most people who work hard on their homework want to make sure that they are doing it correctly. When you are working from home, however, you don’t have your teacher to tell you whether or not your answers are correct. There are a number of ways to check math work you do outside of school. By checking your own work, having someone else check your work, or using online tools, you can make sure your solutions are correct before turning in your work.

Checking By Yourself

• If you are doing multiplication, you can check your work by doing repeated addition.

Asking for Help

• Some good sites for going over how to do math problems quickly are Math is Fun [5] X Research source and Virtual Nerd. [6] X Research source

• When you compare your answer with a friend, make sure you are not just changing your answers without learning where you made your mistake. If your friend found the correct answer, have him or her show you how to solve the problem.

• If you do your work at home but don’t feel confident about it, talk to your teacher as soon as possible the next day. They can quickly check your work, and you might have time to correct your answers before turning it in. Likely, you will get credit for trying your best.

Using Resources

• Work through your problems first, and only use the calculator to check your answers. You need to show your work so that your teacher knows you understand how to solve the problems.
• If you don’t have a calculator, you can find a number of online calculators by simply searching for them on Google.

• For algebra, you can use an equation calculator, like Symbolab. [7] X Research source
• For geometry, you can simply type what you are looking for into Google, and a calculator will pop up. For example, if you are finding the area of a triangle, type “area of a triangle” into Google. Then insert your known values into the calculator (such as base and height), and Google will supply the answer.
• There are a number of converters online. Math is Fun has a unit converter that can help you convert from one unit of measurement to another, such as inches to centimeters. [8] X Research source Convert Me has conversion calculators for most measurements, including speed, temperature, and capacity. [9] X Research source

• As when using a calculator or online tools, try doing the problems on your own first, then check your answers.

Expert Q&A

You Might Also Like

• ↑ Sean Alexander, MS. Academic Tutor. Expert Interview. 14 May 2020.
• ↑ http://mathandreadinghelp.org/how_to_estimate_a_math_problem.html
• ↑ http://www.virtualnerd.com/middle-math/equations-functions/expressions/inverse-operations-definition
• ↑ http://www.futurity.org/learning-students-teaching-741342/
• ↑ http://mathisfun.com/
• ↑ http://www.virtualnerd.com/
• ↑ https://www.symbolab.com/solver/equation-calculator
• ↑ https://www.mathsisfun.com/unit-conversion-tool.php
• ↑ http://www.convert-me.com/en/

About this article

To check your math homework yourself, try plugging your answer back into the equation you started with. For example, if you solved for x, plug the value you got for x into the equation and check to see if the equation makes sense. If it doesn't, you know there's something off about your answer. Another way you can check your work is by using an alternative method to solve the problem. If you get the same answer using a different method, there's a good chance your original answer was right. For example, if you're trying to solve 45×3, you could also solve the problem using addition by adding 45+45+45 to get 135. If 135 is the answer you got using multiplication, you know your answer is correct. For more expert math-checking tips, read the full article below! Did this summary help you? Yes No

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Learning Objectives

By the end of this section, you will be able to:

• Simplify fractions
• Multiply and divide fractions
• Add and subtract fractions
• Use the order of operations to simplify fractions

Warm-up \(\PageIndex{1}\)

Compute the following

• \(16\div 2\)
• \(-16\div -8\)
• \(6\div -6\)

What is a Fraction?

Now try \(1\div 2\). Is this an integer? No, it's just \(1\div 2\)

Conceptually this is asking how many friends you can feed with 1 slice of pizza if each friend eats 2 slices. Well, you can feed half of a friend, that is \(\frac{1}{2}\). If we expand our numbers once again we can accommodate these new numbers we will call fractions. Fractions represent smaller parts of whole numbers. If we now allow fractions, we get the rationals, \(\mathbb{Q}\). Rationals are any number that can be written as an integer over an integer.

A fraction is written \(\dfrac{a}{b}\), where \(b\neq 0\) and

\(a\) is the numerator and \(b\) is the denominator .

A fraction represents parts of a whole. The denominator \(b\) is the number of equal parts the whole has been divided into, and the numerator \(a\) indicates how many parts are included.

Let's create a fraction for example, take a random integer.

7? Good choice! Take another integer.

3? Another good choice!Taking 7 over 3 we get \(\frac{7}{3}\). Really this is expressing the number we get when we divide 7 by 3.

Where does the negative sign go in a fraction? Usually the negative sign is in front of the fraction, but you will sometimes see a fraction with a negative numerator, or sometimes with a negative denominator. Remember that fractions represent division. When the numerator and denominator have different signs, the quotient is negative.

\[\dfrac{−1}{3}=−\dfrac{1}{3} \; \; \; \; \; \; \dfrac{\text{negative}}{\text{positive}}=\text{negative}\]

\[\dfrac{1}{−3}=−\dfrac{1}{3} \; \; \; \; \; \; \dfrac{\text{positive}}{\text{negative}}=\text{negative}\]

PLACEMENT OF NEGATIVE SIGN IN A FRACTION

For any positive numbers \(a\) and \(b\),

\[\dfrac{−a}{b}=\dfrac{a}{−b}=−\dfrac{a}{b}\]

Example \(\PageIndex{1}\)

If we have -7 or -3 but not both then we would get \(-\frac{7}{3}\) This is the same as \(\frac{-7}{3}\) or \(\frac{7}{-3}\).

\(\frac{-7}{3} = \frac{7}{-3} = -\frac{7}{3}\)

Any integer can be turned into a fraction with 1 as the denominator e.g \(3=\frac{3}{1}\).

Let's take a look at when we will get a nice integer from division.

Factor Trees

Definition: divisible.

A number \(x\) is "divisible" by another number \(y\) if \(x\div y\) is an integer

Example \(\PageIndex{2}\)

9 is divisible by 3 since \(9\div 3=3\) 9 is not divisible by 2 since \(9\div 2\) is not an integer.

Definition: Prime

A "prime number" is an integer that is only divisible by itself and 1 as well as negative itself and -1.

Example \(\PageIndex{3}\)

7 is prime since it is not divisible by any integer except for \(\pm 7\) and \(\pm 1\)

9 is not prime since 9 is divisible by 3 which is not \(\pm 9\) or \(\pm 1\).

We can "decompose" numbers into the prime numbers that were multiplied together to create them. This is called factoring.

Example \(\PageIndex{4}\)

• \(24 = 2 \cdot 2 \cdot 2 \cdot 3\)
• \(30 = 2 \cdot 3 \cdot 5\)
• \(90 = 2 \cdot 3\cdot 3 \cdot 5\)

A popular trick to use for factoring numbers is called a factor tree . Let's take a look at a simple example on how to do this. Let's decompose 6 into its prime factors

This involves dividing numbers until you get numbers that are prime. Here we note 6 is divisible by 3 and \(6\div 3=2\) so we broke 6 up into \(3\cdot 2\). We can't break this up anymore since 3 and 2 are prime.

Example \(\PageIndex{5}\)

Decompose 24 using a factor tree.

You can divide 24 by 4 to get 6. You can decompose 6 into 3 and 2. While you can decompose 4 into 2 and 2. So you can decompose 24 into \(2\cdot 3\cdot 2\cdot 2\) we see that 3 and 2 are prime so we can't decompose anymore. Notice that the factors produced are the same as in the previous example.

Exercise \(\PageIndex{6}\)

Decompose 30 using a factor tree.

30 is divisible by 5 and \(30\div 5=6\) which we can decompose into 3 and 2.

So \(30=5\cdot 3\cdot 2\). This agrees with the answer in the previous example.

We see this isn't the only way to decompose 30 but you will still get the same result. For example you could have used 3 and 10 and decomposed 10 into 5 and 2 but the result is still \(30=5\cdot 3\cdot 2\)

Exercise \(\PageIndex{7}\)

Decompose 90 using a factor tree.

We can break 90 up into 3 and 30 and decompose 30.

So \(90=3\cdot 3\cdot 5\cdot 2\). This agrees with the example in the previous example.

Simplify Fractions

Try to input \(\frac{4}{8}\) and \(\frac{1}{2}\) into your calculator. What do you get? Why do you think the both inputs give you .5? It is because both of them express the same number. That is, 4 is half of 8 and 1 is half of 2. We can simplify \(\frac{4}{8}\) by decomposing 4 and 8 into a product of its primes, that is \(\frac{4}{8}=\frac{2\cdot2}{2\cdot 2\cdot 2}\). Now using the fact that we can break up a fraction, we can break up \(\frac{2\cdot2}{2\cdot 2\cdot 2}=\frac{2\cdot2\cdot 1}{2\cdot 2\cdot 2}=\frac{2}{2}\cdot \frac{2}{2}\cdot \frac{1}{2}=1\cdot1\cdot\frac{1}{2}=\frac{1}{2}\). This is why it is ok to cancel terms that are multiplied from the numerator and denominator. It is also common to just cross things out as in \(\frac{2\cdot2}{2\cdot 2\cdot 2}=\frac{\cancel{2}\cdot\cancel{2}}{\cancel{2}\cdot \cancel{2}\cdot 2}=\frac{1}{2}\).

