problem solving of fractions

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Problem Solving using Fractions

Fractions are numbers that exist between whole numbers. We get fractions when we divide whole numbers into equal parts. Here we will learn to solve some real-life problems using fractions. ...Read More Read Less

Table of Contents

What are Fractions?

Types of fractions.

• Fractions with like and unlike denominators
• Operations on fractions
• Fractions can be multiplied by using
• Let’s take a look at a few examples

Solved Examples

• Frequently Asked Questions

Equal parts of a whole or a collection of things are represented by fractions . In other words a fraction is a part or a portion of the whole. When we divide something into equal pieces, each part becomes a fraction of the whole.

For example in the given figure, one pizza represents a whole. When cut into 2 equal parts, each part is half of the whole, that can be represented by the fraction  \(\frac{1}{2}\) . 

Similarly, if it is divided into 4 equal parts, then each part is one fourth of the whole, that can be represented by the fraction \(\frac{1}{4}\) .

Proper fractions

A fraction in which the numerator is less than the denominator value is called a  proper fraction.

For example ,  \(\frac{3}{4}\) ,  \(\frac{5}{7}\) ,  \(\frac{3}{8}\)   are proper fractions.

Improper fractions 

A fraction with the numerator higher than or equal to the denominator is called an improper fraction .

Eg \(\frac{9}{4}\) ,  \(\frac{8}{8}\) ,  \(\frac{9}{4}\)   are examples of improper fractions.

Mixed fractions

A mixed number or a mixed fraction is a type of fraction which is a combination of both a whole number and a proper fraction.

We express improper fractions as mixed numbers.

For example ,  5\(\frac{1}{3}\) ,  1\(\frac{4}{9}\) ,  13\(\frac{7}{8}\)   are mixed fractions.

Unit fraction

A unit fraction is a fraction with a numerator equal to one. If a whole or a collection is divided into equal parts, then exactly 1 part of the total parts represents a unit fraction .

Fractions with Like and Unlike Denominators

Like fractions are those in which two or more fractions have the same denominator, whereas unlike fractions are those in which the denominators of two or more fractions are different.

For example,  

\(\frac{1}{4}\)  and  \(\frac{3}{4}\)  are like fractions as they both have the same denominator, that is, 4.

\(\frac{1}{3}\)  and  \(\frac{1}{4}\)   are unlike fractions as they both have a different denominator.

Operations on Fractions

We can perform addition, subtraction, multiplication and division operations on fractions.

Fractions with unlike denominators can be added or subtracted using equivalent fractions. Equivalent fractions can be obtained by finding a common denominator. And a common denominator is obtained either by determining a common multiple of the denominators or by calculating the product of the denominators.

There is another method to add or subtract mixed numbers, that is, solve the fractional and whole number parts separately, and then, find their sum to get the final answer.

Fractions can be Multiplied by Using:

Division operations on fractions can be performed using a tape diagram and area model. Also, when a fraction is divided by another fraction then we can solve it by multiplying the dividend with the reciprocal of the divisor. 

Let’s Take a Look at a Few Examples

Addition and subtraction using common denominator

( \(\frac{1}{6} ~+ ~\frac{2}{5}\) )

We apply the method of equivalent fractions. For this we need a common denominator, or a common multiple of the two denominators 6 and 5, that is, 30.

\(\frac{1}{6} ~+ ~\frac{2}{5}\)

= \(\frac{5~+~12}{30}\)  

=  \(\frac{17}{30}\) 

( \(\frac{5}{2}~-~\frac{1}{6}\) )

= \(\frac{12~-~5}{30}\)

= \(\frac{7}{30}\)

Examples of Multiplication and Division

Multiplication:

(\(\frac{1}{6}~\times~\frac{2}{5}\))

= (\(\frac{1~\times~2}{6~\times~5}\))                                       [Multiplying numerator of fractions and multiplying denominator of fractions]

=  \(\frac{2}{30}\)

(\(\frac{2}{5}~÷~\frac{1}{6}\))

= (\(\frac{2 ~\times~ 5}{6~\times~ 1}\))                                     [Multiplying dividend with the reciprocal of divisor]

= (\(\frac{2 ~\times~ 6}{5 ~\times~ 1}\))

= \(\frac{12}{5}\)

Example 1: Solve \(\frac{7}{8}\) + \(\frac{2}{3}\)

Let’s add \(\frac{7}{8}\)  and  \(\frac{2}{3}\)   using equivalent fractions. For this we need to find a common denominator or a common multiple of the two denominators 8 and 3, which is, 24.

\(\frac{7}{8}\) + \(\frac{2}{3}\)

= \(\frac{21~+~16}{24}\)    

= \(\frac{37}{24}\)

Example 2: Solve \(\frac{11}{13}\) – \(\frac{12}{17}\)

Solution:  

Let’s subtract  \(\frac{12}{17}\) from \(\frac{11}{13}\)   using equivalent fractions. For this we need a common denominator or a common multiple of the two denominators 13 and 17, that is, 221.

\(\frac{11}{13}\) – \(\frac{12}{17}\)

= \(\frac{187~-~156}{221}\)

= \(\frac{31}{221}\)

Example 3: Solve \(\frac{15}{13} ~\times~\frac{18}{17}\)

Multiply the numerators and multiply the denominators of the 2 fractions.

\(\frac{15}{13}~\times~\frac{18}{17}\)

= \(\frac{15~~\times~18}{13~~\times~~17}\)

= \(\frac{270}{221}\)

Example 4: Solve \(\frac{25}{33}~\div~\frac{41}{45}\)

Divide by multiplying the dividend with the reciprocal of the divisor.

\(\frac{25}{33}~\div~\frac{41}{45}\)

= \(\frac{25}{33}~\times~\frac{41}{45}\)                            [Multiply with reciprocal of the divisor \(\frac{41}{45}\) , that is, \(\frac{45}{41}\)  ]

= \(\frac{25~\times~45}{33~\times~41}\)

= \(\frac{1125}{1353}\)

Example 5: 

Sam was left with   \(\frac{7}{8}\)  slices of chocolate cake and    \(\frac{3}{7}\)  slices of vanilla cake after he shared the rest with his friends. Find out the total number of slices of cake he had with him. Sam shared   \(\frac{10}{11}\)  slices from the total number he had with his parents. What is the number of slices he has remaining?

To find the total number of slices of cake he had after sharing we need to add the slices of each cake he had,

=   \(\frac{7}{8}\) +   \(\frac{3}{7}\)   

=   \(\frac{49~+~24}{56}\)

=   \(\frac{73}{56}\)

To find out the remaining number of slices Sam has   \(\frac{10}{11}\)  slices need to be deducted from the total number,

= \(\frac{73}{56}~-~\frac{10}{11}\)

=   \(\frac{803~-~560}{616}\)

=   \(\frac{243}{616}\)

Hence, after sharing the cake with his friends, Sam has  \(\frac{73}{56}\) slices of cake, and after sharing with his parents he had  \(\frac{243}{616}\)  slices of cake left with him.

