simplifying fractions problem solving

Equivalent Fractions Lesson

Methods to simplify fraction, general steps.

Let's examine the fraction 2/4.

If you look at the picture above, you can see that the simplified fraction ½ and the original fraction (2/4) are equal. They both take up the same amount of the pizza.

Practice how to Simplify Fraction

Remember the first step in how to simplify fraction is to identify the largest number that divides both the numerator (3) and the denominator (6).

3 is what we want because it evenly divides both 3 and 6. The final simplified fraction is ½. (see picture for visual)

Remember the first thing to do is identify the largest number that divides both the numerator (6) and the denominator (9).

Remember the first step in how to simplify fraction is to identify the largest number that divides both the numerator (2) and the denominator (10).

Remember the first step in how to simplify fraction is to identify the largest number that divides both the numerator (3) and the denominator (15).

Remember the first step in how to simplify fraction is to identify the largest number that divides both the numerator (6) and the denominator (8).

Remember the first thing to do is identify the largest number that divides both the numerator (12) and the denominator (15).

Remember the first step in how to simplify fraction is to identify the largest number that divides both the numerator (12) and the denominator (28).

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Simplifying Fractions Worksheet

Welcome to our Simplifying Fractions Worksheet page. Here you will find a wide range of graded printable fraction worksheets which will help your child to practice converting fractions to their simplest form.

Try our NEW quick quiz at the bottom of this page to test your skills online.

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Simplifying Fractions Worksheet page

We have a selection of worksheets designed to help your child understand how to simplify fractions.

The sheets are graded so that the easier ones are at the top.

The first sheet in the section is supported and the highest common factor is already provided.

The last two sheets are the hardest and is a great challenge for more able mathematicians.

Using these sheets will help your child to:

• practice simplifying a range of fractions;
• apply their times tables knowledge.

Quicklinks to...

How to simplify fractions, simplifying fractions worksheets.

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Simplifying Fractions Online Quiz

Simplifying fractions is also sometimes called reducing fractions to their simplest (or lowest) form.

This involves dividing both the numerator and denominator by a common factor to reduce the fraction to the equivalent fraction with the smallest possible numerator and denominator.

The printable fraction page below contains more support, examples and practice about simplifying fractions.

The Simplifying Fractions calculator will also show you how worked examples of how to simplify a fraction if you are really stuck!

• How to Simplify Fractions support page
• Simplify Fractions Practice Zone

• Simplify Fraction Calculator

These sheets get progressively harder, with sheet 1 being the easiest and sheet 6 being the hardest.

Sheet 7 involves simplifying fractions with negative numerators, negative denominators or both.

• Simplifying Fractions Sheet 1 (supported)
• PDF version
• Simplifying Fractions Sheet 2
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• Simplifying Fractions Sheet 5
• Simplifying Fractions Sheet 6 (harder)
• Simplifying Fractions Sheet 7 (includes negative numbers)

Simplifying Fractions Walkthrough Video

This short video walkthrough shows several problems from our Simplifying Fractions Worksheet 2 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

More Recommended Math Resources

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Simplifying Fractions

To simplify a fraction, divide the top and bottom by the highest number that can divide into both numbers exactly.

Simplifying (or reducing ) fractions means to make the fraction as simple as possible.

Why say four-eighths ( 4 8 ) when we really mean half ( 1 2 ) ?

How do I Simplify a Fraction ?

There are two ways to simplify a fraction:

Try to exactly divide (only whole number answers) both the top and bottom of the fraction by 2, 3, 5, 7 ,... etc, until we can't go any further.

Example: Simplify the fraction 24 108 :

That is as far as we can go. The fraction simplifies to 2 9

Example: Simplify the fraction 10 35 :

Dividing by 2 doesn't work because 35 can't be exactly divided by 2 (35/2 = 17½)

Likewise we can't divide exactly by 3 (10/3 = 3 1 3 and also 35/3=11 2 3 )

No need to check 4 (we checked 2 already, and 4 is just 2×2).

But 5 does work!

That is as far as we can go. The fraction simplifies to 2 7

Notice that after checking 2 we didn't need to check 4 (4 is 2×2)?

We also don't need to check 6 when we have checked 2 and 3 (6 is 2x3).

In fact, when checking from smallest to largest we use prime numbers :

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, ...

Divide both the top and bottom of the fraction by the Greatest Common Factor (you have to work it out first!).

Example: Simplify the fraction 8 12 :

The largest number that goes exactly into both 8 and 12 is 4, so the Greatest Common Factor is 4 .

Divide both top and bottom by 4:

That is as far as we can go. The fraction simplifies to 2 3

Simplifying Fractions Automatically

OK, there is a third method, use this tool:

Fractions on the Number Line

Also ... see an animation of Fractions on the Number Line where you can see many common fractions and their simpler version.

We also have a chart of fractions with the simplest fraction highlighted.

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• Fractions - converting

Simplifying fractions

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Rewriting fractions in their simplest form

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Simplifying Fractions

Simplifying a fraction means reducing a fraction to its simplest form. A fraction is in its simplest form if its numerator and denominator have no common factors other than 1. An important step that we do while we solve fraction problems is to reduce them to the simplest form. Though we simplify them, the value of the fraction is going to remain unchanged. This means the simplified fraction and the actual fraction form a pair of equivalent fractions. In this article, we will learn a few easy ways of simplifying fractions.

How to Simplify Fractions?

Simplifying a fraction implies reducing a fraction to its lowest form. A fraction is in its simplest form if its numerator and denominator are co-prime or have no common factors except 1. The simplest form of a fraction is equivalent to the given fraction. For example, the fraction 3/4 is in the simplest form because 3 and 4 have no common factor except 1. Let's try simplifying the fraction 8/24 step by step.

Simplifying Fractions Step by Step

Here is a step-by-step process for you to understand the process of simplifying a fraction. Consider the fraction, 8/24 and follow the steps mention below to understand how to simplify the fraction 8/24.