There are many ways to write a fraction, some may say there is an infinite way to write the same fraction, but we usually write it in simplest form, that is when we can no longer cancel anything from the top and bottom.

Fractions that have the same value are equivalent fractions .

The Equivalent Fractions Property allows us to find equivalent fractions and also simplify fractions.

If \(a\), \(b\), and \(c\) are numbers where \(b\neq 0,c\neq 0\),

then \(\dfrac{a}{b}=\dfrac{a·c}{b·c}\) and \(\dfrac{a·c}{b·c}=\dfrac{a}{b}.\)

A fraction is considered simplified if there are no common factors, other than 1, in its numerator and denominator.

For example,

\(\dfrac{2}{3}\) is simplified because there are no common factors of \(2\) and \(3\).

\(\dfrac{10}{15}\) is not simplified because \(5\) is a common factor of \(10\) and \(15\).

We simplify, or reduce, a fraction by removing the common factors of the numerator and denominator. A fraction is not simplified until all common factors have been removed. If an expression has fractions, it is not completely simplified until the fractions are simplified.

Sometimes it may not be easy to find common factors of the numerator and denominator. When this happens, it is a good idea to factor the numerator and the denominator into prime numbers using the factor tree, then cancel out the common factors using the Equivalent Fractions Property.

Example \(\PageIndex{8}\)

Simplify \(\dfrac{120}{252}\)

Simplify \(\dfrac{−315}{770}\).

Simplify \(−\dfrac{69}{120}\).

\(−\dfrac{23}{40}\)

EXAMPLE \(\PageIndex{9}\)

Simplify \(−\dfrac{120}{192}\).

\(−\dfrac{5}{8}\)

Multiplying Fractions

Multiplying fractions is a simple operation. All you do is multiple the numerator with the numerator and the denominator with the denominator. Let's first get an intuitive idea on why that works. First say you have \(\frac{1}{3}\) of a pizza and you multiplied it by 3, that is you put 3 \(\frac{1}{3}\) pizzas together. You would get 1 whole pizza! In math, this would look like \(3\cdot \frac{1}{3}=\frac{3}{1}\cdot\frac{1}{3}=\frac{3\cdot 1}{1\cdot3}=\frac{3}{3}=1\).

We can also go backwards as in we can rewrite \(\frac{2}{3}\) as \(2\cdot \frac{1}{3}\).

What about the denominators? Why do we multiply those? Say you have a whole pizza and you divide it into 3 equal slices. You then cut a slice in half to get two slices. We see that the small slices from the 2nd cut make up \(\frac{1}{6}\) of a pizza. This makes sense because if you cut each slice in half, you would have 6 equally sized slices and 1 slice from that would be \(\frac{1}{6}\) a pizza. So we divided a pizza by 3 and then each slice in 2. We can express this using an equation as \(\frac{1}{3}\cdot\frac{1}{2}=\frac{1}{3}\div 2=(1\div 3)\div 2=\frac{1}{6}\).

Now let's put all that intuition together.

Example \(\PageIndex{10}\)

\[\frac{2}{3}\cdot \frac{7}{5}\]

\begin{align*} \frac{2}{3}\cdot \frac{7}{5}&=\frac{2\cdot 7}{3\cdot 5}\\ &=\frac{14}{15} \end{align*}

We that was way easier than all that intuition.

Let's do some more examples,

Exercise \(\PageIndex{11}\)

Compute the following:

• \(\frac{1}{4}\cdot \frac{1}{4}\)
• \(\frac{1}{3}\cdot -\frac{2}{3}\)
• \(-\frac{2}{3}\cdot -\frac{4}{5}\)
• \(\frac{1\cdot 1}{4\cdot 4}=\frac{1}{16} \)
• \(-\frac{1\cdot 2}{3\cdot 3}=-\frac{2}{9} \)
• \(--\frac{2\cdot 4}{3\cdot 5}=\frac{8}{15} \)

Now lets combine these strategies to compute and simplify a product of fractions.

Example \(\PageIndex{12}\)

Compute \(\dfrac{2}{3}\cdot\dfrac{27}{4}\)

Compound Fractions and Dividing Fractions

The numerators or denominators of some fractions contain fractions themselves. A fraction in which the numerator or the denominator is a fraction is called a compound fraction. Some people may use complex fraction but we will see later that this is actually terrible and horrible terminology. Still just know that complex fraction is the same as a compound fraction.

Definition: COMPOUND FRACTION

A compound fraction is a fraction in which the numerator or the denominator contains a fraction.

Some examples of compound fractions are:

\[\dfrac{\frac{6}{7}}{3} \quad \dfrac{\frac{3}{4}}{\frac{5}{8}} \quad \dfrac{\frac{x}{2}}{ \frac{5}{6}}\]

To simplify a compound fraction, remember that the fraction bar means division. For example, the compound fraction \(\dfrac{\frac{3}{4}}{\frac{5}{8}}\) means \(\dfrac{3}{4}÷\frac{5}{8}.\)

Surprisingly, division is just as easy as multiplication! All we need to do is take the top fraction and multiply it by the "reciprocal" of the bottom fraction.

Definition: RECIPROCAL

The reciprocal of a number is the multiplicative inverse. That is, the number you need to multiply to it to get 1.

This is very easy for the rationals as we just need to switch the numerator with the denominator.

Example \(\PageIndex{13}\)

The reciprocal of \(2=\dfrac{1}{2}\) is \(\dfrac{1}{2}\) since \(2\cdot \dfrac{1}{2}=1\).

The reciprocal of \(\dfrac{3}{2}\) is \(\frac{2}{3}\) since \(\dfrac{3}{2}\cdot\dfrac{2}{3}=1\)

Now we can look at an intuitive example of dividing by a fraction. Lets say a child eats half a slice of pizza and you have a pizza that contains 8 slices. How many children can you feed with 8 slices? Well each child eats half a slice so you would be able to feed 2 children with each slice and you have 8 slices, so you can feed 16 children. In an equation, this looks like \[\dfrac{\dfrac{8}{1}}{\dfrac{1}{2}}=\dfrac{8}{1}\cdot\dfrac{2}{1}=\dfrac{16}{1}=16\]

Now lets get a bit more complicated with...teenagers...that eat \(\dfrac{3}{4}\) of a slice each. That is, each teenager eat 3 quarter slices. Say you have \(\dfrac{3}{2}\) slices of pizza, that is 3 half slices. How many teenagers can you feed with that? Well let's rewrite \(\dfrac{3}{2}\) as \(3 \cdot \dfrac{1}{2}\) and save the multiplication with \(\dfrac{1}{2}\) for later. Let's cut up 3 slices into quarter slices so we have \(3\cdot 4=12\) quarter slices. each teenager eats 3 quarter slices so we can feed \(\dfrac{12}{3}=4\) teenagers. BUT WAIT we had 3 half slices so we can actually feed \(4\cdot \dfrac{1}{2}=\dfrac{4}{2}=2\) teenagers. This is just \[\dfrac{\dfrac{3}{2}}{\dfrac{3}{4}}=\dfrac{3}{2}\cdot\dfrac{4}{3}=\dfrac{12}{6}=2\]

WOW that was way easier than the intuition. You don't need to remember the intuitive examples for the test but hopefully you now understand why you are doing what you are doing. Now lets take a look at a step by step problem. To help with the examples, remember "invert and multiply" ; this means that to divide, we flip over the denominator and multiply it by the numerator.

Example \(\PageIndex{14}\)

Compute \(\dfrac{\dfrac{9}{2}}{\dfrac{27}{4}}\)

This is the same process as above just with an extra step in the beginning.

Example \(\PageIndex{15}\)

Compute \(−\dfrac{7}{18}÷(−\dfrac{14}{27}).\)

Divide: \(−\dfrac{7}{27}÷(−\dfrac{35}{36})\).

\(\dfrac{4}{15}\)

Divide: \(−\dfrac{5}{14}÷(−\dfrac{15}{28}).\)

\(\dfrac{2}{3}\)

Add and Subtract Fractions

Let's move on to addition. Say you have half a pizza and your friend has half a pizza, then between the two of you, you all have a whole pizza. That is, \(\frac{1}{2}+\frac{1}{2} = \frac{2}{2} = 1\). Note that we added the numerators together and left the denominators unchanged.

When we multiplied fractions, we just multiplied the numerators and multiplied the denominators right straight across. To add or subtract fractions, they must have a common denominator.

FRACTION ADDITION AND SUBTRACTION

If \(a\), \(b\), and \(c\) are numbers where \(c≠0\), then

\[\dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c} \text{ and } \dfrac{a}{c}−\dfrac{b}{c}=\dfrac{a−b}{c}\]

To add or subtract fractions, add or subtract the numerators and place the result over the common denominator.