Example 6: Tiffany squeezed oranges to make orange juice for her juice stand. She was able to get 25 ml from one orange. How many oranges does she need to squeeze to fill a jar of   \(\frac{15}{8}\) liters? Each cup that she sells carries 200 ml and she sells each cup for 64 cents. How much money does she make at her juice stand?

First  \(\frac{15}{8}\) l needs to be converted to milliliters.

\(\frac{15}{8}\)l into milliliters =  \(\frac{15}{8}\) x 1000 = 1875 ml

To find the number of oranges, divide the total required quantity by the quantity of juice that one orange can give.

The number of oranges required for 1875 m l of juice =  \(\frac{1875}{25}\) ml = 75 oranges

To find the number of cups she sells, the total quantity of juice is to be divided by the quantity of juice that 1 cup has

=  \(\frac{1875}{200}~=~9\frac{3}{8}\) cups

We know that, the number of cups cannot be a fraction, it has to be a whole number. Also each cup must have 200ml. Hence with the quantity of juice she has she can sell 9 cups,   \(\frac{3}{8}\) th  of a cup cannot be sold alone.

Money made on selling 9 cups = 9 x 64 = 576 cents

Hence she makes 576 cents from her juice stand.

What is a mixed fraction?

A mixed fraction is a number that has a whole number and a fractional part. It is used to represent values between whole numbers.

How will you add fractions with unlike denominators?

When adding fractions with unlike denominators, take the common multiple of the denominators of both the fractions and then convert them into equivalent fractions. 

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Questions and problems with solutions on fractions are presented. Detailed solutions to the examples are also included. In order to master the concepts and skills of fractions, you need a thorough understanding (NOT memorizing) of the rules and properties and lot of practice and patience. I hope the examples, questions, problems in the links below will help you.

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• Evaluate Fractions of Quantities .
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• Adding Fractions. Add fractions with same denominator or different denominator. Several examples with detailed solutions and exercises.
• Multiply Fractions. Multiply a fraction by another fraction or a number by a fraction. Examples with solutions and exercises.
• Divide Fractions. Divide a fraction by a fraction, a fraction by a number of a number by a fraction. Several examples with solutions and exercises with answers.

Fractions Per Grade

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How to Solve Fraction Questions in Math

Last Updated: April 7, 2024 Fact Checked

This article was co-authored by Mario Banuelos, PhD and by wikiHow staff writer, Sophia Latorre . Mario Banuelos is an Assistant Professor of Mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution, and data science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the University of California, Merced. Mario has taught at both the high school and collegiate levels. There are 7 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 1,195,916 times.

Fraction questions can look tricky at first, but they become easier with practice and know-how. Start by learning the terminology and fundamentals, then pratice adding, subtracting, multiplying, and dividing fractions. [1] X Research source Once you understand what fractions are and how to manipulate them, you'll be breezing through fraction problems in no time.

Doing Calculations with Fractions

• For instance, to solve 5/9 + 1/9, just add 5 + 1, which equals 6. The answer, then, is 6/9 which can be reduced to 2/3.

• For instance, to solve 6/8 - 2/8, all you do is take away 2 from 6. The answer is 4/8, which can be reduced to 1/2.

• For example, if you need to add 1/2 and 2/3, start by determining a common multiple. In this case, the common multiple is 6 since both 2 and 3 can be converted to 6. To turn 1/2 into a fraction with a denominator of 6, multiply both the numerator and denominator by 3: 1 x 3 = 3 and 2 x 3 = 6, so the new fraction is 3/6. To turn 2/3 into a fraction with a denominator of 6, multiply both the numerator and denominator by 2: 2 x 2 = 4 and 3 x 2 = 6, so the new fraction is 4/6. Now, you can add the numerators: 3/6 + 4/6 = 7/6. Since this is an improper fraction, you can convert it to the mixed number 1 1/6.
• On the other hand, say you're working on the problem 7/10 - 1/5. The common multiple in this case is 10, since 1/5 can be converted into a fraction with a denominator of 10 by multiplying it by 2: 1 x 2 = 2 and 5 x 2 = 10, so the new fraction is 2/10. You don't need to convert the other fraction at all. Just subtract 2 from 7, which is 5. The answer is 5/10, which can also be reduced to 1/2.

• For instance, to multiply 2/3 and 7/8, find the new numerator by multiplying 2 by 7, which is 14. Then, multiply 3 by 8, which is 24. Therefore, the answer is 14/24, which can be reduced to 7/12 by dividing both the numerator and denominator by 2.

• For example, to solve 1/2 ÷ 1/6, flip 1/6 upside down so it becomes 6/1. Then just multiply 1 x 6 to find the numerator (which is 6) and 2 x 1 to find the denominator (which is 2). So, the answer is 6/2 which is equal to 3.

Joseph Meyer

Think about fractions as portions of a whole. Imagine dividing objects like pizzas or cakes into equal parts. Visualizing fractions this way improves comprehension, compared to relying solely on memorization. This approach can be helpful when adding, subtracting, and comparing fractions.

Practicing the Basics

• For instance, in 3/5, 3 is the numerator so there are 3 parts and 5 is the denominator so there are 5 total parts. In 7/8, 7 is the numerator and 8 is the denominator.

• If you need to turn 7 into a fraction, for instance, write it as 7/1.

• For example, if you have the fraction 15/45, the greatest common factor is 15, since both 15 and 45 can be divided by 15. Divide 15 by 15, which is 1, so that's your new numerator. Divide 45 by 15, which is 3, so that's your new denominator. This means that 15/45 can be reduced to 1/3.

• Say you have the mixed number 1 2/3. Stary by multiplying 3 by 1, which is 3. Add 3 to 2, the existing numerator. The new numerator is 5, so the mixed fraction is 5/3.

Tip: Typically, you'll need to convert mixed numbers to improper fractions if you're multiplying or dividing them.

• Say that you have the improper fraction 17/4. Set up the problem as 17 ÷ 4. The number 4 goes into 17 a total of 4 times, so the whole number is 4. Then, multiply 4 by 4, which is equal to 16. Subtract 16 from 17, which is equal to 1, so that's the remainder. This means that 17/4 is the same as 4 1/4.

Fraction Calculator, Practice Problems, and Answers

Community Q&A

• Take the time to carefully read through the problem at least twice so you can be sure you know what it's asking you to do. Thanks Helpful 2 Not Helpful 2
• Check with your teacher to find out if you need to convert improper fractions into mixed numbers and/or reduce fractions to their lowest terms to get full marks. Thanks Helpful 2 Not Helpful 1
• To take the reciprocal of a whole number, just put a 1 over it. For example, 5 becomes 1/5. Thanks Helpful 1 Not Helpful 1

You Might Also Like

• ↑ https://www.sparknotes.com/math/prealgebra/fractions/terms/
• ↑ https://www.bbc.co.uk/bitesize/articles/z9n4k7h
• ↑ https://www.mathsisfun.com/fractions_multiplication.html
• ↑ https://www.mathsisfun.com/fractions_division.html
• ↑ https://medium.com/i-math/the-no-nonsense-straightforward-da76a4849ec
• ↑ https://www.youtube.com/watch?v=PcEwj5_v75g
• ↑ https://sciencing.com/solve-math-problems-fractions-7964895.html

About This Article

To solve a fraction multiplication question in math, line up the 2 fractions next to each other. Multiply the top of the left fraction by the top of the right fraction and write that answer on top, then multiply the bottom of each fraction and write that answer on the bottom. Simplify the new fraction as much as possible. To divide fractions, flip one of the fractions upside-down and multiply them the same way. If you need to add or subtract fractions, keep reading! Did this summary help you? Yes No

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Fractions  - Adding and Subtracting Fractions

Fractions  -, adding and subtracting fractions, fractions adding and subtracting fractions.