• Step 1: Write the factors of numerator and denominator.

The factors of 8 and 24 are

• Factors of 8 : 1, 2, 4, and 8
• Factors of 24 : 1, 2, 3, 4, 6, 8, 12, and 24

Step 2: Determine the common factors of numerator and denominator. The common factors of 8 and 24 are 1, 2, 4, and 8.

Step 3: Divide the numerator and denominator by the common factors until they have no common factor except 1. The fraction so obtained is in the simplest form. Let's start dividing by 2, then 8/24 = (8/2)/(24/2) = 4/12. We will continue to divide by 2 until we can't go any further. So, we have (4/2)/(12/2) = 2/6 = (2/2)/(6/2) = 1/3.

Thus, 1/3 is the simplest form of the fraction 8/24.

Now, let us also discuss an easy way to simplify fractions. We can make a complicated fraction as simple as possible by following the process of simplifying the fraction. In order to find the simplified form of a fraction, take a look at an easy way to simplify the fraction. Here we have three-sixths of a pizza.

Why say three-sixths when you really mean half?

Simplifying a fraction means making a fraction as simple as possible. A quick way to find the simplest form of a fraction is to work out with the highest common factor. Follow the steps given below to learn the shortest way.

• Step 2: Determine the highest common factor of numerator and denominator.
• Step 3: Divide the numerator and denominator by their highest common factor (HCF). The fraction so obtained is in the simplest form.

Let's get back to the same problem of simplifying the fraction 8/24. The highest common factor of 8 and 24 is 8. Dividing the numerator 8 and the denominator 24 by 8 will directly give us the simplest form of the fraction, that is, 1/3. So, the shortest way to break down a fraction into its simplest form is to divide the numerator and denominator by its highest common factor.

Simplifying Fractions with Variables

You can also simplify the fraction containing variables in the numerator and denominator. Use the expanded form of each term in the numerator and denominator to make it easy for you to simplify the fraction with variables.

Let's simply the fraction (x 2 y)/(xy).

Express the numerator and denominator as the product of variables.

(x 2 y)/(xy) = (x × x × y)/(x × y)

Cancel out the common variables.

(x 2 y)/(xy) = (x × x × y)/(x × y) = x

We hope simplifying fractions with variables have been easy for you.

Simplifying Fractions with Exponents

You can simplify the fraction containing exponents in the numerator and denominator. Use the expanded form of exponents in the numerator and denominator to make it easy for you to simplify the fraction with exponents. To make a number easy to read, we sometimes make use of exponents . Suppose we have the fraction 3 5 /3 2 . We will express the numerator and denominator as the product of numbers and then cancel out the common numbers.

3 5 /3 2 = (3 × 3 × 3 × 3 × 3)/(3 × 3) = 3 × 3 × 3 = 27

So, you finally learned the way of simplifying fractions with exponents.

Simplifying Mixed Fractions

A mixed fraction is a mixture of a whole and a proper fraction . In order to simplify a mixed fraction , you need to simplify the fractional part only. For that write the numerator and the denominator in factored form and cancel out the common factors. The resultant will be the new numerator and the new denominator of the mixed fraction.

For example: Simplify the mixed fraction \(3\dfrac{4}{10}\).

To simplify the mixed fraction \(3\dfrac{4}{10}\), simplify only the fractional part. Write the numerator and denominator of the fractional part in factored form and cancel out the common factors.

4/10 = (2 × 2)/(2 × 5) = 2/5

Therefore, the mixed fraction \(3\dfrac{4}{10}\) can be simplified as \(3\dfrac{2}{5}\).

Simplifying Improper Fractions

Improper fractions are those in which the numerator is greater than or equal to the denominator. To simplify improper fractions we need to convert them to mixed fractions, and for that, we need to divide the numerator by the denominator. Then, we write it in the mixed number form by placing the quotient as the whole number, the remainder as the numerator, and the divisor as the denominator. Let us go through the following example to understand this better.

For example, to simplify the improper fraction 11/4, we need to divide 11 by 4 and get the values of quotient and remainder after performing division. When we divide 11/4, we get 2 as the quotient and 3 as the remainder. Therefore, the simplified form of the improper fraction 11/4 is \(2\dfrac{3}{4}\).

Related Articles

Check these interesting articles related to simplifying fractions.

• Reduce Fractions
• Simplify Fractions Calculator
• Reducing Fractions Worksheets

Simplifying Fractions Examples

Example 1: Sally loves growing flowers in her garden. Can you tell which flowers she grows the most? Express the part of those flowers in the form of the simplest fraction.

The large area of the garden is filled with red flowers. So, Sally loves to grow red flowers the most. Red flowers cover 8/12 of her garden. Let's express the fraction 8/12 in its simplest form using the HCF method. Factors of 8: 1, 2, 4, and 8. And, factors of 12: 1, 2, 3, 4, 6, and 12. The highest common factor of 8 and 12 is 4, so divide 8 and 12 by 4, i.e. 8/12 = (8 ÷ 4)/(12 ÷ 4) = 2/3. Since 2 and 3 have no common factors except 1, 2/3 is the simplest form of 8/12. So, Sally loves growing red flowers the most. It is represented as 2/3.

Example 2: Jolly is playing with her magic disc. The disc is divided into 16 equal parts as shown. What part of the disc is colored blue? Can you express this fraction in the simplest form?

The fraction representing the blue shaded region in the disc is 8/16. Let's find the highest common factor of 8 and 16. Factors of 8: 1, 2, 4, and 8, and factors of 16: 1, 2, 4, 8, and 16. We observe the highest common factor of 8 and 16 is 8. For simplifying the fraction, let's divide the numerator and the denominator of 8/16 by the highest common factor, that is (8/8)/(16/8) = 1/2. This means half of the disc is colored blue. So, the simplest form of 8/16 is 1/2.

Example 3: Find the simplest form of the fraction 11/33.