What if the denominators are different? Then make them the same! We can make them the same by using a fundamental trick of math

Theorem: 1st fundamental trick of math \(\PageIndex{16}\)

A number multiplied by 1 is the same number. That is, if \(a\) is any number, then \(a\cdot 1=a\)

That doesn't seem like much of a trick but there are many creative ways to write the number 1.

For example \(\frac{2}{2}\) and \(\frac{62}{62}\) are 1.

Definition: Least Common Multiple (LCM)

The least common multiple (LCM) of two integers \(x,y\) is the smallest integer, \(c\) such that \(c\) is divisible by \(x\) and \(y\).

Example \(\PageIndex{17}\)

The LCM of 4 and 6 is 12 because 4 and 6 divide 12 and 12 is the smallest integer that both 6 and 4 divide evenly.

The LCM of 4 and 6 is not 24 because, even though 4 and 6 divide 24, it is not the smallest integer that both 6 and 4 divide evenly.

Let's do an example of how to find the LCM

Example \(\PageIndex{18}\)

Find the lcm of 8 and 12.

Note: Starting from left to right, we write down the three 2s we got from 8. We skip the two 2s from 12 since we already picked up three 2s from 8, and we pick up a 3 since we didn't already have it.

The least common denominator (LCD) of two fractions is the smallest number that can be used as a common denominator of the fractions. The LCD of the two fractions is the least common multiple (LCM) of their denominators.

Definition: LEAST COMMONE DENOMINATOR

The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.

After we find the least common denominator of two fractions, we convert the fractions to equivalent fractions with the LCD. Putting these steps together allows us to add and subtract fractions because their denominators will be the same!

Let's first do an intuitive example.

Let's say you have half a pizza and a quarter of a pizza. How much pizza do you have all together and why is it \(\frac{3}{4}\)th of a pizza? We broke up the half of a pizza into 2 quarters of a pizza and then added them to the quarter of a pizza to get 3 quarters of a pizza. In an equation this looks like \(\dfrac{1}{2}+\dfrac{1}{4}=\dfrac{2}{4}+\dfrac{1}{4}=\dfrac{3}{4}\)

Did you notice that 4 is the LCM of 2 and 4? If we want to add fractions all we do is make them have the same denominator and the denominator that is easiest to work with is the LCM!

Example \(\PageIndex{19}\)

Compute \(\dfrac{3}{10}+\dfrac{2}{15}\)

Step 3: multiply the 1st numerator and denominator by the 1st number above.

\(\dfrac{3\cdot 3}{10\cdot 3}=\dfrac{9}{30}\)

This is where we multiply by a 1 since \(\dfrac{3}{10}=\dfrac{3}{10}\cdot 1=\dfrac{3}{10}\cdot\frac{3}{3}=\dfrac{3\cdot 3}{10\cdot 3}\). Same thing goes for the next step.

This is the same procedure for subtraction too.

Example \(\PageIndex{20}\)

Compute \(\dfrac{2}{3}-\dfrac{4}{5}\)

\(\frac{15}{3}=5\)

\(\frac{15}{5}=3\)

Lets take a look at some more examples.

EXAMPLE \(\PageIndex{21}\)

Add: \(\dfrac{7}{12}+\dfrac{11}{15}\).

\(\dfrac{79}{60}\)

EXAMPLE \(\PageIndex{22}\)

Add: \(\dfrac{13}{15}+\dfrac{17}{20}\).

\(\dfrac{103}{60}\)

We now have all four operations for fractions. The Table below summarizes fraction operations.

Use the Order of Operations to Simplify Fractions

The fraction bar in a fraction acts as grouping symbol. The order of operations then tells us to simplify the numerator and then the denominator. Then we divide.

SIMPLIFY AN EXPRESSION WITH A FRACTION BAR.

• Simplify the expression in the numerator. Simplify the expression in the denominator.
• Simplify the fraction.

EXAMPLE \(\PageIndex{23}\)

Simplify: \(\dfrac{4(−3)+6(−2)}{−3(2)−2}\).

The fraction bar acts like a grouping symbol. So completely simplify the numerator and the denominator separately.

\(\begin{array}{lc} \text{} & \dfrac{4(−3)+6(−2)}{−3(2)−2} \\[5pt] \text{Multiply.} & \dfrac{−12+(−12)}{−6−2} \\[5pt] \text{Simplify.} & \dfrac{−24}{−8} \\[5pt] \text{Divide.} & 3 \end{array}\)

EXAMPLE \(\PageIndex{24}\)

Simplify:\(\dfrac{8(−2)+4(−3)}{−5(2)+3}\).

EXAMPLE \(\PageIndex{25}\)

Simplify: \(\dfrac{7(−1)+9(−3)}{−5(3)−2}\).

Now we’ll look at compound fractions where the numerator or denominator contains an expression that can be simplified. So we first must completely simplify the numerator and denominator separately using the order of operations. Then we divide the numerator by the denominator as the fraction bar means division.

EXAMPLE \(\PageIndex{26}\)

Simplify \(\frac{\frac{1}{2}-\frac{5}{2}}{\frac{3}{5}+\frac{1}{5}}\)

EXAMPLE \(\PageIndex{27}\)

Simplify: \(\dfrac{\left(\frac{1}{3}\right)}{2+2}\).

\(\frac{1}{12}\)

EXAMPLE \(\PageIndex{28}\)

Simplify: \(\dfrac{1+4\cdot 4}{\left(\frac{1}{4}\right)}\).

SIMPLIFY COMPOUND FRACTIONS.

• Simplify the numerator.
• Simplify the denominator.
• Divide the numerator by the denominator.
• Simplify if possible.

EXAMPLE \(\PageIndex{29}\)

Simplify: \(\dfrac{\dfrac{1}{2}+\dfrac{2}{3}}{\dfrac{3}{4}−\dfrac{1}{6}}\).

It may help to put parentheses around the numerator and the denominator.

\(\begin{array}{lc}\text{} & \dfrac{\dfrac{1}{2}+\dfrac{2}{3}}{\dfrac{3}{4}−\dfrac{1}{6}} \\[6pt] \text{Simplify the numerator }(LCD=6)\text{ and } \\[6pt] \text{simplify the denominator }(LCD=12). & \dfrac{\left(\dfrac{3}{6}+\dfrac{4}{6}\right)}{\left(\dfrac{9}{12}−\dfrac{2}{12}\right)} \\[6pt] \text{Simplify.} & \left(\dfrac{7}{6}\right)\left(\dfrac{7}{12}\right) \\[6pt] \text{Divide the numerator by the denominator.} & \dfrac{7}{6}÷\dfrac{7}{12} \\[6pt] \text{Simplify.} & \dfrac{7}{6}⋅\dfrac{12}{7} \\[6pt] \text{Divide out common factors.} & \dfrac{\cancel{7}⋅\cancel{6}⋅2}{ \cancel{6}⋅\cancel{7}⋅1} \\[6pt] \text{Simplify.} & 2 \end{array}\)

EXAMPLE \(\PageIndex{30}\)

Simplify: \( \dfrac{\dfrac{1}{3}+\dfrac{1}{2}}{ \dfrac{3}{4}−\dfrac{1}{3}}\).

EXAMPLE \(\PageIndex{31}\)

Simplify: \(\dfrac{\dfrac{2}{3}−\dfrac{1}{2}}{ \dfrac{1}{4}+\dfrac{1}{3}}\).

\(\frac{2}{7}\)

Key Concepts

• If \(a\), \(b\), and \(c\) are numbers where \(b≠0,c≠0\), then

\(\dfrac{a}{b}=\dfrac{a·c}{b·c}\) and \(\dfrac{a·c}{b·c}=\dfrac{a}{b}.\)

• Rewrite the numerator and denominator to show the common factors. If needed, factor the numerator and denominator into prime numbers first.
• Simplify using the Equivalent Fractions Property by dividing out common factors.
• Multiply any remaining factors.

\(\dfrac{a}{b}·\dfrac{c}{d}=\dfrac{ac}{bd}\)

To multiply fractions, multiply the numerators and multiply the denominators.

\(\dfrac{a}{b}÷\dfrac{c}{d}=\dfrac{a}{b}⋅\dfrac{d}{c}\)

To divide fractions, we multiply the first fraction by the reciprocal of the second.

\(\dfrac{a}{c}+\dfrac{b}{c}=\dfrac{a+b}{c} \text{ and } \dfrac{a}{c}−\dfrac{b}{c}=\dfrac{a−b}{c}\)

• Yes—go to step 2.
• Find the LCD.
• Change each fraction into an equivalent fraction with the LCD as its denominator.
• Add or subtract the fractions.
• Simplify, if possible.