Fractions: Adding and Subtracting Fractions

Lesson 3: adding and subtracting fractions.

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Adding and subtracting fractions

In the previous lessons, you learned that a fraction is part of a whole. Fractions show how much you have of something, like 1/2 of a tank of gas or 1/3 of a cup of water.

In real life, you might need to add or subtract fractions. For example, have you ever walked 1/2 of a mile to work and then walked another 1/2 mile back? Or drained 1/4 of a quart of gas from a gas tank that had 3/4 of a quart in it? You probably didn't think about it at the time, but these are examples of adding and subtracting fractions.

Click through the slideshow to learn how to set up addition and subtraction problems with fractions.

Let's imagine that a cake recipe tells you to add 3/5 of a cup of oil to the batter.

You also need 1/5 of a cup of oil to grease the pan. To see how much oil you'll need total, you can add these fractions together.

When you add fractions, you just add the top numbers, or numerators .

That's because the bottom numbers, or denominators , show how many parts would make a whole.

We don't want to change how many parts make a whole cup ( 5 ). We just want to find out how many parts we need total.

So we only need to add the numerators of our fractions.

We can stack the fractions so the numerators are lined up. This will make it easier to add them.

And that's all we have to do to set up an addition example with fractions. Our fractions are now ready to be added.

We'll do the same thing to set up a subtraction example. Let's say you had 3/4 of a tank of gas when you got to work.

If you use 1/4 of a tank to drive home, how much will you have left? We can subtract these fractions to find out.

Just like when we added, we'll stack our fractions to keep the numerators lined up.

This is because we want to subtract 1 part from 3 parts.

Now that our example is set up, we're ready to subtract!

Try setting up these addition and subtraction problems with fractions. Don't try solving them yet!

You run 4/10 of a mile in the morning. Later, you run for 3/10 of a mile.

You had 7/8 of a stick of butter and used 2/8 of the stick while cooking dinner.

Your gas tank is 2/5 full, and you put in another 2/5 of a tank.

Solving addition problems with fractions

Now that we know how to write addition problems with fractions, let's practice solving a few. If you can add whole numbers , you're ready to add fractions.

Click through the slideshow to learn how to add fractions.

Let's continue with our previous example and add these fractions: 3/5 of cup of oil and 1/5 of a cup of oil.

Remember, when we add fractions, we don't add the denominators.

This is because we're finding how many parts we need total. The numerators show the parts we need, so we'll add 3 and 1 .

3 plus 1 equals 4 . Make sure to line up the 4 with the numbers you just added.

The denominators will stay the same, so we'll write 5 on the bottom of our new fraction.

3/5 plus 1/5 equals 4/5 . So you'll need 4/5 of a cup of oil total to make your cake.

Let's try another example: 7/10 plus 2/10 .

Just like before, we're only going to add the numerators. In this example, the numerators are 7 and 2 .

7 plus 2 equals 9 , so we'll write that to the right of the numerators.

Just like in our earlier example, the denominator stays the same.

So 7/10 plus 2/10 equals 9/10 .

Try solving some of the addition problems below.

Solving subtraction problems with fractions

Subtracting fractions is a lot like regular subtraction. If you can subtract whole numbers , you can subtract fractions too!

Click through the slideshow to learn how to subtract fractions.

Let's use our earlier example and subtract 1/4 of a tank of gas from 3/4 of a tank.

Just like in addition, we're not going to change the denominators.

We don't want to change how many parts make a whole tank of gas. We just want to know how many parts we'll have left.

We'll start by subtracting the numerators. 3 minus 1 equals 2 , so we'll write 2 to the right of the numerators.

Just like when we added, the denominator of our answer will be the same as the other denominators.

So 3/4 minus 1/4 equals 2/4 . You'll have 2/4 of a tank of gas left when you get home.

Let's try solving another problem: 5/6 minus 3/6 .

We'll start by subtracting the numerators.

5 minus 3 equals 2 . So we'll put a 2 to the right of the numerators.

As usual, the denominator stays the same.

So 5/6 minus 3/6 equals 2/6 .

Try solving some of the subtraction problems below.

After you add or subtract fractions, you may sometimes have a fraction that can be reduced to a simpler fraction. As you learned in Comparing and Reducing Fractions , it's always best to reduce a fraction to its simplest form when you can. For example, 1/4 plus 1/4 equals 2/4 . Because 2 and 4 can both be divided 2 , we can reduce 2/4 to 1/2 .

Adding fractions with different denominators

On the last page, we learned how to add fractions that have the same denominator, like 1/4 and 3/4 . But what if you needed to add fractions with different denominators? For example, our cake recipe might say to blend 1/4 cup of milk in slowly and then dump in another 1/3 of a cup.

In Comparing and Reducing Fractions , we compared fractions with a different bottom number, or denominator. We had to change the fractions so their denominators were the same. To do that, we found the lowest common denominator , or LCD .

We can only add or subtract fractions if they have the same denominators. So we'll need to find the lowest common denominator before we add or subtract these fractions. Once the fractions have the same denominator, we can add or subtract as usual.

Click through the slideshow to learn how to add fractions with different denominators.

Let's add 1/4 and 1/3 .

Before we can add these fractions, we'll need to change them so they have the same denominator .

To do that, we'll have to find the LCD , or lowest common denominator, of 4 and 3 .

It looks like 12 is the smallest number that can be divided by both 3 and 4, so 12 is our LCD .

Since 12 is the LCD, it will be the new denominator for our fractions.

Now we'll change the numerators of the fractions, just like we changed the denominators.

First, let's look at the fraction on the left: 1/4 .

To change 4 into 12 , we multiplied it by 3 .

Since the denominator was multiplied by 3 , we'll also multiply the numerator by 3 .

1 times 3 equals 3 .

1/4 is equal to 3/12 .

Now let's look at the fraction on the right: 1/3 . We changed its denominator to 12 as well.

Our old denominator was 3 . We multiplied it by 4 to get 12.

We'll also multiply the numerator by 4 . 1 times 4 equals 4 .

So 1/3 is equal to 4/12 .

Now that our fractions have the same denominator, we can add them like we normally do.

3 plus 4 equals 7 . As usual, the denominator stays the same. So 3/12 plus 4/12 equals 7/12 .

Try solving the addition problems below.

Subtracting fractions with different denominators

We just saw that fractions can only be added when they have the same denominator. The same thing is true when we're subtracting fractions. Before we can subtract, we'll have to change our fractions so they have the same denominator.