Let us use the HCF method of simplifying fractions to solve this question. The highest common factor of 11 and 33 is 11. So, divide both numerator and denominator by 11, i.e 11/33 = (11 ÷ 11)/(33 ÷ 11) = 1/3. Therefore, the simplest form of 11/33 is 1/3.

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FAQs on Simplifying Fractions

What does simplifying fractions mean.

Simplifying fractions mean reducing the fraction in its lowest form. It helps us to do calculations involving fractions much easily. For an instance, it is easier to add 1/2 and 1/2 as compared to 2/4 + 4/8.

What is the Rule for Simplifying Fractions?

The rule of simplifying fractions is to cancel out the common factors in the numerator and the denominator of the given fraction. In other words, we have to make sure that the numerator and denominator should be co-prime numbers .

What are the Steps in Simplifying Fractions?

Follow the steps mentioned below to reduce a fraction to its simplest form:

• Find the highest common factor of the numerator and denominator.
• Divide the numerator and denominator by the highest common factor .

The fraction so obtained is in the simplest form.

How do you Simplify Large Fractions?

Large fractions can be simplified by dividing the numerator and denominator by the common prime factors to reduce it to the simplest form.

How to Teach Simplifying Fractions?

Simplifying fractions usually come in grade 5 or 6. To teach simplifying fractions, follow the points given below:

• Allow learners to work on hands-on activities including rectangular or circular fraction models to arrive at an understanding that 2/4 is the same as 1/2.
• Use real-life examples of simplifying fractions.
• Use simplifying fractions worksheets .

How to Explain Simplifying Fractions?

A fraction is said to be in the simplest form when there is no common factor of numerator and denominator other than 1. For example, 11/23 is a simplified fraction as 11 and 23 do not have any common factors .

How to Convert an Improper Fraction to its Simplified Form?

Divide the numerator by denominator to obtain quotient and remainder . Then, the mixed fraction or the simplified fraction can be written as \(\text{Quotient}\dfrac{\text{Remainder}}{\text{Divisor}}\).

How are Fractions Reduced to their Simplified Form?

To reduce a fraction into its simplest form, divide the numerator and denominator by their highest common factor.

What is the Easiest way to Simplifying Fractions?

One of the quickest ways to reduce a fraction to its simplest form is to divide the numerator and denominator of the fraction by their highest common factor.

Equivalent and Simplifying Fractions Practice Questions

Click here for questions, click here for answers, gcse revision cards.

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Simplifying Fractions Worksheets

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This collection of simplifying fractions worksheets includes exercises on simplifying proper fractions, improper fractions, and mixed numbers, as well as using the GCF and more. Refer to the included answer key for quick assistance. Download these free worksheets for essential practice.

Simplifying Fractions Using Models

Examine each visual model in this pdf resource and write the simplified fractions. The diagram on the right illustrates the simplified fraction: shaded parts indicate the numerator, and total parts represent the denominator.

Simplifying Fractions | Word Problems

Apply your fraction simplification skills to solve real-world problems in this section of simplifying fractions worksheets. Understand each scenario and simplify the fractions involved in every problem.

Simplifying Fractions Using GCF Method

Simplify the fractions by finding the greatest common factor (GCF) of the numerator and denominator, and dividing both by the GCF. This results in a fraction equivalent to the original but in its lowest terms.

Simplifying Proper Fractions | Easy

Reduce the proper fractions to their lowest terms to complete this easy-level simplifying proper fractions worksheet set. Break down both numbers into their prime factors and cancel common factors.

Simplifying Proper Fractions | Moderate

Simplifying fractions makes them easier to understand and work with. This moderately challenging exercise features two-digit numbers that require multiple steps of canceling common factors.

Simplifying Improper Fractions

Regardless of whether a fraction is proper or improper, the simplification process remains the same. Be aware of the fact that a simplified improper fraction is best expressed as a mixed number.

Simplifying Mixed Numbers

Simplify the fractions in mixed numbers with ease! Cancel out the common factors in the fractional part and rewrite them in their simplest form; the whole number part remains unchanged.

Simplifying Fractions | Mixed Review

Check your skills with these printable revision sheets designed for 5th grade and 6th grade learners. Practice the process of simplifying both proper and improper fractions to their lowest terms repeatedly.

Related Printable Worksheets

▶ Equivalent Fractions

▶ Adding Fractions

▶ Subtracting Fractions

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Calcworkshop

Simplify Fractions Easy How-To w/ 8 Step-by-Step Examples!

// Last Updated: November 8, 2020 - Watch Video //

How to simplify fractions?

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

Great question!

And in today’s math lesson, you’re going learn two different methods to do just that.

The word simplify means to make something easier to do or understand.

So, reducing or simplifying fractions means we make the fraction as simple as possible.

We do this by dividing the numerator and the denominator by the largest number that can divide into both numbers exactly. In other words, we divide the top and bottom by the biggest number they have in common.

Note that the numerator and denominator are called “terms” of a fraction. So, if we simplify a fraction, we reduce the fraction to the simplest terms.

For example, notice the three rectangles below where the left-hand side of each rectangle is shaded and the fraction that results represents the shaded part out of the whole rectangle.

Three Equivalent Fractions — Visual

All three images represent the same part to whole , which indicates that each resulting fraction is equivalent to the other. But what is important to recognize is that while they are equal, only one fraction is in simplest terms — 1/2.

And just as this example indicates, our goal is to transform a fraction by creating an equivalent fraction whose terms no longer have any common factors as noted by Lumen Learning .

So, how do we reduce fractions?

There are two methods:

• Guess and Check
• Greatest Common Factor (GCF)

Guess And Check Method

The guess and check method is when we choose a number we know divides evenly into both the numerator and denominator, but we aren’t sure if it’s the largest. So, we may need to continue to reduce the fraction further in necessary.

Worked Example #1

Let’s look at a specific problem.

Suppose we want the simplified fraction of 24/36.