\(\dfrac{−a}{b}=\dfrac{a}{−b}=−\dfrac{a}{b}\)

• Divide the numerator by the denominator. Simplify if possible.

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Fractions Homework: Assignments and Activities

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Students begin to study fractions in third grade. Keep reading to learn what to expect from fraction homework assignments. Below are tips on how to help your child at home as well as sample problems with explanations.

What Do Fraction Homework Assignments Include?

Depending on what grade your child is in, fraction assignments may include adding and subtracting fractions with like denominators or unlike denominators. If your child is in later grades, fraction homework may also include multiplying and dividing fractions.

When adding and subtracting fractions with like denominators, only look at the numbers in the numerators. For example, 2/4 + 1/4 = (2+1)/4 = 3/4. The denominator always remains the same.

When working with unlike denominators, the first step is to make the denominator the same. Consider the problem 1/6 + 2/3. The denominator for both fractions should be six, so multiply the second fraction by two (2/3 x 2/2 = 4/6). Then add: 1/6 + 4/6 = 5/6.

For multiplying fractions, simply multiply the numerators together and the denominators together. In the problem 4/7 x 2/5, multiply (4 x 2)/(7 x 5) = 8/35. Similarly, with division problems, turn the second fraction into a reciprocal by inverting it. The problem 3/5 ÷ 2/3 should look like this: 3/5 x 3/2 = 9/10. Remind your child to look at the answer to a problem closely to see if the fraction can be simplified, or reduced, into a smaller fraction.

Although additional problems and worksheets can be helpful, activities can be both fun and educational. For instance, have your child add fractions using drawings. For the problem 3/5 + 1/5, have your child draw a circle. Divide it into five equal parts and color three parts. Then, color one more part. Ultimately, there should be four out of five parts colored because the answer is 4/5.

Sample Assignments by Concept

Like denominators, unlike denominators, multiplication.

5/9 ÷ 3/2

Other Articles You May Be Interested In

Fractions can be a confusing topic for some students. Read on to learn how you can help your children better understand the uses of fractions.

Children often struggle to master concepts such as addition and subtraction, multiplication and division, fractions, and math involving time and money. Read this article to learn how you can help your elementary school aged children minimize their homework hassles.

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Video transcript

Fraction Math: How to Do Fractions for Beginners

We deal with fractions every day. But what exactly is a fraction? How do we get to know them better? In this tutorial we will explore the basics and practice together, so fractions can become valuable helpers in everyday life and beyond.

Part 1. Fraction as a share

Let's imagine a whole pie divided into 4 equal parts. One part is shaded red.

One red part out of four equal parts means 1/4 of a whole is shaded. If we think of equal parts of a whole as shares, one share of a pie here is shaded red.

The number 1 above the line is called a Numerator . It shows how many shares are shaded. The number 4 below the line is called a Denominator . It shows how many equal shares a whole is divided into. Let's look at another example.

The new pie above is divided into 6 equal shares. Therefore, the denominator will equal 6. Out of these 6 equal shares 3 are shaded red. Therefore, the numerator will equal 3. In other words, 3/6 of the pie is shaded.

Now let's test what we have learned so far. As you know, there are 24 hours in a whole day. If you spent 6 hours studying, what fraction of the day did you spend studying?

What fraction of a day is 6 hours?

Choose 1 answer

A day is divided into 24 equal shares called hours. So the Denominator will be 24. Think of the 6 hours spent studying as 6 shaded shares of the pie. That will make the Numerator equal 6. The fraction we are looking for is 6/24 .

Part 2. Simplifying fractions

Remember the pie from previous example? It had 3/6 of it shaded red. Let's add two new pies and look at them together.

The first pie is divided into 4 shares and two are shaded red. But as we can see that's half the pie. The second pie is divided into 6 shares and three are shaded red. Half of the pie again. Finally, the third pie is divided into two halves and one half is shaded red.

Since it's half a pie that's shaded in either case, we can conclude that the fractions are equal: 2/4 = 3/6 = 1/2 .

Finally, by multiplying or dividing both the numerator and denominator by the same number, the fraction will stay the same (except the case when division is by zero, which is outside of the scope of this article and will not be considered here).

This rule helps simplify fractions and makes using them easier. As an example, let's consider 4/12. Dividing numerator and denominator by 4 gives us (4 : 4 ) / (12 : 4 ) = 1 / 3. It's time to test your knowledge.

What fraction is the same as 2/5?

Part 3. comparing fractions.

When we see two pieces of a pie, we can usually tell which one is larger. Similarly with fractions, there is a simple way of comparing them to each other.

Say we need to compare 1/3 and 2/7. Since they have different denominators, they have a different number of parts. So the First step must be to find the common ground . We do it by finding a common denominator .

One of the methods for finding a common denominator of two or more fractions is to multiply the denominators with each other. 3 times 7 = 21 .

Now that we found the common denominator, we need to replace each fraction's own denominator with the common denominator.

The first fraction is 1/3, so we divide 21 by 3 and resulting 7 gets multiplied by that fractions numerator. Since the numerator equals 1, we get 7 times 1 = 7 .

The second fraction is 2/7, so 21 divided by 7 results in 3. Multiplying 3 times this fractions numerator, gives us 3 times 2 = 6 .  

Now that the fractions have the same denominator, we can finally compare them. 7 shares is more than 6 shares, therefore 7/21 is greater than 6/21.

The mathematical symbol denoting our result is the > sign. 7/21 > 6/21 . It is read as  " greater-than ." The symbol denoting lesser-than looks like this: < . We can rewrite our result like this: 6/21 < 7/21 .

Compare 3/4 and 5/7

Part 4. adding fractions.

To add fractions, we again need to find a common denominator. Let's look at the following example.

We need to add 2/7 and 3/9 . The common denominator is 7 times 9 = 63 . The next step would be to replace each fraction's own denominator with the common one.

For the first fraction, 63 divided by 7 = 9 and 9 times 2 = 18 . The result is 18/63 . For the second one, 63 divided by 9 = 7 and 7 times 3 = 21 . The result is 21/63 .

Next, we add the numerators. 18 plus 21 = 39, which leaves us with the sum of 39/63 .

As a useful habit, always check if the resulting fraction can be further simplified.

We know that 39 is evenly divisible by 3. 63 is also evenly divisible by 3. Since both numerator and denominator are divided by the same number, the fraction will remain the same. 39 divided by 3 = 13 and 63 divided by 3 = 21 . Our final result is 13/21 .

What if we need to add mixed numbers? To add mixed numbers, we first add the whole numbers together and then the fractions.

For example, to add 1 and a half to 2 and a half , add 1 and 2 = 3 , then add 1/2 and 1/2 = 1 . Finally, add 3 and 1 = 4 . Let's have some practice and remember how to simplify results.

What is the result of 4/6 + 2/9?

Part 5. subtracting fractions.

We'll start with two simple fractions. Subtract 1/3 from 3/5. As in the case of addition, we need to find a common denominator. So if we multiply our denominators, that equals 3 times 5 = 15 .

Next, we replace old denominators with the common one.  

Then we need to find our numerators. For the first fraction, 15 divided by 5 = 3 and 3 times 3 = 9 . The result is 9/15 . For the second one, 15 divided by 3 = 5 and 5 times 1 = 5 . The result is 5/15 .

The last step is to subtract the adjusted numerators: 9 minus 5 = 4. The resulting fraction equals 4/15 .  

Let's now look at the case when we need to subtract a fraction from a whole number. Let's begin with 1 - 2/7 .

You remember from previous sections that a whole number is like a pie that is completely shaded. Thus, if a pie is divided into 3 parts, all 3 parts are shaded. If it is divided into 7 parts, then 7 parts will be shaded. So, 1 = 3/3 = 7/7 etc.

Since we need to subtract 2/7 , we'll turn 1 whole into 7/7 to make our task easy. 7/7 minus 2/7 = 5/7 . If the whole number is other than 1 , we write it as a mixed number and follow the steps from the last example.

So let's subtract 2/7 from 3 .

Often, as a result of calculations, we may end up with a fraction where the numerator is greater than or equal to the denominator. Such fractions are called improper fractions. For example 5/3 (five thirds), 7/2 (seven halves) and so on. They can be converted to mixed numbers and vice versa.

All the rules covered so far apply to improper fractions as well.

What is the result of 9/11 - 3/4?

Part 6. multiplying fractions.

Suppose we need to multiply two fractions, 2/5 times 3/7 . The numerator of the product will be the product of the numerators of these fractions: 2 times 3 = 6. The denominator of the product will be the product of denominators of these fractions: 5 times 7 = 35 . Thus, 2/5 times 3/7 = 6/35 .

If we need to multiply a fraction by a whole number , the numerator of the product will be the product of the numerator of the fraction and that whole number . The denominator of the product will remain the same as the denominator of the fraction .

For example, 3/10 times 5 = 15/10 . To simplify, we divide the numerator and denominator by 5 and get 3/2.