Click through the slideshow to learn how to subtract fractions with different denominators.

Let's try subtracting 1/3 from 3/5 .

First, we'll change the denominators of both fractions to be the same by finding the lowest common denominator .

It looks like 15 is the smallest number that can be divided evenly by 3 and 5 , so 15 is our LCD.

Now we'll change our first fraction. To change the denominator to 15 , we'll multiply the denominator and the numerator by 3 .

5 times 3 equals 15 . So our fraction is now 9/15 .

Now let's change the second fraction. To change the denominator to 15 , we'll multiply both numbers by 5 to get 5/15 .

Now that our fractions have the same denominator, we can subtract like we normally do.

9 minus 5 equals 4 . As always, the denominator stays the same. So 9/15 minus 5/15 equals 4/15 .

Try solving the subtraction problems below.

Adding and subtracting mixed numbers

Over the last few pages, you've practiced adding and subtracting different kinds of fractions. But some problems will need one extra step. For example, can you add the fractions below?

In Introduction to Fractions , you learned about mixed numbers . A mixed number has both a fraction and a whole number . An example is 2 1/2 , or two-and-a-half . Another way to write this would be 5/2 , or five-halves . These two numbers look different, but they're actually the same.

5/2 is an improper fraction . This just means the top number is larger than the bottom number. Even though improper fractions look strange, you can add and subtract them just like normal fractions. Mixed numbers aren't easy to add, so you'll have to convert them into improper fractions first.

Let's add these two mixed numbers: 2 3/5 and 1 3/5 .

We'll need to convert these mixed numbers to improper fractions. Let's start with 2 3/5 .

As you learned in Lesson 2 , we'll multiply the whole number, 2 , by the bottom number, 5 .

2 times 5 equals 10 .

Now, let's add 10 to the numerator, 3 .

10 + 3 equals 13 .

Just like when you add fractions, the denominator stays the same. Our improper fraction is 13/5 .

Now we'll need to convert our second mixed number: 1 3/5 .

First, we'll multiply the whole number by the denominator. 1 x 5 = 5 .

Next, we'll add 5 to the numerators. 5 + 3 = 8 .

Just like last time, the denominator remains the same. So we've changed 1 3/5 to 8/5 .

Now that we've changed our mixed numbers to improper fractions, we can add like we normally do.

13 plus 8 equals 21 . As usual, the denominator will stay the same. So 13/5 + 8/5 = 21/5 .

Because we started with a mixed number, let's convert this improper fraction back into a mixed number.

As you learned in the previous lesson , divide the top number by the bottom number. 21 divided by 5 equals 4, with a remainder of 1 .

The answer, 4, will become our whole number.

And the remainder , 1, will become the numerator of the fraction.

So 2 3/5 + 1 3/5 = 4 1/5 .

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4.9: Solving Equations with Fractions

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Undoing Subtraction

We can still add the same amount to both sides of an equation without changing the solution.

Solve for x : \(x - \frac{5}{6} = \frac{1}{3}\).

To “undo” subtracting 5/6, add 5/6 to both sides of the equation and simplify.

\[ \begin{aligned} x - \frac{5}{6} = \frac{1}{3} ~ & \textcolor{red}{ \text{ Original equation.}} \\ x - \frac{5}{6} + \frac{5}{6} = \frac{1}{3} + \frac{5}{6} ~ & \textcolor{red}{ \text{ Add } \frac{5}{6} \text{ to both sides.}} \\ x = \frac{1 \cdot 2}{3 \cdot 2} + \frac{5}{6} ~ & \textcolor{red}{ \text{ Equivalent fractions, LCD = 6.}} \\ x = \frac{2}{6} + \frac{5}{6} ~ & \textcolor{red}{ \text{ Simplify.}} \\ x = \frac{7}{6} ~ & \textcolor{red}{ \text{ Add.}} \end{aligned}\nonumber \]

It is perfectly acceptable to leave your answer as an improper fraction. If you desire, or if you are instructed to do so, you can change your answer to a mixed fraction (7 divided by 6 is 1 with a remainder of 1). That is \(x = 1 \frac{1}{6}\).

Checking the Solution

Substitute 7/6 for x in the original equation and simplify.

\[ \begin{aligned} x - \frac{5}{6} = \frac{1}{3} ~ & \textcolor{red}{ \text{ Original equation.}} \\ \frac{7}{6} - \frac{5}{6} = \frac{1}{3} ~ & \textcolor{red}{ \text{ Substitute 7/6 for } x.} \\ \frac{2}{6} = \frac{1}{3} ~ & \textcolor{red}{ \text{ Subtract.}} \\ \frac{1}{3} = \frac{1}{3} ~ & \textcolor{red}{ \text{ Reduce.}} \end{aligned}\nonumber \]

Because the last statement is true, we conclude that 7/6 is a solution of the equation x − 5/6 = 1/3.

Undoing Addition

You can still subtract the same amount from both sides of an equation without changing the solution.

Solve for x : \(x + \frac{2}{3} = - \frac{3}{5}\).

To “undo” adding 2/3, subtract 2/3 from both sides of the equation and simplify.

\[ \begin{aligned} x + \frac{2}{3} = - \frac{3}{5} ~ & \textcolor{red}{ \text{ Original equation.}} \\ x + \frac{2}{3} - \frac{2}{3} = - \frac{3}{5} - \frac{2}{3} ~ & \textcolor{red}{ \text{ Subtract } \frac{2}{3} \text{ from both sides.}} \\ x = - \frac{3 \cdot 3}{5 \cdot 3} - \frac{2 \cdot 5}{3 \cdot 5} ~ & \textcolor{red}{ \text{ Equivalent fractions, LCD = 15.}} \\ x = - \frac{9}{15} - \frac{10}{15} ~ & \textcolor{red}{ \text{ Simplify.}} \\ x = - \frac{19}{15} ~ & \textcolor{red}{ \text{ Subtract.}} \end{aligned}\nonumber \]

Readers are encouraged to check this solution in the original equation.

Solve for x : \(x + \frac{3}{4} = - \frac{1}{2}\)

Undoing Multiplication

We “undo” multiplication by dividing. For example, to solve the equation 2 x = 6, we would divide both sides of the equation by 2. In similar fashion, we could divide both sides of the equation

\[ \frac{3}{5} x = \frac{4}{10}\nonumber \]

by 3/5. However, it is more efficient to take advantage of reciprocals. For convenience, we remind readers of the Multiplicative Inverse Property .

Multiplicative Inverse Property

Let a / b be any fraction. The number b / a is called the multiplicative inverse or reciprocal of a / b . The product of reciprocals is 1.

\[ \frac{a}{b} \cdot \frac{b}{a} = 1.\nonumber \]

Let’s put our knowledge of reciprocals to work.

Solve for x : \(\frac{3}{5}x = \frac{4}{10}\).