Using the “guess and check method,” we may notice that 24 and 36 are both divisible by 3.

And after reducsing both terms and get 8/12.

Finding Equivalent Fractions — Example

Namely, they are both divisible by 4. This means we need to simplify further.

Notice that this new fraction of 2/3 is fully simplified because neither the numerator nor the denominator has any factors left in common.

Simplifying Fraction — Example

Whereas the greatest common factor (GCF) method will always give us the largest number for which we should divide.

Worked Example #2

Now, let’s work the same example using the GCF method.

First, let’s use factor trees to find the prime factorization of both the numerator and denominator.

And then we identify the GCF from the prime factorization. Remember, when we find the GCF from a list of prime factors, we choose the fewest of what is common.

GCF Using Prime Factorization

This means that when reducing the fraction 24/36, we should divide both terms by 12, as this is the GCF for both terms.

Reduce Fractions To Lowest Term

Worksheet (PDF) — Hands on Practice

Put that pencil to paper in these easy to follow worksheets — test your knowledge!

Simplifying Fractions — Practice Problems Simplifying Fractions — Step-by-Step Solutions

Final Thoughts

Both methods are perfectly acceptable, and it comes down to personal preference as to which technique you wish to employ.

It is apparent that if your “guess” is also the GCF, you will simplify your fraction fast, as the GCF will always yield the lowest possible reduction.

Throughout this lesson, we will look at numerous examples of how to reduce fractions to simplest form as well as some applications problems where we will first create a fraction and then reduce it to the lowest terms.

Let’s jump right in!

Video Tutorial — Full Lesson w/ Detailed Examples

• Introduction to Video: Simplifying Fractions
• 00:00:34 – How do we simplify fractions?
• 00:11:29 – Reduce each fraction to simplest terms (Examples #1-6)
• 00:25:34 – Write the fraction from the given table and reduce your answer (Examples #7-8)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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How to Simplify Fractions? (+FREE Worksheet!)

Simplifying fractions means making the fractions as simple as possible. You can simplify fractions in a few simple steps. In this post, you will learn how to simplify fractions. So join us.

First of all, it is good to know that in simplifying fractions, the actual value of the fraction will not change.

Each fraction consists of two numbers. The number at the top of the fraction is called the numerator, and the number at the bottom of the fraction is called the denominator.

But how can you know if the fraction is as simple as possible? When a fraction is in its simplest form, its numerator and denominator can no longer be divided by the same whole number except \(1\).

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Related topics.

• How to Add and Subtract Fractions
• How to Multiply and Divide Fractions
• How to Add Mixed Numbers
• How to Multiply Mixed Numbers
• How to Divide Mixed Numbers

Step-by-step guide to Simplify Fractions

• Step 1: First, find the common factors of the numerator and denominator. Evenly divide both the top and bottom of the fraction by the common factors \(2, 3, 5, 7\), … etc.
• Step 2: You should divide the numerator and denominator by the common factors until they no longer be divided by the same whole number except \(1\). In this case, the fraction is as simple as possible.

Simplifying Fractions – Example 1:

Simplify . \( \frac{18}{24} \)

To simplify \(\frac{18}{24}\) , find a number that both \(18\) and \(24\) are divisible by. Both are divisible by \( 6\) . Then: \(\frac{18}{24}=\frac{18 \ \div \ 6 }{24 \ \div \ 6 }=\frac{3}{4}\)

Simplifying Fractions – Example 2:

Simplify . \( \frac{72}{90} \)

To simplify \(\frac{72}{90}\), find a number that both \(72\) and \(90\) are divisible by. Both are divisible by \(9\) and \( 18\). Then: \(\frac{72}{90}=\frac{72 \ \div 9}{ 90 \ \div \ 9 } =\frac{8}{10}\), \(8\) and \(10\) are divisible by \(2\), Then: \(\frac{8}{10}= \frac{8\ \div 2}{ 10 \ \div \ 2 }= \frac{4}{5}\) or \(\frac{72}{90}=\frac{72 \ \div 18 }{90 \ \div 18}=\frac{4}{5}\)

Simplifying Fractions – Example 3:

Simplify . \( \frac{12}{20} \)

To simplify \(\frac{12}{20}\), find a number that both \(12\) and \(20\) are divisible by. Both are divisible by \(4\). Then: \(\frac{12}{20}=\frac{12÷4}{20÷4}=\frac{3}{5}\)

Simplifying Fractions – Example 4:

Simplify . \( \frac{64}{80} \)

To simplify \(\frac{64}{80}\), find a number that both \(64\) and \(80\) are divisible by. Both are divisible by \(8\) and \(16\). Then: \(\frac{64}{80}=\frac{64÷8}{80÷8}=\frac{8}{10}\) , \(8\) and \(10\) are divisible by \(2\), then: \(\frac{8}{10}= \frac{8\ \div 2}{ 10 \ \div \ 2 } =\frac{4}{5}\) or \(\frac{64}{80}=\frac{64÷16}{80÷16}=\frac{4}{5}\)

Exercises for Simplifying Fractions

Simplify the fractions..

• \(\color{blue}{\frac{22}{36}}\)
• \(\color{blue}{\frac{8}{10}}\)
• \(\color{blue}{\frac{12}{18}}\)
• \(\color{blue}{\frac{6}{8}}\)
• \(\color{blue}{\frac{13}{39}}\)
• \(\color{blue}{\frac{5}{20}}\)

Download the Simplifying Fractions Worksheet

• \(\color{blue}{\frac{11}{18}}\)
• \(\color{blue}{\frac{4}{5}}\)
• \(\color{blue}{\frac{2}{3}}\)
• \(\color{blue}{\frac{3}{4}}\)
• \(\color{blue}{\frac{1}{3}}\)
• \(\color{blue}{\frac{1}{4}}\)

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Simplifying Fractions

Reduce those clunky fractions down to something more manageable. 