Finally, if we need to multiply mixed numbers, first we convert them to improper fractions, then multiply them as we did above. The example below shows the steps.

Part 7. Dividing fractions

To divide fractions, flip the divisor so its numerator becomes the new denominator and denominator becomes the new numerator . Then just multiply the fractions like we did before.

For example, divide 3/7 by 2/5. After flipping, 2/5 becomes 5/2 and we end up multiplying 3/7 times 5/2 = 15/14 .

To divide fraction by a whole number, we invert that number and it becomes 1 divided by that number .

For instance, 2 becomes 1/2 , 9 becomes 1/9 etc. Next, we multiply as above. As you probably guessed already, dividing mixed numbers works the same way. Let's look at the example below.

Let's test your knowledge.

What is the result of 11/3 divided by 11/7?

Part 8. some practical examples.

In order to find a fraction of some number, we need to multiply the given number by that fraction .

Imagine, your school textbook has 200 pages. If you read 3/5 of the textbook, how many pages have you read? We are given the number which equals 200. To find 3/5 of 200, we multiply 200 times 3/5 and get   120 pages.

Solve the next question on your own. My birthday cake had 12 pieces. A few friends came by and enjoyed 2/3 of the cake. How many pieces did my friends have?

How many pieces did my friends have?

Finally, there is one more case I want to explore. What if we know what a given fraction of some number equals and we need to find that number?

For example, we know my friends had 8 pieces of the birthday cake and that was 2/3 of the whole cake . How many pieces did the cake have in the beginning? In order to find that whole number , we need to divide 8 by 2/3 , which is 12 .

Solve the next question on your own. A race car drove 900 meters on a track, which is 3/5 of the whole distance. What's the length of the race track?  

What is the length of the race track?

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Sat / act prep online guides and tips, how to do homework: 15 expert tips and tricks.

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Everyone struggles with homework sometimes, but if getting your homework done has become a chronic issue for you, then you may need a little extra help. That’s why we’ve written this article all about how to do homework. Once you’re finished reading it, you’ll know how to do homework (and have tons of new ways to motivate yourself to do homework)!

We’ve broken this article down into a few major sections. You’ll find:

• A diagnostic test to help you figure out why you’re struggling with homework
• A discussion of the four major homework problems students face, along with expert tips for addressing them
• A bonus section with tips for how to do homework fast

By the end of this article, you’ll be prepared to tackle whatever homework assignments your teachers throw at you .

So let’s get started!

How to Do Homework: Figure Out Your Struggles 

Sometimes it feels like everything is standing between you and getting your homework done. But the truth is, most people only have one or two major roadblocks that are keeping them from getting their homework done well and on time. 

The best way to figure out how to get motivated to do homework starts with pinpointing the issues that are affecting your ability to get your assignments done. That’s why we’ve developed a short quiz to help you identify the areas where you’re struggling. 

Take the quiz below and record your answers on your phone or on a scrap piece of paper. Keep in mind there are no wrong answers! 

1. You’ve just been assigned an essay in your English class that’s due at the end of the week. What’s the first thing you do?

A. Keep it in mind, even though you won’t start it until the day before it’s due  B. Open up your planner. You’ve got to figure out when you’ll write your paper since you have band practice, a speech tournament, and your little sister’s dance recital this week, too.  C. Groan out loud. Another essay? You could barely get yourself to write the last one!  D. Start thinking about your essay topic, which makes you think about your art project that’s due the same day, which reminds you that your favorite artist might have just posted to Instagram...so you better check your feed right now. 

2. Your mom asked you to pick up your room before she gets home from work. You’ve just gotten home from school. You decide you’ll tackle your chores: 

A. Five minutes before your mom walks through the front door. As long as it gets done, who cares when you start?  B. As soon as you get home from your shift at the local grocery store.  C. After you give yourself a 15-minute pep talk about how you need to get to work.  D. You won’t get it done. Between texts from your friends, trying to watch your favorite Netflix show, and playing with your dog, you just lost track of time! 

3. You’ve signed up to wash dogs at the Humane Society to help earn money for your senior class trip. You: 

A. Show up ten minutes late. You put off leaving your house until the last minute, then got stuck in unexpected traffic on the way to the shelter.  B. Have to call and cancel at the last minute. You forgot you’d already agreed to babysit your cousin and bake cupcakes for tomorrow’s bake sale.  C. Actually arrive fifteen minutes early with extra brushes and bandanas you picked up at the store. You’re passionate about animals, so you’re excited to help out! D. Show up on time, but only get three dogs washed. You couldn’t help it: you just kept getting distracted by how cute they were!

4. You have an hour of downtime, so you decide you’re going to watch an episode of The Great British Baking Show. You: 

A. Scroll through your social media feeds for twenty minutes before hitting play, which means you’re not able to finish the whole episode. Ugh! You really wanted to see who was sent home!  B. Watch fifteen minutes until you remember you’re supposed to pick up your sister from band practice before heading to your part-time job. No GBBO for you!  C. You finish one episode, then decide to watch another even though you’ve got SAT studying to do. It’s just more fun to watch people make scones.  D. Start the episode, but only catch bits and pieces of it because you’re reading Twitter, cleaning out your backpack, and eating a snack at the same time.

5. Your teacher asks you to stay after class because you’ve missed turning in two homework assignments in a row. When she asks you what’s wrong, you say: 

A. You planned to do your assignments during lunch, but you ran out of time. You decided it would be better to turn in nothing at all than submit unfinished work.  B. You really wanted to get the assignments done, but between your extracurriculars, family commitments, and your part-time job, your homework fell through the cracks.  C. You have a hard time psyching yourself to tackle the assignments. You just can’t seem to find the motivation to work on them once you get home.  D. You tried to do them, but you had a hard time focusing. By the time you realized you hadn’t gotten anything done, it was already time to turn them in. 

Like we said earlier, there are no right or wrong answers to this quiz (though your results will be better if you answered as honestly as possible). Here’s how your answers break down: 

• If your answers were mostly As, then your biggest struggle with doing homework is procrastination. 
• If your answers were mostly Bs, then your biggest struggle with doing homework is time management. 
• If your answers were mostly Cs, then your biggest struggle with doing homework is motivation. 
• If your answers were mostly Ds, then your biggest struggle with doing homework is getting distracted. 

Now that you’ve identified why you’re having a hard time getting your homework done, we can help you figure out how to fix it! Scroll down to find your core problem area to learn more about how you can start to address it. 

And one more thing: you’re really struggling with homework, it’s a good idea to read through every section below. You may find some additional tips that will help make homework less intimidating. 

How to Do Homework When You’re a Procrastinator  

Merriam Webster defines “procrastinate” as “to put off intentionally and habitually.” In other words, procrastination is when you choose to do something at the last minute on a regular basis. If you’ve ever found yourself pulling an all-nighter, trying to finish an assignment between periods, or sprinting to turn in a paper minutes before a deadline, you’ve experienced the effects of procrastination. 

If you’re a chronic procrastinator, you’re in good company. In fact, one study found that 70% to 95% of undergraduate students procrastinate when it comes to doing their homework. Unfortunately, procrastination can negatively impact your grades. Researchers have found that procrastination can lower your grade on an assignment by as much as five points ...which might not sound serious until you realize that can mean the difference between a B- and a C+. 

Procrastination can also negatively affect your health by increasing your stress levels , which can lead to other health conditions like insomnia, a weakened immune system, and even heart conditions. Getting a handle on procrastination can not only improve your grades, it can make you feel better, too! 

The big thing to understand about procrastination is that it’s not the result of laziness. Laziness is defined as being “disinclined to activity or exertion.” In other words, being lazy is all about doing nothing. But a s this Psychology Today article explains , procrastinators don’t put things off because they don’t want to work. Instead, procrastinators tend to postpone tasks they don’t want to do in favor of tasks that they perceive as either more important or more fun. Put another way, procrastinators want to do things...as long as it’s not their homework! 

3 Tips f or Conquering Procrastination 

Because putting off doing homework is a common problem, there are lots of good tactics for addressing procrastination. Keep reading for our three expert tips that will get your homework habits back on track in no time. 

#1: Create a Reward System

Like we mentioned earlier, procrastination happens when you prioritize other activities over getting your homework done. Many times, this happens because homework...well, just isn’t enjoyable. But you can add some fun back into the process by rewarding yourself for getting your work done. 

Here’s what we mean: let’s say you decide that every time you get your homework done before the day it’s due, you’ll give yourself a point. For every five points you earn, you’ll treat yourself to your favorite dessert: a chocolate cupcake! Now you have an extra (delicious!) incentive to motivate you to leave procrastination in the dust. 

If you’re not into cupcakes, don’t worry. Your reward can be anything that motivates you . Maybe it’s hanging out with your best friend or an extra ten minutes of video game time. As long as you’re choosing something that makes homework worth doing, you’ll be successful. 