To “undo” multiplying by 3/5, multiply both sides by the reciprocal 5/3 and simplify.

\[ \begin{aligned} \frac{3}{5} x = \frac{4}{10} ~ & \textcolor{red}{ \text{ Original equation.}} \\ \frac{5}{3} \left( \frac{3}{5} x \right) = \frac{5}{3} \left( \frac{4}{10} \right) & ~ \textcolor{red}{ \text{ Multiply both sides by 5/3.}} \\ \left( \frac{5}{3} \cdot \frac{3}{5} \right) x = \frac{20}{30} ~ & \textcolor{red}{ \begin{array}{l} \text{ On the left, use the associative property to regroup.} \\ \text{ On the right, multiply.} \end{array}} \\ 1x = \frac{2}{3} ~ & \textcolor{red}{ \begin{array}{l} \text{ On the left, } \frac{5}{3} \cdot \frac{3}{5} = 1. \\ \text{ On the right, reduce: } \frac{20}{30} = \frac{2}{3}. \end{array}} \\ x = \frac{2}{3} ~ & \textcolor{red}{ \text{ On the left, } 1x = x.} \end{aligned}\nonumber \]

Substitute 2/3 for x in the original equation and simplify.

\[ \begin{aligned} \frac{3}{5} x = \frac{4}{10} ~ & \textcolor{red}{ \text{ Original equation.}} \\ \frac{3}{5} \left( \frac{2}{3} \right) = \frac{4}{10} ~ & \textcolor{red}{ \text{ Substitute 2/3 for }x.} \\ \frac{6}{15} = \frac{4}{10} ~ & \textcolor{red}{ \text{ Multiply numerators; multiply denominators.}} \\ \frac{2}{5} = \frac{2}{5} ~ & \textcolor{red}{ \text{ Reduce both sides to lowest terms.}} \end{aligned}\nonumber \]

Because this last statement is true, we conclude that 2/3 is a solution of the equation (3/5) x = 4/10.

Solve for y : \( \frac{2}{3} y = \frac{4}{5}\)

Solve for x : \(- \frac{8}{9} x = \frac{5}{18}\).

To “undo” multiplying by −8/9, multiply both sides by the reciprocal −9/8 and simplify.

\[ \begin{aligned} - \frac{8}{9} x = \frac{5}{18} ~ & \textcolor{red}{ \text{ Original equation.}} \\ - \frac{9}{8} \left( - \frac{8}{9} x \right) = - \frac{9}{8} \left( \frac{5}{18} \right) ~ & \textcolor{red}{ \text{ Multiply both sides by } -9/8.} \\ \left[ - \frac{9}{8} \cdot \left( - \frac{8}{9} \right) \right] x = - \frac{3 \cdot 3}{2 \cdot 2 \cdot 2} \cdot \frac{5}{2 \cdot 3 \cdot 3} ~ & \textcolor{red}{ \begin{array}{l} \text{ On the left, use the associative property to regroup.} \\ \text{ On the right, prime factor.} \end{array}} 1x = \frac{ \cancel{3} \cdot \cancel{3}}{2 \cdot 2 \cdot 2} \cdot \frac{5}{2 \cdot \cancel{3} \cdot \cancel{3}} ~ & \textcolor{red}{ \begin{array}{l} \text{ On the left, } - \frac{9}{8} \cdot \left( - \frac{8}{9} \right) = 1. \\ \text{ On the right, cancel common factors.} \end{array}} \\ x = - \frac{5}{16} ~ & \textcolor{red}{ \text{ On the left, } 1x = x. \text{ Multiply on the right.}} \end{aligned}\nonumber \]

Solve for z: \(− \frac{2}{7} z = \frac{4}{21}\)

Clearing Fractions from the Equation

Although the technique demonstrated in the previous examples is a solid mathematical technique, working with fractions in an equation is not always the most efficient use of your time.

To clear all fractions from an equation, multiply both sides of the equation by the least common denominator of the fractions that appear in the equation.

Let’s put this idea to work.

In Example 1, we were asked to solve the following equation for x :

\[x - \frac{5}{6} = \frac{1}{3}.\nonumber \]

Take a moment to review the solution technique in Example 1. We will now solve this equation by first clearing all fractions from the equation.

Multiply both sides of the equation by the least common denominator for the fractions appearing in the equation.

\[ \begin{aligned} x - \frac{5}{6}= \frac{1}{3} ~ & \textcolor{red}{ \text{ Original equation.}} \\ 6 \left( x - \frac{5}{6} \right) = 6 \left( \frac{1}{3} \right) ~ & \textcolor{red}{ \text{ Multiply both sides by 6.}} \\ 6x - 6 \left( \frac{5}{6} \right) = 6 \left( \frac{1}{3} \right) ~ & \textcolor{red}{ \text{ Distribute the 6.}} \\ 6x-5 = 2 ~ & \textcolor{red}{ \text{ On each side, multiply first.}} \\ ~ & \textcolor{red}{6 \left( \frac{5}{6} \right) = 5 \text{ and } 6 \left( \frac{1}{3} \right) = 2.} \end{aligned}\nonumber \]

Note that the equation is now entirely clear of fractions, making it a much simpler equation to solve.

\[ \begin{aligned} 6x - 5 + 5 = 2 + 5 ~ & \textcolor{red}{ \text{ Add 5 to both sides.}} \\ 6x = 7 ~ & \textcolor{red}{ \text{ Simplify both sides.}} \\ \frac{6x}{6} = \frac{7}{6} ~ & \textcolor{red}{ \text{ Divide both sides by 6.}} \\ x = \frac{7}{6} ~ & \textcolor{red}{ \text{ Simplify.}} \end{aligned}\nonumber \]

Note that this is the same solution found in Example 1.

Solve for t : \(t - \frac{2}{7} = - \frac{1}{4}\)

In Example 4, we were asked to solve the following equation for x .

\[- \frac{8}{9}x = \frac{5}{18}\nonumber \]

Take a moment to review the solution in Example 4. We will now solve this equation by first clearing all fractions from the equation.

Multiply both sides of the equation by the least common denominator for the fractions that appear in the equation.

\[ \begin{aligned} - \frac{8}{9} x = \frac{5}{18} ~ & \textcolor{red}{ \text{ Original equation.}} \\ 18 \left( - \frac{8}{9} x \right) = 18 \left( \frac{5}{18} \right) ~ & \textcolor{red}{ \text{ Multiply both sides by 18.}} \\ -16x=5 ~ & \textcolor{red}{ \text{ On each side, cancel and multiply.}} \\ ~ & \textcolor{red}{ 18 \left( - \frac{8}{9} \right) = -16 \text{ and } 18 \left( \frac{5}{18} \right) = 5.} \end{aligned}\nonumber \]

Note that the equation is now entirely free of fractions. Continuing,

\[ \begin{aligned} \frac{-16x}{-16} = \frac{5}{-16} ~ & \textcolor{red}{ \text{ Divide both sides by } -16.} \\ x = - \frac{5}{16} ~ & \textcolor{red}{ \text{ Simplify.}} \end{aligned}\nonumber \]

Note that this is the same as the solution found in Example 4.