Author Taylor Hartley

Expert Reviewer Jill Padfield

Published: August 24, 2023

• Key takeaways
• Simplifying fractions makes them easier to work with – Reducing fractions makes them easier to visualize and work into other math problems.
• It’s all about the GCF – The greatest common factor (GCF) of both the numerator and denominator will help you figure out if the fraction is in its simplest form.
• 1 factor to rule them all – You’ll know that you have a simplified fraction if the GCF of both the numerator and the denominator is 1.

Table of contents

How to simplify fractions

How to convert improper fractions to mixed numbers, how to simplify mixed fractions, let’s practice together, practice problems.

In your adventures with math, you might find yourself with a fraction like 2967/5934. Not only is it a bit of a mouthful, but it’s also hard to work with in additional math problems. This is where simplifying fractions comes in handy. Through the simplification process, something as big and clunky as 2967/5934 can be reduced down to 1/2! Now that is a much easier number to play with. 

An important thing to keep in mind is that simplifying fractions does not change their value. It may seem like turning a bunch of big numbers like 2967/5934 into the seemingly smaller 1/2 would mean the fraction’s value is smaller, but that’s not the case at all. In both fractions, the top number (the numerator) is exactly half of the bottom number (the denominator). Both fractions represent the value of one half. All we’ve done is make the way the value is represented more manageable.   

It may also help to visualize this a bit. Think about slicing up a birthday cake. You can slice the cake into 100 pieces or 4 pieces, but you still have the same amount of cake.  That is why 25 pieces of the 100 piece cake is the exact same as 1 piece of the 4 piece cake. One big piece of cake is easier to eat than 25 tiny pieces, right? That’s why simplifying fractions is so helpful.

By the end of the simplification process, the goal is that the greatest common factor (between the numerator and the denominator) is 1. Remember, a factor is a perfectly divisible number. This means you can divide a factor by another number and have no remainders . For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. This is because you can perfectly divide 12 by all those numbers. 

Therefore, in order to simplify a fraction, you will need to find the factors of both the numerator and the denominator. 

Find the factors

Let’s work with the fraction 12/36. 

To begin simplifying, we need to find the factors of both the numerator (12) and the denominator (36). The simplest way to do this is to start with 1 and begin dividing the original number by larger and larger numbers until the quotient (the answer to the division problem) is 1. Any quotients you get that are whole numbers mean that the divisor (the number you are currently dividing by) is a factor. 

For 12, we can start by dividing by 1, which gets us a quotient of 12. All numbers are divisible by 1, so that’s a freebie. We then move on to 2, which gets us 6. This is a whole number, so 2 is a factor. And so on. 

When you finish this process for both 12 and 36, you will find the following factors: 

12 has factors of 1, 2, 3, 4, 6, and 12

36 has factors of 1, 2, 3, 4, 6, 9, 12, 18, and 36

When you look at these two lists of factors, you can see that, for both 12 and 36, the greatest common factor (GCF) is 12. Keep this GCF handy because you’ll need it for the next step!

Finding factors can take a little bit of time. Luckily, there are a few tricks to speed up some parts of the process.. 

• All numbers are divisible by 1 and itself
• If the number is even, then it is divisible by 2
• If you add up each digit and that number is divisible by 3 (for example 18: 1 + 8 = 9), then the number is divisible by 3. 
• If the ones digit is a 0 or a 5, then it is divisible by 5.

Divide by the GCF

Now that you have the GCF, which is 12 in this case, all you need to do is divide the numerator and the denominator by that number. Remember, we are trying to simplify the fraction 12/36.

This leaves us with the simplified fraction of 1/3! 

Check your work by factoring out the numerator and denominator again! This makes sure that they do not have any common factors larger than 1. 

When the numerator is larger than the denominator, you have an improper fraction on your hands. Let’s learn how to clean that up! 

For example, we might have the fraction 23/6. 23 is obviously larger than 6, so we need to reduce it. 

The first step is to divide the numerator by the denominator. This is 23 ÷ 6, which gets us 3 with a remainder of 5. If you need help getting this answer, make sure to check out our how-to guide on division. 

Next, you take the whole number quotient (3) and put it in front of the fraction. You then take the remainder (5) and put that over the original denominator (6). This gives you the mixed fraction of 3 5/6.

Fortunately, simplifying mixed fractions is nice and simple. You can basically ignore the whole number on the left and simplify the fraction as explained before. Let’s take a look at an example.

We have the mixed fraction 2 15/45, which clearly needs to be simplified. Now, how do we do this? Let’s start by putting that 2 to the side and factoring out the numerator and denominator of the remaining fraction.

15 has factors of 1, 3, 5, and 15

45 has factors of 1, 3, 5, 9, 15, and 45

The GCF between those two sets is 15, so we will divide both the numerator and the denominator by 15.

Now we bring the whole number back in, and, voila, we have our simplified mixed fraction: 2 1/3!

1. Simplify the fraction 12/24

When we factor out both the 12 and the 24, the GCF is 12. When we divide both by 12, we get the simplified fraction of 1/2.

2. Convert the fraction 15/4 to a mixed number.

Since the numerator is greater than the denominator, this is an improper fraction. We need to first divide the numerator by the denominator, which will give us 3 with a remainder of 3. We then pop that 3 over the denominator 4 to end up with the mixed fraction of 3 3/4.

3. Convert the mixed fraction 3 1/2 into an improper fraction and then simplify.

This might seem a little tricky, but think, you just have to work in reverse. Instead of dividing numbers, multiply them! Multiply the denominator by the whole number and then add that to the numerator. That will get you 7/2. Now, check to see if there is a GCF greater than 1. Looks like the GCF of both 7 and 2 is 1. This means 7/2 is the simplest version of this improper fraction. 

Ready to give it a go?

You now have the basics needed to tackle some of the more common fraction simplification problems. Dig into the following questions and test your understanding. Remember that you can also look back at the guide if you bump into any problems.

Click to reveal the answer.

The answer is 1/5 .