#2: Have a Homework Accountability Partner 

If you’re having trouble getting yourself to start your homework ahead of time, it may be a good idea to call in reinforcements . Find a friend or classmate you can trust and explain to them that you’re trying to change your homework habits. Ask them if they’d be willing to text you to make sure you’re doing your homework and check in with you once a week to see if you’re meeting your anti-procrastination goals. 

Sharing your goals can make them feel more real, and an accountability partner can help hold you responsible for your decisions. For example, let’s say you’re tempted to put off your science lab write-up until the morning before it’s due. But you know that your accountability partner is going to text you about it tomorrow...and you don’t want to fess up that you haven’t started your assignment. A homework accountability partner can give you the extra support and incentive you need to keep your homework habits on track. 

#3: Create Your Own Due Dates 

If you’re a life-long procrastinator, you might find that changing the habit is harder than you expected. In that case, you might try using procrastination to your advantage! If you just can’t seem to stop doing your work at the last minute, try setting your own due dates for assignments that range from a day to a week before the assignment is actually due. 

Here’s what we mean. Let’s say you have a math worksheet that’s been assigned on Tuesday and is due on Friday. In your planner, you can write down the due date as Thursday instead. You may still put off your homework assignment until the last minute...but in this case, the “last minute” is a day before the assignment’s real due date . This little hack can trick your procrastination-addicted brain into planning ahead! 

If you feel like Kevin Hart in this meme, then our tips for doing homework when you're busy are for you. 

How to Do Homework When You’re too Busy

If you’re aiming to go to a top-tier college , you’re going to have a full plate. Because college admissions is getting more competitive, it’s important that you’re maintaining your grades , studying hard for your standardized tests , and participating in extracurriculars so your application stands out. A packed schedule can get even more hectic once you add family obligations or a part-time job to the mix. 

If you feel like you’re being pulled in a million directions at once, you’re not alone. Recent research has found that stress—and more severe stress-related conditions like anxiety and depression— are a major problem for high school students . In fact, one study from the American Psychological Association found that during the school year, students’ stress levels are higher than those of the adults around them. 

For students, homework is a major contributor to their overall stress levels . Many high schoolers have multiple hours of homework every night , and figuring out how to fit it into an already-packed schedule can seem impossible. 

3 Tips for Fitting Homework Into Your Busy Schedule

While it might feel like you have literally no time left in your schedule, there are still ways to make sure you’re able to get your homework done and meet your other commitments. Here are our expert homework tips for even the busiest of students. 

#1: Make a Prioritized To-Do List 

You probably already have a to-do list to keep yourself on track. The next step is to prioritize the items on your to-do list so you can see what items need your attention right away. 

Here’s how it works: at the beginning of each day, sit down and make a list of all the items you need to get done before you go to bed. This includes your homework, but it should also take into account any practices, chores, events, or job shifts you may have. Once you get everything listed out, it’s time to prioritize them using the labels A, B, and C. Here’s what those labels mean:

• A Tasks : tasks that have to get done—like showing up at work or turning in an assignment—get an A. 
• B Tasks : these are tasks that you would like to get done by the end of the day but aren’t as time sensitive. For example, studying for a test you have next week could be a B-level task. It’s still important, but it doesn’t have to be done right away.
• C Tasks: these are tasks that aren’t very important and/or have no real consequences if you don’t get them done immediately. For instance, if you’re hoping to clean out your closet but it’s not an assigned chore from your parents, you could label that to-do item with a C.

Prioritizing your to-do list helps you visualize which items need your immediate attention, and which items you can leave for later. A prioritized to-do list ensures that you’re spending your time efficiently and effectively, which helps you make room in your schedule for homework. So even though you might really want to start making decorations for Homecoming (a B task), you’ll know that finishing your reading log (an A task) is more important. 

#2: Use a Planner With Time Labels

Your planner is probably packed with notes, events, and assignments already. (And if you’re not using a planner, it’s time to start!) But planners can do more for you than just remind you when an assignment is due. If you’re using a planner with time labels, it can help you visualize how you need to spend your day.

A planner with time labels breaks your day down into chunks, and you assign tasks to each chunk of time. For example, you can make a note of your class schedule with assignments, block out time to study, and make sure you know when you need to be at practice. Once you know which tasks take priority, you can add them to any empty spaces in your day. 

Planning out how you spend your time not only helps you use it wisely, it can help you feel less overwhelmed, too . We’re big fans of planners that include a task list ( like this one ) or have room for notes ( like this one ). 

#3: Set Reminders on Your Phone 

If you need a little extra nudge to make sure you’re getting your homework done on time, it’s a good idea to set some reminders on your phone. You don’t need a fancy app, either. You can use your alarm app to have it go off at specific times throughout the day to remind you to do your homework. This works especially well if you have a set homework time scheduled. So if you’ve decided you’re doing homework at 6:00 pm, you can set an alarm to remind you to bust out your books and get to work. 

If you use your phone as your planner, you may have the option to add alerts, emails, or notifications to scheduled events . Many calendar apps, including the one that comes with your phone, have built-in reminders that you can customize to meet your needs. So if you block off time to do your homework from 4:30 to 6:00 pm, you can set a reminder that will pop up on your phone when it’s time to get started. 

This dog isn't judging your lack of motivation...but your teacher might. Keep reading for tips to help you motivate yourself to do your homework.

How to Do Homework When You’re Unmotivated 

At first glance, it may seem like procrastination and being unmotivated are the same thing. After all, both of these issues usually result in you putting off your homework until the very last minute. 

But there’s one key difference: many procrastinators are working, they’re just prioritizing work differently. They know they’re going to start their homework...they’re just going to do it later. 

Conversely, people who are unmotivated to do homework just can’t find the willpower to tackle their assignments. Procrastinators know they’ll at least attempt the homework at the last minute, whereas people who are unmotivated struggle with convincing themselves to do it at a ll. For procrastinators, the stress comes from the inevitable time crunch. For unmotivated people, the stress comes from trying to convince themselves to do something they don’t want to do in the first place. 

Here are some common reasons students are unmotivated in doing homework : 

• Assignments are too easy, too hard, or seemingly pointless 
• Students aren’t interested in (or passionate about) the subject matter
• Students are intimidated by the work and/or feels like they don’t understand the assignment 
• Homework isn’t fun, and students would rather spend their time on things that they enjoy 

To sum it up: people who lack motivation to do their homework are more likely to not do it at all, or to spend more time worrying about doing their homework than...well, actually doing it.

3 Tips for How to Get Motivated to Do Homework

The key to getting homework done when you’re unmotivated is to figure out what does motivate you, then apply those things to homework. It sounds tricky...but it’s pretty simple once you get the hang of it! Here are our three expert tips for motivating yourself to do your homework. 

#1: Use Incremental Incentives

When you’re not motivated, it’s important to give yourself small rewards to stay focused on finishing the task at hand. The trick is to keep the incentives small and to reward yourself often. For example, maybe you’re reading a good book in your free time. For every ten minutes you spend on your homework, you get to read five pages of your book. Like we mentioned earlier, make sure you’re choosing a reward that works for you! 

So why does this technique work? Using small rewards more often allows you to experience small wins for getting your work done. Every time you make it to one of your tiny reward points, you get to celebrate your success, which gives your brain a boost of dopamine . Dopamine helps you stay motivated and also creates a feeling of satisfaction when you complete your homework !  

#2: Form a Homework Group 

If you’re having trouble motivating yourself, it’s okay to turn to others for support. Creating a homework group can help with this. Bring together a group of your friends or classmates, and pick one time a week where you meet and work on homework together. You don’t have to be in the same class, or even taking the same subjects— the goal is to encourage one another to start (and finish!) your assignments. 

Another added benefit of a homework group is that you can help one another if you’re struggling to understand the material covered in your classes. This is especially helpful if your lack of motivation comes from being intimidated by your assignments. Asking your friends for help may feel less scary than talking to your teacher...and once you get a handle on the material, your homework may become less frightening, too. 

#3: Change Up Your Environment 

If you find that you’re totally unmotivated, it may help if you find a new place to do your homework. For example, if you’ve been struggling to get your homework done at home, try spending an extra hour in the library after school instead. The change of scenery can limit your distractions and give you the energy you need to get your work done. 

If you’re stuck doing homework at home, you can still use this tip. For instance, maybe you’ve always done your homework sitting on your bed. Try relocating somewhere else, like your kitchen table, for a few weeks. You may find that setting up a new “homework spot” in your house gives you a motivational lift and helps you get your work done. 

Social media can be a huge problem when it comes to doing homework. We have advice for helping you unplug and regain focus.

How to Do Homework When You’re Easily Distracted

We live in an always-on world, and there are tons of things clamoring for our attention. From friends and family to pop culture and social media, it seems like there’s always something (or someone!) distracting us from the things we need to do.