Solve for u :

\[ - \frac{7}{9} u = \frac{14}{27}\nonumber \]

Solve for x : \(\frac{2}{3}x + \frac{3}{4} = \frac{1}{2}\).

\[ \begin{aligned} \frac{2}{3} x + \frac{3}{4} = \frac{1}{2} ~ & \textcolor{red}{ \text{ Original equation.}} \\ 12 \left( \frac{2}{3} x + \frac{3}{4} = \right) = 12 \left( \frac{1}{2} \right) ~ & \textcolor{red}{ \text{ Multiply both sides by 12.}} \\ 12 \left( \frac{2}{3}x \right) + 12 \left( \frac{3}{4} \right) = 12 \left( \frac{1}{2} \right) ~ & \textcolor{red}{ \text{ On the left, distribute 12.}} \\ 8x + 9 = 6 ~ & \textcolor{red}{ \text{ Multiply: } 12 \left( \frac{2}{3} x \right) = 8x, ~ 12 \left( \frac{3}{4} \right) = 9,} \\ ~ & \textcolor{red}{ \text{ and } 12 \left( \frac{1}{2} \right) = 6.} \end{aligned}\nonumber \]

Note that the equation is now entirely free of fractions. We need to isolate the terms containing x on one side of the equation.

\[ \begin{aligned} 8x + 9 - 9 = 6 - 9 ~ & \textcolor{red}{ \text{ Subtract 9 from both sides.}} \\ 8x = - 3 ~ & \textcolor{red}{ \text{ Simplify both sides.}} \\ \frac{8x}{8} = \frac{-3}{8} ~ & \textcolor{red}{ \text{ Divide both sides by 8.}} \\ x = - \frac{3}{8} ~ & \textcolor{red}{ \text{ Simplify both sides.}} \end{aligned}\nonumber \]

Solve for r : \(\frac{3}{4} r + \frac{2}{3} = \frac{1}{2}\)

Solve for x : \( \frac{2}{3} - \frac{3x}{4} = \frac{x}{2} - \frac{1}{8}.\)

Multiply both sides of the equation by the least common denominator for the fractions in the equation.

\[ \begin{aligned} \frac{2}{3} - \frac{3x}{4} = \frac{x}{2} - \frac{1}{8} ~ & \textcolor{red}{ \text{ Original equation.}} \\ 24 \left( \frac{2}{3} - \frac{3x}{4} \right) = 24 \left( \frac{x}{2} - \frac{1}{8} \right) ~ & \textcolor{red}{ \text{ Multiply both sides by 24.}} \\ 24 \left( \frac{2}{3} \right) - 24 \left( \frac{3x}{4} \right) = 24 \left( \frac{x}{2} \right) - 24 \left( \frac{1}{8} \right) ~ & \textcolor{red}{ \text{ On both sides, distribute 24.}} \\ 16 - 18x = 12x - 3 ~ & \textcolor{red}{ \text{ Left: } 24 \left( \frac{2}{3} \right) = 16, ~ 24 \left( \frac{3x}{4} \right) = 18x.} \\ ~ & \textcolor{red}{ \text{ Right: } 24 \left( \frac{x}{2} \right) = 12x, ~ 24 \left( \frac{1}{8} \right) = 3.} \end{aligned}\nonumber \]

\[ \begin{aligned} 16 - 18x - 12x = 12x - 3 - 12x ~ & \textcolor{red}{ \text{ Subtract } 12x \text{ from both sides.}} \\ 16 - 30x = -3 ~ & \textcolor{red}{ \begin{aligned} \text{ Left: } -18x - 12x = -30x. \\ \text{ Right: } 12x - 12x = 0. \end{aligned}} \\ 16 - 30x - 16 = -3 - 16 ~ & \textcolor{red}{ \text{ Subtract 16 from both sides.}} \\ -30x = -19 ~ & \textcolor{red}{ \begin{aligned} \text{ Left: } 16-16=0. \\ \text{ Right: } -3 - 16 = -19. \end{aligned}} \\ \frac{-30x}{-30} = \frac{-19}{-30} ~ & \textcolor{red}{ \text{ Divide both sides by } -30.} \\ x = \frac{19}{30} ~ & \textcolor{red}{ \text{ Simplify both sides.}} \end{aligned}\nonumber \]

Solve for s : \( \frac{3}{2} - \frac{2s}{5} = \frac{s}{3} - \frac{1}{5}\).

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• descending\:order\:\frac{1}{2},\:\frac{3}{6},\:\frac{7}{2}
• decimal\:to\:fraction\:0.35
• What is a mixed number?
• A mixed number is a combination of a whole number and a fraction.
• How can I compare two fractions?
• To compare two fractions, first find a common denominator, then compare the numerators.Alternatively, compare the fractions by converting them to decimals.
• How do you add or subtract fractions with different denominators?
• To add or subtract fractions with different denominators, convert the fractions to have a common denominator. Then you can add or subtract the numerators of the fractions, leaving the denominator unchanged.

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Fraction Word Problems: Examples

Related Pages More Fraction Word Problems Harder Fraction Word Problems Singapore Math Lessons Fraction Problems Using Algebra

Lessons on solving fraction word problems using visual methods like bar models or tape diagrams.

Printable “Fraction Word Problems” Worksheets: Fraction Word Problems (Add, Subtract) 2-Step Fraction Word Problems (Add, Subtract) 1-Step Mixed Number Word Problems (Add, Subtract) 2-Step Mixed Number Word Problems (Add, Subtract) Fraction Word Problems (Add, Subtract, Multiply) Fraction Word Problems (Tape Diagrams)

Here are some examples and solutions of fraction word problems. The first example is a one-step word problem. The second example shows how blocks can be used to help illustrate the problem. The third example is a two-step word problem.

More examples and solutions using the bar modeling method to solve fraction word problems are shown in the videos. The bar modeling method, also called tape diagrams, are used in Singapore Math and the Common Core.

3 units = 24 1 unit = 24 ÷ 3 = 8 5 units = 5 × 8 = 40

There were 40 children in the group.

He sold 80 teddy bears.

Step 2: Find how much money he received. 80 × 12 = 960

He received $960.

Bar Modeling With Fractions

• Grace thought that a plane journey would take 7/10 hr but the actual journey took 1/5 hr longer. How long did the actual journey take?
• Timothy took 2/3 hr to paint a portrait. This was 1/3 hr shorter than the time he took to paint scenery. How long did he take to paint scenery?

How To Solve Real World Problems Involving Multiplication Of Fractions By Using Visual Fraction Models Or Equations To Represent The Problem?

• At the animal shelter 4/6 of the animals are cats. Of the cats 1/2 are male. What fraction of the animals at the shelter are male cats?
• A taco recipe called for 2/3 cup of cheese per taco. If Andrew wanted to make 3 tacos, how much cheese would he need?

How To Solve Word Problems Using Tape Diagrams And Fraction-By-Fraction Multiplication?

• Ethan is icing 30 cupcakes. He spreads mint icing on 1/5 of the cupcakes and chocolate on 1/2 of the remaining cupcakes. The rest will get vanilla frosting. How many cupcakes have vanilla frosting?
• Maddox puts 1/4 of her lawn-mowing money in savings and uses 1/2 of the remaining money to pay back her sister. If she has $15 left, how much did she have at first?