The answer is 1/3 .

The answer is 3 3/8 . 

The answer is 3 .

The answer is 23/4 .

Parent Guide

The answer is 1/5 

How did we get here? 

You can go through the process of factoring. 10 ⮞ 1, 2, 5, and 10. 50 ⮞ 1, 2, 5, 10, 25, and 50. The GCF is 10, and when you divide both the numerator and denominator, you get 1/5. 

The answer is 1/3

Go through the process of factoring. 21 ⮞ 1, 3, 7, and 21. 63 ⮞ 1, 3, 7, 9, 21, and 63. The GCF is 21, and when you divide both the numerator and denominator, you get 1/3. 

The answer is 3 3/8

• Start by dividing the numerator by the denominator. 27 ÷ 8 = 3 with a remainder of 3. 
• Now take the remainder and place it as the new numerator over the original denominator. This gets you 3/8. 
• Lastly, put that fraction next to the 3 you got by dividing the numerator by the denominator. You now have 3 3/8. 

The answer is 3

How did we get here?

• Start by dividing the numerator by the denominator. 33 ÷ 11 = 3.
• This gives you a whole number, so you are all done! The answer is 3.

The answer is 23/4

• Start by multiplying the whole number by the denominator. 5 X 4 = 20.
• Now add that 20 to the existing numerator. 20 + 3 = 23. 
• You now have 23/4! Double check that this is the simplest form by factoring out and looking for a GCF greater than 1. Since there isn’t one, this fraction is as simple as possible while still being an improper fraction.

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FAQs about math strategies for kids

We understand that diving into new information can sometimes be overwhelming, and questions often arise. That’s why we’ve meticulously crafted these FAQs, based on real questions from students and parents. We’ve got you covered!

Look for the greatest common factor (GCF) of the numerator and denominator and then divide both by that number. 

Ignore the whole number and just focus on the fraction. Go through the same process of simplification that you’d use on a regular fraction.

Use some tricks to reduce the numbers into more manageable options. If both numbers are even, you can go ahead and divide by 2. If the digits in each number add up to a multiple of 3, you can divide both by 3. If both numbers end in 0 or 5, you can divide them both by 5. From there, you can easily factor out the smaller numbers. 

You will need to reduce the improper fraction into a mixed fraction. Divide the numerator by the denominator and set that number aside. Use any remainder as the new numerator for your fraction. Pop that above the existing denominator and then simplify the fraction, if necessary. Now you have a simplified mixed fraction. 

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Taylor Hartley

Taylor Hartley is an author and an English teacher based in Charlotte, North Carolina. When she's not writing, you can find her on the rowing machine or lost in a good novel.

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Simplifying Proper Fractions to Lowest Terms (Easier Questions) (A)

Welcome to The Simplifying Proper Fractions to Lowest Terms (Easier Questions) (A) Math Worksheet from the Fractions Worksheets Page at Math-Drills.com. This math worksheet was created or last revised on 2020-01-20 and has been viewed 615 times this week and 5,089 times this month. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math.

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Simplifying Fractions

How to simplify fractions.

A fraction is considered to be “simplified” when it is expressed in the lowest term . That means the only common divisor between the numerator and denominator is [latex]1[/latex], and no other.

METHODS IN SIMPLIFYING FRACTIONS

Method 1: Simplify Fractions by Repeated Division

• Keep dividing the numerator and denominator by a common divisor until such time that the only remaining common divisor is [latex]1[/latex].
• Although there is no right way which common divisor to use in the beginning, I would suggest using the first five ([latex]5[/latex]) prime numbers in order as possible common divisor:

[latex]2[/latex], [latex]3[/latex], [latex]5[/latex], [latex]7[/latex], [latex]11[/latex], …

Method 2: Simplify Fractions Using the Greatest Common Factor

• Find the greatest common factor (GCF) of the numerator and denominator.
• Divide the top and bottom numbers of the fraction by the GCF to reduce to the lowest term.
• You can find the GCF either by trial and error when the numbers are relatively small, or by using Prime Factorization .

This is a simple illustration showing the fraction [latex]\Large{8 \over {12}}[/latex] is being reduced to its simplest form. Can you see a pattern?

Let’s go over a few more examples with detailed explanations.

Examples of How to Simplify Fractions

Example 1 : Simplify the fraction below.

Simplify using Method 1: Repeated Division Method

It is obvious that [latex]1[/latex] is not the only common divisor between the numerator and denominator. Since they are both even numbers, they must be divisible by [latex]2[/latex].

• Divide the top and bottom by [latex]2[/latex]. Here’s what we got after doing so.

The output fraction after dividing the top and bottom by [latex]2[/latex] is [latex]\Large{2 \over 4}[/latex]. Can we stop here? Not yet! They can still be reduced by a second division of [latex]2[/latex].

• Divide again the top and bottom by [latex]2[/latex]. The answer is [latex]\Large{1 \over 2}[/latex] (as the simplest form of [latex]\Large{4 \over 8}[/latex] because the only divisor of its numerator and denominator is [latex]1[/latex].

Simplify using Method 2: Greatest Common Factor Method

In the above solution using repeated division, we have simplified [latex]\Large{4 \over 8}[/latex] by dividing its numerator and denominator two times by the number [latex]2[/latex]. But wait! Is there a shortcut? Some of you may have observed that using a common divisor of [latex]4[/latex] can directly simplify it with a single step!

In fact, the Greatest Common Factor (GCF) of this fraction is [latex]4[/latex] because it is the LARGEST number that evenly divides the numerator and denominator. Because the numbers are small, the GCF can be determined by trial and error.

Example 2 : Simplify the fraction below.

Start simplifying using the first few prime numbers ([latex]2[/latex], [latex]3[/latex], [latex]5[/latex], [latex]7[/latex], [latex]11[/latex], etc).

• Divide the top and bottom numbers by the first prime number which is [latex]2[/latex].