The 24/7 world we live in has affected our ability to focus on tasks for prolonged periods of time. Research has shown that over the past decade, an average person’s attention span has gone from 12 seconds to eight seconds . And when we do lose focus, i t takes people a long time to get back on task . One study found that it can take as long as 23 minutes to get back to work once we’ve been distracte d. No wonder it can take hours to get your homework done! 

3 Tips to Improve Your Focus

If you have a hard time focusing when you’re doing your homework, it’s a good idea to try and eliminate as many distractions as possible. Here are three expert tips for blocking out the noise so you can focus on getting your homework done. 

#1: Create a Distraction-Free Environment

Pick a place where you’ll do your homework every day, and make it as distraction-free as possible. Try to find a location where there won’t be tons of noise, and limit your access to screens while you’re doing your homework. Put together a focus-oriented playlist (or choose one on your favorite streaming service), and put your headphones on while you work. 

You may find that other people, like your friends and family, are your biggest distraction. If that’s the case, try setting up some homework boundaries. Let them know when you’ll be working on homework every day, and ask them if they’ll help you keep a quiet environment. They’ll be happy to lend a hand! 

#2: Limit Your Access to Technology 

We know, we know...this tip isn’t fun, but it does work. For homework that doesn’t require a computer, like handouts or worksheets, it’s best to put all your technology away . Turn off your television, put your phone and laptop in your backpack, and silence notifications on any wearable tech you may be sporting. If you listen to music while you work, that’s fine...but make sure you have a playlist set up so you’re not shuffling through songs once you get started on your homework. 

If your homework requires your laptop or tablet, it can be harder to limit your access to distractions. But it’s not impossible! T here are apps you can download that will block certain websites while you’re working so that you’re not tempted to scroll through Twitter or check your Facebook feed. Silence notifications and text messages on your computer, and don’t open your email account unless you absolutely have to. And if you don’t need access to the internet to complete your assignments, turn off your WiFi. Cutting out the online chatter is a great way to make sure you’re getting your homework done. 

#3: Set a Timer (the Pomodoro Technique)

Have you ever heard of the Pomodoro technique ? It’s a productivity hack that uses a timer to help you focus!

Here’s how it works: first, set a timer for 25 minutes. This is going to be your work time. During this 25 minutes, all you can do is work on whatever homework assignment you have in front of you. No email, no text messaging, no phone calls—just homework. When that timer goes off, you get to take a 5 minute break. Every time you go through one of these cycles, it’s called a “pomodoro.” For every four pomodoros you complete, you can take a longer break of 15 to 30 minutes.

The pomodoro technique works through a combination of boundary setting and rewards. First, it gives you a finite amount of time to focus, so you know that you only have to work really hard for 25 minutes. Once you’ve done that, you’re rewarded with a short break where you can do whatever you want. Additionally, tracking how many pomodoros you complete can help you see how long you’re really working on your homework. (Once you start using our focus tips, you may find it doesn’t take as long as you thought!)

Two Bonus Tips for How to Do Homework Fast

Even if you’re doing everything right, there will be times when you just need to get your homework done as fast as possible. (Why do teachers always have projects due in the same week? The world may never know.)

The problem with speeding through homework is that it’s easy to make mistakes. While turning in an assignment is always better than not submitting anything at all, you want to make sure that you’re not compromising quality for speed. Simply put, the goal is to get your homework done quickly and still make a good grade on the assignment! 

Here are our two bonus tips for getting a decent grade on your homework assignments , even when you’re in a time crunch. 

#1: Do the Easy Parts First 

This is especially true if you’re working on a handout with multiple questions. Before you start working on the assignment, read through all the questions and problems. As you do, make a mark beside the questions you think are “easy” to answer . 

Once you’ve finished going through the whole assignment, you can answer these questions first. Getting the easy questions out of the way as quickly as possible lets you spend more time on the trickier portions of your homework, which will maximize your assignment grade. 

(Quick note: this is also a good strategy to use on timed assignments and tests, like the SAT and the ACT !) 

#2: Pay Attention in Class 

Homework gets a lot easier when you’re actively learning the material. Teachers aren’t giving you homework because they’re mean or trying to ruin your weekend... it’s because they want you to really understand the course material. Homework is designed to reinforce what you’re already learning in class so you’ll be ready to tackle harder concepts later.

When you pay attention in class, ask questions, and take good notes, you’re absorbing the information you’ll need to succeed on your homework assignments. (You’re stuck in class anyway, so you might as well make the most of it!) Not only will paying attention in class make your homework less confusing, it will also help it go much faster, too.

What’s Next?

If you’re looking to improve your productivity beyond homework, a good place to begin is with time management. After all, we only have so much time in a day...so it’s important to get the most out of it! To get you started, check out this list of the 12 best time management techniques that you can start using today.

You may have read this article because homework struggles have been affecting your GPA. Now that you’re on the path to homework success, it’s time to start being proactive about raising your grades. This article teaches you everything you need to know about raising your GPA so you can

Now you know how to get motivated to do homework...but what about your study habits? Studying is just as critical to getting good grades, and ultimately getting into a good college . We can teach you how to study bette r in high school. (We’ve also got tons of resources to help you study for your ACT and SAT exams , too!)

These recommendations are based solely on our knowledge and experience. If you purchase an item through one of our links, PrepScholar may receive a commission.

Ashley Sufflé Robinson has a Ph.D. in 19th Century English Literature. As a content writer for PrepScholar, Ashley is passionate about giving college-bound students the in-depth information they need to get into the school of their dreams.

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Teaching approaches: checking-homework Challenge

By Jane Sjoberg

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These are just a few ideas of how to make the whole-class correction of homework less of a chore and more of an active challenge. The suggestions given are specifically geared to be used when correcting exercises set from a workbook or worksheet as homework but some ideas may also be used when giving feedback for tasks set in class.