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Exploring Fractions

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Grade 5 addition and subtraction of fractions worksheets

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• Convert decimals to fractions, with simplification
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Click a Box in the Middle Column for Fractions Math Practice

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Equivalent Fractions Quiz

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___ See Decimals & Percentages Page for fraction conversions to percents and decimals ___

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Online Calculators

Fractions Calculator

Calculator Use

Use this fraction calculator for adding, subtracting, multiplying and dividing fractions. Answers are fractions in lowest terms or mixed numbers in reduced form.

Input proper or improper fractions, select the math sign and click Calculate. This is a fraction calculator with steps shown in the solution.

If you have negative fractions insert a minus sign before the numerator. So if one of your fractions is -6/7, insert -6 in the numerator and 7 in the denominator.

To do math with mixed numbers (whole numbers and fractions) use the Mixed Numbers Calculator .

Math on Fractions with Unlike Denominators

There are 2 cases where you need to know if your fractions have different denominators:

• if you are adding fractions
• if you are subtracting fractions

How to Add or Subtract Fractions

• Find the least common denominator
• You can use the LCD Calculator to find the least common denominator for a set of fractions
• For your first fraction, find what number you need to multiply the denominator by to result in the least common denominator
• Multiply the numerator and denominator of your first fraction by that number
• Repeat Steps 3 and 4 for each fraction
• For addition equations, add the fraction numerators
• For subtraction equations, subtract the fraction numerators
• Convert improper fractions to mixed numbers
• Reduce the fraction to lowest terms

How to Multiply Fractions

• Multiply all numerators together
• Multiply all denominators together
• Reduce the result to lowest terms

How to Divide Fractions

• Rewrite the equation as in "Keep, Change, Flip"
• Keep the first fraction
• Change the division sign to multiplication
• Flip the second fraction by switching the top and bottom numbers

Fraction Formulas

There is a way to add or subtract fractions without finding the least common denominator (LCD) . This method involves cross multiplication of the fractions. See the formulas below.

You may find that it is easier to use these formulas than to do the math to find the least common denominator.

The formulas for multiplying and dividing fractions follow the same process as described above.

Adding Fractions

The formula for adding fractions is:

Example steps:

Subtracting Fractions

The formula for subtracting fractions is:

Multiplying Fractions

The formula for multiplying fractions is:

Dividing Fractions

The formula for dividing fractions is:

Related Calculators

To perform math operations on mixed number fractions use our Mixed Numbers Calculator . This calculator can also simplify improper fractions into mixed numbers and shows the work involved.

If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator .

For an explanation of how to factor numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator .

If you are simplifying large fractions by hand you can use the Long Division with Remainders Calculator to find whole number and remainder values.

This calculator performs the reducing calculation faster than other calculators you might find. The primary reason is that it utilizes Euclid's Algorithm for reducing fractions which can be found on The Math Forum .

Cite this content, page or calculator as:

Furey, Edward " Fractions Calculator " at https://www.calculatorsoup.com/calculators/math/fractions.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: October 17, 2023

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80 Educational Children's Math Picture Books

R eady for the biggest list of math picture books ? Because I’ve found SO MANY amazing math books, I can’t wait to tell you about them!

Use these at home, in the classroom, or with your homeschool. You’ll discover books about counting , addition, subtraction, number sense, the 100th day, sorting, fractions, division, geometry, problem-solving, money, telling time, multiplication , and algebra.

Three cheers for math!

Table of Contents

Counting math books, the 100th day books, number sense books, telling time books, addition and subtraction books, sorting and pattern books, measurement books, multiplication books, division and fraction books, geometry books, money books, algebra books, math problem-solving books, best math books.

One Big Pair of Underwear

HAHA — this is the silliest “counting” picture book you’ll read! It’s counting, subtracting, and patterns silliness that your kids will adore.

Count your way from one to ten as this family gets ready for dinner including shopping and cooking the food.

You’ll love the clever creations Medina makes with vegetables — 1 avocado deer and 2 radish mice, just to name a few.

Anno’s Counting Book by Mitsumasa Anno

Bold graphic images help children find the black dots from one to ten in different images. Fun!

What’s more relatable than candy? And brightly colored illustrations? This tasty book about large numbers is pitch-perfect.

How Many Bugs in a Box

We love this engaging book. Lift the flaps and see what pops out!

Rhyme and count with these naughty monkeys.

The snake wants to count the mice — for his dinner. Count up and count down.

Monkey counts to ten and back as she bravely faces the crocodile-infested waters in order to get to a banana tree.

Alice needs to find 100 things to bring for the 100th day — but she’s having lots of trouble deciding what.

What is he going to bring for the 100th day of school? You’ll love this delightful rhyming book.

It’s not only the kids that get to bring 100 things to school, Miss Bindergarten is getting together 100 things, too.

Learn about counting by tens as the queens plan a special birthday surprise for the king.

Grapes of Math

Fun and rhyming riddles to help kids learn problem-solving strategies.

Learn about odd and even numbers with this silly story about a boy who discovers that everything in his life is ODD! (Also read: My Even Day and My Half Day .)

Hungry for Math: Poems to Munch On

Just like numbers, ideas are infinite. This is fun story of making the challenging concept of infinity more understandable.

Even Steven is all about, you guessed it, even-numbered things. Then one day, his cousin Odd Todd comes to visit. Which terrifies Even Steven. Because even Odd Todd knocks in odd numbers. . .

Learn about a boy who loved numbers and was known as The Magician from Budapest in this playful mathematical biography.

Go Figure!: A Totally Cool Book About Numbers

Learn more about the numbers in our everyday life, their purpose, and history. Then try some of the fun number magic tricks, puzzles, and activities.

365 Penguins

Penguins are arriving every single day at their doorstep. What are they doing to do?!

How Much Is a Million?

David M. Schwartz, illustrated by  Steven Kellogg

Marvelosissimo the mathematical magician will teach you about really BIG numbers.

Skip count and estimate with pumpkins.

This is a fun book that offers 100 math riddles, each with adaptations for young kids and bigger kids.

Telling Time with Big Mama Cat by Dan Harper

Follow along with the daily schedule and use the movable hands to practice telling time.

Learn about the different measurements of time (seconds, minutes), go through a day and take mini-quizzes to figure out how much you’re learning.

This funny book is all about Mr. Crocodile’s schedule which includes finding and catching some pesky monkeys.

Pigeon Math

Hilarious! Addition and subtraction never felt so fun!!  An increasingly exasperated narrator is TRYING to tell the story about ten pigeons but it’s not going well. Visual support, goofy humor, and plenty of kid-appeal make this a 100% must-own, must-read STEM picture book.

Add the baby animals with the grown-ups to see how many all together.

Jen Arena   (Author),  Stephen Gilpin

A winter addition adventure of snowmen that will get you to 100 total.

A loving family shares a favorite cultural sweet treat and practices counting and subtracting in this beautifully written, Indian-flavored math story! Mama makes 10 gulab jamuns for guests. But, one child eats three. Now there are only 7 for the guests. And another child eats 3 more. Now there are only 4 left. Mamma wonders how she will have time to make more treats for her guests. The kids will help her make them! 