• We still have a common divisor! Divide the top and bottom by the next larger prime number which is [latex]3[/latex]. We should get the final answer after this step.

To find the greatest common divisor, we are going to perform prime factorization  on each number. Next, identify the common factors between them. Finally, multiply the common factors to get the required GCF that can simplify the fraction.

Since GCF = [latex]6[/latex], use this number to divide the numerator and denominator to get the answer in a single step.

Example 3 : Simplify the fraction below.

We can start testing numbers [latex]2[/latex], [latex]3[/latex], [latex]5[/latex], etc. to simplify this. But there is an obvious divisor that stands out! Since both numbers end with zero, they should be divisible by [latex]10[/latex].

Now, [latex]2[/latex] can’t divide both and so try [latex]3[/latex].

Prime factorize each number and get the product of the common factors to obtain the needed GCF.

Simplify the given fraction in one-step using the divisor GCF = [latex]30[/latex].

Example 4 : Simplify the fraction below.

Divide the numerator and denominator by a common divisor of [latex]3[/latex].

Example 5 : Simplify the fraction.

Simplify using the repeated division method.

• Divide both numerator and denominator by [latex]3[/latex], two times !

Example 6 : Simplify the fraction below.

Simplify this fraction by the greatest common factor method.

• Find the GCF by prime factoring both the numerator and denominator. Identify the common factors. Multiply them together to get the required GCF.

• After determining the GCF, divide the numerator and denominator to get the final answer.

Example 7 : Simplify the fraction below.

Find the greatest common factor between the numerator and denominator, and use this number to simplify the fraction.

• Determine the GCF

• Divide the numerator and denominator by GCF = [latex]21[/latex].

You might also like these tutorials:

• Adding and Subtracting Fractions with the Same Denominator
• Add and Subtract Fractions with Different Denominators
• Multiplying Fractions
• Dividing Fractions
• Equivalent Fractions
• Reciprocal of a Fraction

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Fraction Word Problem Worksheets

Featured here is a vast collection of fraction word problems, which require learners to simplify fractions, add like and unlike fractions; subtract like and unlike fractions; multiply and divide fractions. The fraction word problems include proper fraction, improper fraction, and mixed numbers. Solve each word problem and scroll down each printable worksheet to verify your solutions using the answer key provided. Thumb through some of these word problem worksheets for free!

Represent and Simplify the Fractions: Type 1

Presented here are the fraction pdf worksheets based on real-life scenarios. Read the basic fraction word problems, write the correct fraction and reduce your answer to the simplest form.

• Download the set

Represent and Simplify the Fractions: Type 2

Before representing in fraction, children should perform addition or subtraction to solve these fraction word problems. Write your answer in the simplest form.

Adding Fractions Word Problems Worksheets

Conjure up a picture of how adding fractions plays a significant role in our day-to-day lives with the help of the real-life scenarios and circumstances presented as word problems here.

(15 Worksheets)

Subtracting Fractions Word Problems Worksheets

Crank up your skills with this set of printable worksheets on subtracting fractions word problems presenting real-world situations that involve fraction subtraction!

Multiplying Fractions Word Problems Worksheets

This set of printables is for the ardently active children! Explore the application of fraction multiplication and mixed-number multiplication in the real world with this exhilarating practice set.

Fraction Division Word Problems Worksheets

Gift children a broad view of the real-life application of dividing fractions! Let them divide fractions by whole numbers, divide 2 fractions, divide mixed numbers, and solve the word problems here.

Related Worksheets

» Decimal Word Problems

» Ratio Word Problems

» Division Word Problems

» Math Word Problems

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Fraction word prob.

Fraction word problems

Here you will learn about fraction word problems, including solving math word problems within a real-world context involving adding fractions, subtracting fractions, multiplying fractions, and dividing fractions.

Students will first learn about fraction word problems as part of number and operations—fractions in 4 th grade.

What are fraction word problems?

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation.

To solve a fraction word problem, you must understand the context of the word problem, what the unknown information is, and what operation is needed to solve it. Fraction word problems may require addition, subtraction, multiplication, or division of fractions.

After determining what operation is needed to solve the problem, you can apply the rules of adding, subtracting, multiplying, or dividing fractions to find the solution.

For example,

Natalie is baking 2 different batches of cookies. One batch needs \cfrac{3}{4} cup of sugar and the other batch needs \cfrac{2}{4} cup of sugar. How much sugar is needed to bake both batches of cookies?

You can follow these steps to solve the problem:

Step-by-step guide: Adding and subtracting fractions

Step-by-step guide: Adding fractions

Step-by-step guide: Subtracting fractions

Step-by-step guide: Multiplying and dividing fractions

Step-by-step guide: Multiplying fractions

Step-by-step guide: Dividing fractions

Common Core State Standards

How does this relate to 4 th grade math to 6 th grade math?

• Grade 4: Number and Operations—Fractions (4.NF.B.3d) Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
• Grade 4: Number and Operations—Fractions (4.NF.B.4c) Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat \cfrac{3}{8} of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
• Grade 5: Number and Operations—Fractions (5.NF.A.2) Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result \cfrac{2}{5}+\cfrac{1}{2}=\cfrac{3}{7} by observing that \cfrac{3}{7}<\cfrac{1}{2} .
• Grade 5: Number and Operations—Fractions (5.NF.B.6) Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
• Grade 5: Number and Operations—Fractions (5.NF.B.7c) Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{1}{3} cup servings are in 2 cups of raisins?
• Grade 6: The Number System (6.NS.A.1) Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for \cfrac{2}{3} \div \cfrac{4}{5} and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that \cfrac{2}{3} \div \cfrac{4}{5}=\cfrac{8}{9} because \cfrac{3}{4} of \cfrac{8}{9} is \cfrac{2}{3}. (In general, \cfrac{a}{b} \div \cfrac{c}{d}=\cfrac{a d}{b c} \, ) How much chocolate will each person get if 3 people share \cfrac{1}{2} \: lb of chocolate equally? How many \cfrac{3}{4} cup servings are in \cfrac{2}{3} of a cup of yogurt? How wide is a rectangular strip of land with length \cfrac{3}{4} \: m and area \cfrac{1}{2} \: m^2?