• Give students a chance to compare their answers in pairs. Students can then correct/ change/ complete their own answers before a whole class check. This puts students at the centre of the correction process from the start and asks them to reflect upon their own and each other’s answers with a greater degree of learner autonomy.
• Take names out of a hat at random to nominate the students who are to supply answers (make sure this is done in a ‘fun’ way, explaining to students that they have an opportunity to PASS if their name is called).
• Use a ball or a scrunched up ball of newspaper weighted with a thick rubber band (lightweight balls that don’t bounce are best – bouncy balls have a tendency to get lost in the darkest corners of the classroom) to throw at random around the class to see who gets to give their answer to questions. Whoever gets the ball throws it to the next student. Again, give students an opportunity to pass if necessary.
• Alternate between asking for answers to be volunteered and calling on specific students to answer questions. Where the teacher is unfamiliar with the various ability groups in a class, nominating students can be a nightmare, especially if weaker or less confident learners are inadvertently asked to provide their answer to more complex questions. However, nominating is a way of ensuring the participation of those who are less likely to volunteer. Alternating between volunteers and nominated students solves this problem in part, but nominees should always be given the chance to pass if they prefer.
• To ensure that all students participate in the correction process, pre-prepare a grid that includes the question numbers for the various exercises that are to be corrected. Leave a space next to each question number. At the beginning of the lesson, get students to put their name down to answer the various questions. Tell students that, even if they did not do the homework they can still try to answer a question of their choice but do not force students to put their names down. When all the students who wish to participate have put their names down for at least one question, take the list in and use it to call on the students to answer the questions in turn. This ensures that the students called upon will be answering questions they themselves feel confident about (or else questions for which they would prefer individual feedback). If this process is repeated over several lessons, it also gives the teacher a chance to see whether there are students who repeatedly prefer not to be involved in the homework correction process. These students and their individual problems regarding homework can then be dealt with on a one-to-one basis.
• For fill-in-the-gaps exercises or simple one- or two-word answers present feedback in power point or on an OHP. Go through answers one by one giving time for students to check their own work. At the end of each exercise, stop and give students a chance to query, provide alternatives, or request further information regarding specific answers.
• Ask the class to do a quick survey in groups ranking exercises from the most to least difficult, the most to least interesting, the most to least useful etc.. Use student feedback to decide which exercise to correct together first and then give exercises ranked by the majority as the least interesting/difficult on OHP/power point as above to speed up the correction process. This ensures that students will be more alert during the correction of what they perceived to be the most problematic areas of their homework. Homework ranking tasks also provide important feedback to the teacher who may use the data provided to check on the cause of problems areas at a later date. Students may perceive certain exercises as difficult for different reasons – length, typology, unclear instructions, vocabulary density of exercise, grammatical problems, uninteresting topic etc.. A further analysis of these issues may help the teacher to decide which exercises to set or dedicate more time to in the future. Remember to check your students’ ranking of difficult exercises after correction – what students may have originally perceived as problematic may not actually correspond to their own performance. This again may be something that can be discussed and analyzed further at a later date.
• For teachers in a hurry to get correcting out of the way – simply vary the order in which exercises are corrected. This ensures that students are alert and are following the correction process.
• Get students to check through answers in pairs by photocopying the key (readymade or produced by the teacher) or displaying answers on an OHP. Set aside time at the end of the lesson for individual students to discuss problem areas or organize a tutorial session where students can come and discuss problems individually with the teacher while the group works on another task/project work.
• Change the time of the lesson in which homework is corrected. Most students expect homework corrections to come right at the beginning of a lesson and, let’s face it, it’s not the best or most enjoyable way to start off! Try checking homework as a way of ‘calming down’ after a boisterous group-work session or leave it till the end of the lesson. Incidentally, this also works with setting homework. Try varying the point of the lesson at which homework is set to ensure that all the students are paying attention!
• Take in students’ workbooks occasionally or provide photocopies of exercises that can be handed in. Though this does add to the teacher’s workload, it is worth taking a look at how students deal with more mechanical exercises that differ from extended written work which necessarily requires individual marking and feedback. Taking a look at a workbook can provide an idea of problem areas for individual students, again with a view to diagnosing problem areas in structures/ vocabulary or assessing difficulties that may be based on other factors such as lack of interest in the topic, unclear instructions etc.. It may also allow the teacher to gain insight into how much (or how little) homework an individual student is regularly putting in. Following the teacher’s appraisal of the students’ workbooks individual tutorials may be arranged to discuss issues as appropriate.
• Provide mini keys of individual exercises to distribute to pairs. Students then take it in turns to ‘play the teacher’ and check each other’s answers. Where more than two exercises need checking pairs can exchange keys and repeat the process as many times as necessary. The teacher can circulate and deal with queries as pairs are checking. However, remember to provide an opportunity for the discussion of problem areas at the end of the pair-work session or at the end of the lesson.
• Most workbook exercises that need to be checked are not specifically designed to practise pronunciation. Where pronunciation exercises are set make sure that adequate time is given to teacher modelling and student production of target items. In the majority of cases, i.e. where structures, vocabulary and functions are being practised, vary the correction procedure by taking time out along the way to focus on pronunciation/ intonation issues. Even the most boring feedback sessions can be livened up by a rousing choral repetition session!
• Spot check on lexis by occasionally eliciting synonyms/ antonyms/ similar expressions/ analogous idioms of items taken from the exercises being corrected. This also provides an added opportunity for those who did not do the homework to participate in the correction process and allows those who did not necessarily provide a correct answer in an exercise to regain their confidence in being able to answer extra questions. This technique is also useful for involving more competent or confident students. Spot check questions should therefore be carefully gauged to include the whole ability range. Extra questions can also include pronunciation issues by eliciting word stress, number of syllables, homophones etc. The teacher is obviously free to ask spot check questions at any point during the correction process. However, it may be worth just taking a quick look at the exercises that are to be corrected beforehand so that appropriate extra questions may be devised in advance.
• Using photocopies or an OHP transparency, create a multiple choice answer key for a few exercises where three possible answers to each question are provided, only one of which is correct. Students then compare their own answers with the alternatives given. They then choose the answer that they consider correct (which may or may not correspond with their own original answer). This activity gives students a chance to rethink their own answers before the teacher finally provides the key. It also gives less confident students and those who may not have completed the task an opportunity to take part in the correction process.
• Play the ‘Who wants to be a millionaire?’ game when correcting. In this case, students are placed in two teams. Students from each team are called upon alternately to provide answers to each question. Each team has a set number of ‘ask a friend’, ‘fifty-fifty’ and ‘pass’ cards which they can use at their discretion. (Numbers can be decided on the basis of how many students there are in each team. For a class of 12 students with teams of 6 players each, one card of each type should be ample. The ‘cards’ do not have to be made as such. They may be simply registered on the board for each team and rubbed off as they are used). For ‘ask-a-friend’ a student may ask another member of his/her team to provide the answer. For ‘fifty-fifty’ the teacher gives two alternative answers and the student must choose which he/she considers correct. (This may need some prior preparation, depending on the teacher’s ability to come up with sneaky alternatives!) If the student passes, the answer is given by the teacher and no points are scored. One word of warning – as this game has a strong competitive element, please make sure that an equal number of questions is given to each team and that a variety of exercises is ensured. It is a good idea to split individual exercises into two halves and give teams an equal number of questions each. If an exercise has an odd number of answers, the teacher can simply provide the answer to the first question as an example.
• Finally, be upbeat about homework correction. Camp up the performance if necessary with a round of applause for correct answers. Sound effects for applause can be recorded or included in power point presentations or the students themselves can be encouraged to clap when correct answers are given. With younger students, take care that clapping does not turn to booing wrong answers, however. If this is a risk, you might consider a collective round of applause at the end of each exercise corrected. Also remember that homework feedback which involves student participation may be an intense source of satisfaction when students are able to provide the right answer but it can also be a source of embarrassment for those who are unable to do so. Make sure lots of praise and encouragement is given for answers that are even partly correct and, where possible, give positive feedback for areas that are not necessarily the focus of the exercise (such as good pronunciation in the case of grammatical errors or wrong answers in comprehension exercises).

Remember: students quickly tune in to the mood of their teacher. If the teacher presents homework correction as a valid and interesting part of the learning process it will be infectious and homework corrections need never be boring again!

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You'll Have No Words Seeing This Precious 2-Year-Old Genius Do Multiplication on AGT

Simon Cowell pleads, “Get us a calculator!” and asks Baby Dev to negotiate his next deal in this incredible AGT Season 19 Audition.

While most toddlers are stacking blocks and coloring with crayons, this pint-sized genius does addition, subtraction, and multiplication on national television.

How to Watch

Watch America’s Got Talent Tuesdays at 8/7c on NBC and next day on Peacock . 

Devan is the youngest Act ever to light up the America’s Got Talent stage, and in the Season 19 premiere, we can see why. The sweet boy knocked everyone’s socks off as he sailed through three different math equations that, to be honest, had the Judges stumped .

“We’re all sitting here thinking the same thing: get us a calculator,” said Simon Cowell after the performance, adding, “I now feel really stupid.”

RELATED:  Who Are the America's Got Talent Season 19 Judges?

Baby Dev’s father, Duane, a retired police officer, told NBC Insider he noticed something very special about his son early on: “At 4 months old, we realized his love for numbers.”

Duane explained that when he exposed his son to early learning shows, Baby Dev would suddenly cry when they switched away from math. “And when we turned it back, he would stop. We’re like, all right, he has this love and passion for numbers,” he said.

How old is Baby Devan?

Devan is 2 years old, the youngest-ever contestant on AGT . 

From the moment Baby Dev fist-bumped Terry Crews backstage before his Season 19 debut, AGT fans were charmed. The precious boy laughed, jumped, and squealed with delight after solving equations and politely saying “hello” and “thank you” to the Judges while on stage with his proud dad.

“His first word before mama and dada was seven,” Duane told the Judges. “That’s my lucky number,” exclaimed Simon. And it seemed to be Baby Dev’s, too. Three whiteboards were set up on stage — two for multiplication and one for addition — with Judges calling out random numbers. When Baby Dev quickly solved 7 x 9, there was a stunned silence before the crowd erupted in applause.

How did Devan develop his math skills?

Duane explained to NBC Insider how he nurtured his son’s penchant for math.

“At age 1, we had bought him a writing tablet. We would practice writing numbers with him from 1 to 10… and we would practice writing every day, and by 15 months old, he knew how to write numbers on his own.” After mastering addition, the math prodigy moved on to subtraction and his times tables.

“We can just be in bed, and he’ll be like… ‘Math, please. I wanna do math, please,’ and then he’ll go to his writing board and just do math equations,” said his dad, who noted that the little boy always loved counting everything. “Cars on the street, birds, trees… he has number magnets that he carries with him like it’s a toy.”

Baby Dev does not receive formal tutoring, and as one audience member pointed out, “He’s not even using his fingers” to count. However, he might have one strict requirement when calculating: Not being interrupted. As Baby Dev tackled a math problem and jotted down numbers, Howie Mandel loudly whispered, “We get to see the process.”

We can just be in bed, and he’ll be like… ‘Math, please. I wanna do math, please!’” Duane, Baby Dev's dad

The toddler shot him a look that could freeze water. After a long pause and some shushing directed toward Mandel, Baby Dev continued on and solved the final equation. He was unanimously voted on to the next round — but he may have something extra on his plate, too.

When Simon asked, “Devon, will you help me negotiate my next deal?” the little cutie responded, “Yes!”

Obviously this charming youngster moved on to the next round of the competition where fans are surely eager to see what mathematical wizardry he'll come up with next. 

Watch all-new episodes of  America’s Got Talent , airing Tuesdays at 8/7c on NBC   and streaming the next day on  Peacock .

-  Reporting by McKenzie Jean-Philippe

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