The Chicken Problem

This is a Peg and Cat picture book story their perfect picnic that goes totally crazy with runaway chickens.  Peg is “ totally freaking out ” and needs to get the one hundred chickens back in the coop. Peg and Cat must solve the chicken problem fast. I love the illustrations, the problem-solving characters, and the silly story.

Comic Book Math ~ Fun-Schooling Journal: Adding, Writing & Subtracting Games

by Sarah Janisse Brown

Use your imagination and practice math skills in a fun way. 

Subtract your way through this goofy story about an elevator going down.

Animal stories help kids learn the basics of putting numbers in groups and taking numbers away.

Count and add the animals on the back of the trucks.

Go on a butterfly addition hunt and see who will win.

When the music stops, someone is out. Subtract to see how many are left.

The O’Malleys pass the time on a long car trip by counting up different color cars using tally marks. The winner is the one who tallies the most.

Arithmechicks Take Away: A Math Story

This gives kids photographs from which they can make decisions about sorting. Use with actual physical objects to make the lessons more concrete.

Blockhead: The Life of Fibonacci

Fibonacci sees patterns in nature and develops the Fibonacci Sequence.

Learn about all the spirals in nature.

What groups can you sort out of Packy the Packrat’s stuff?

Fannie in the Kitchen: The Whole Story from Soup to Nuts of How Fannie Farmer Invented Recipes with Precise Measurements  

Kitchen measurements equal delicious foods.

Measuring Penny by Loreen Leedy

Lisa loves measurement, so she starts measuring her dog, Penny.

How Big is a Foot by Rolf Myller

The king needs to figure out how big of a bed to make for his queen. This introduces standardizing measurements.

An inchworm shows the bird why he shouldn’t be eaten — because he can measure anything!

Amanda learns that multiplication is the fastest way to count.

Kings Chessboard

Multiplying Menace: The Revenge of Rumpelstiltskin

by Pam Calvert and Wayne Geehan

This is a fun multiplication story about mischievous Rumplestiltskin and his multiplication stick.

Gorgeous illustrations illustrate this fable about a smart girl who outsmarts a king.

This is an introduction to multiplication and factorals.

Spaghetti And Meatballs For All!  

by Marilyn Burns and Debbie Tilley

Yummy! It’s time for spaghetti. But how much does everyone get to eat?

Equal Shmequal

, illustrated by  Philomena O’Neill

Mouse helps her friends how to equally divide up teams for a game of tug of war.

Elinor J Pinczes , illustrated by  Bonnie MacKain

If 100 ants are marching to a picnic, how should they sort themselves into a line? 1 line of 100? 2 lines of 50? 

The Doorbell Rang

Pat Hutchins

More and more friends arrive to share Ma’s cookies. How many cookies should each person get?

The Lion’s Share

The shared meal keeps getting divided in half leaving only a crumb for the ant. So she and the other guests bake cakes for the king. Which they have to divide.

Using the illustrations, readers get to answer division and fraction questions. What fraction of the cow is blue? Fun farm math!

Fractions in Disguise

by Edward Einhorn and David Clark

This is a mystery story about finding a missing fraction — clever!

by  Dayle Ann Dodds , illustrated by  Abby Carter

The Strawberry Inn is filled with five visitors who all want a piece of one cake. How will Miss Blue solve this problem?

Learn the basic shapes with this cute introductory book.

Lia and Luis Puzzled by Ana Crespo, illustrated by Giovana Medeiros

Grandma gives the twins a puzzle they must complete to discover what the surprise is. What will it be? First, the twins will have to collaborate and use geometry and sorting to put the puzzle together. Lia and Luis are Brazilian American and the story includes words in Portuguese like the word for Grandma and yay.

by Cindy Neuschwander and Bryan Langdo

To get to the pharaoh’s burial tomb, the kids must decode the geometric hieroglyphics.

Sir Cumference and the First Round Table by

Cindy Neuschwander and Wayne Geehan

The king needs a place for his your knights to sit and discuss battle and peace plans. Luckily Sir Cumference, Lady Di of Ameter, and their son Radius can help.

by Cindy Neuschwander and Wayne Geehan

Radius must use his wits and math skills to rescue the missing king.

When a Line Bends . . . A Shape Begins

Learn about shapes in this brightly illustrated beginning circus story.

The name says it all — learn about perimeter, area, and volume with this crew of monsters.

What’s Your Angle, Pythagoras?

Pythagoras discovered through experimentation that there are mathematical principles that always stay the same — like with right triangles.

The Greedy Triangle

Marilyn Burns , illustrated by  Gordon Silveria

This triangle doesn’t just want to have three angles, he is greedy for more angles which changes his shape completely. 

To successfully journey back to earth, Captain Invincible must use his knowledge of 3D shapes.

Grandfather Tang’s Story by Ann Tonpert, illustrated by Robert Andrew Parker

Moving the tangram shapes, help narrate the story of two fox fairies.

In this Three Little Pigs math story, the pigs must learn geometric shapes and tangrams.

Alexander trades his one dollar for many coins because he misses the point of how much things are worth, placing importance on the number of monies he has more than the value. Hilarious.

Count five pennies, count two nickels, and add them up.

Grandma’s birthday is coming. Watch as Max and Ruby learn about how much things cost and what the best presents really are.

From the history of bartering things to the creation of different types of money, this is a great informational math book about money.

Little Critter needs to earn money so that he can buy a skateboard.

Interesting information about collecting coins, plus a place to start collecting.

Pigs Will Be Pigs: Fun with Math and Money by Amy Axelrod, illustrated by Sharon McGinley-Nally

David A. Adler ,  Edward Miller

Find the unknown number of creepy things by using addition, subtraction, multiplication, and division.

The Deductive Detective

This entertaining math picture book incorporates math with the mystery genre. Detective Duck needs to use his deductive reasoning to figure out which of the twelve animal bakers stole the cake from the cake contest.  He follows the clues, subtracting each suspect as he rules them out.  Until only one animal is left! Can you use your thinking skills to figure out the culprit before Detective Duck?

Frank adopts Lucky from a shelter. Together, they have fun, educational adventures around the neighborhood. For example, Frank learns about math and puzzles, thinking about how much hair Lucky sheds and dividing up and sharing the bed with Lucky. The author makes the duo’s learning fun and embedded throughout the day, whether it’s geography, science, or math. Love it.

One Minute Mysteries: 65 Short Mysteries You Solve With Math!

by Eric Yoder and Natalie Yoder

Real-world math brainteasers. 

by Jon Scieszka and Lane Smith

If you’ve ever been a victim of a MATH CURSE, you know how horrible it can be. Because you can break the curse. FUN and funny!

by Greg Tang and Greg Paprocki

Using real artwork, this is a math picture book where kids solve math problems and appreciate famous art.

The Book of Perfectly Perilous Math: 24 Death-Defying Challenges for Young Mathematicians

Math for All Seasons

Put on your thinking caps. Look closely at the illustrations to solve the math problems.

Find books about place value , too!

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