[FREE] Fraction Operations Worksheet (Grade 4 to 6)

Use this quiz to check your grade 4 to 6 students’ understanding of fraction operations. 10+ questions with answers covering a range of 4th to 6th grade fraction operations topics to identify areas of strength and support!

How to solve fraction word problems

In order to solve fraction word problems:

Determine what operation is needed to solve.

Write an equation.

Solve the equation.

State your answer in a sentence.

Fraction word problem examples

Example 1: adding fractions (like denominators).

Julia ate \cfrac{3}{8} of a pizza and her brother ate \cfrac{2}{8} of the same pizza. How much of the pizza did they eat altogether?

The problem states how much pizza Julia ate and how much her brother ate. You need to find how much pizza Julia and her brother ate altogether , which means you need to add.

2 Write an equation.

3 Solve the equation.

To add fractions with like denominators, add the numerators and keep the denominators the same.

4 State your answer in a sentence.

The last step is to go back to the word problem and write a sentence to clearly say what the solution represents in the context of the problem.

Julia and her brother ate \cfrac{5}{8} of the pizza altogether.

Example 2: adding fractions (unlike denominators)

Tim ran \cfrac{5}{6} of a mile in the morning and \cfrac{1}{3} of a mile in the afternoon. How far did Tim run in total?

The problem states how far Tim ran in the morning and how far he ran in the afternoon. You need to find how far Tim ran in total , which means you need to add.

To add fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before adding.

\cfrac{5}{6}+\cfrac{1}{3}= \, ?

The least common multiple of 6 and 3 is 6, so 6 can be the common denominator.

That means \cfrac{1}{3} will need to be changed so that its denominator is 6. To do this, multiply the numerator and the denominator by 2.

\cfrac{1 \times 2}{3 \times 2}=\cfrac{2}{6}

Now you can add the fractions and simplify the answer.

\cfrac{5}{6}+\cfrac{2}{6}=\cfrac{7}{6}=1 \cfrac{1}{6}

Tim ran a total of 1 \cfrac{1}{6} miles.

Example 3: subtracting fractions (like denominators)

Pia walked \cfrac{4}{7} of a mile to the park and \cfrac{3}{7} of a mile back home. How much farther did she walk to the park than back home?

The problem states how far Pia walked to the park and how far she walked home. Since you need to find the difference ( how much farther ) between the two distances, you need to subtract.

To subtract fractions with like denominators, subtract the numerators and keep the denominators the same.

\cfrac{4}{7}-\cfrac{3}{7}=\cfrac{1}{7}

Pia walked \cfrac{1}{7} of a mile farther to the park than back home.

Example 4: subtracting fractions (unlike denominators)

Henry bought \cfrac{7}{8} pound of beef from the grocery store. He used \cfrac{1}{3} of a pound of beef to make a hamburger. How much of the beef does he have left?

The problem states how much beef Henry started with and how much he used. Since you need to find how much he has left , you need to subtract.

To subtract fractions with unlike denominators, first find a common denominator and then change the fractions accordingly before subtracting.

\cfrac{7}{8}-\cfrac{1}{3}= \, ?

The least common multiple of 8 and 3 is 24, so 24 can be the common denominator.

That means both fractions will need to be changed so that their denominator is 24.

To do this, multiply the numerator and the denominator of each fraction by the same number so that it results in a denominator of 24. This will give you an equivalent fraction for each fraction in the problem.

\begin{aligned}&\cfrac{7 \times 3}{8 \times 3}=\cfrac{21}{24} \\\\ &\cfrac{1 \times 8}{3 \times 8}=\cfrac{8}{24} \end{aligned}

Now you can subtract the fractions.

\cfrac{21}{24}-\cfrac{8}{24}=\cfrac{13}{24}

Henry has \cfrac{13}{24} of a pound of beef left.

Example 5: multiplying fractions

Andre has \cfrac{3}{4} of a candy bar left. He gives \cfrac{1}{2} of the remaining bit of the candy bar to his sister. What fraction of the whole candy bar does Andre have left now?

It could be challenging to determine the operation needed for this problem; many students may automatically assume it is subtraction since you need to find how much of the candy bar is left.

However, since you know Andre started with a fraction of the candy bar and you need to find a fraction OF a fraction, you need to multiply.

The difference here is that Andre did NOT give his sister \cfrac{1}{2} of the candy bar, but he gave her \cfrac{1}{2} of \cfrac{3}{4} of a candy bar.

To solve the word problem, you can ask, “What is \cfrac{1}{2} of \cfrac{3}{4}? ” and set up the equation accordingly. Think of the multiplication sign as meaning “of.”

\cfrac{1}{2} \times \cfrac{3}{4}= \, ?

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

\cfrac{1}{2} \times \cfrac{3}{4}=\cfrac{3}{8}

Andre gave \cfrac{1}{2} of \cfrac{3}{4} of a candy bar to his sister, which means he has \cfrac{1}{2} of \cfrac{3}{4} left. Therefore, Andre has \cfrac{3}{8} of the whole candy bar left.

Example 6: dividing fractions

Nia has \cfrac{7}{8} cup of trail mix. How many \cfrac{1}{4} cup servings can she make?

The problem states the total amount of trail mix Nia has and asks how many servings can be made from it.

To solve, you need to divide the total amount of trail mix (which is \cfrac{7}{8} cup) by the amount in each serving ( \cfrac{1}{4} cup) to find out how many servings she can make.

To divide fractions, multiply the dividend by the reciprocal of the divisor.

\begin{aligned}& \cfrac{7}{8} \div \cfrac{1}{4}= \, ? \\\\ & \downarrow \downarrow \downarrow \\\\ &\cfrac{7}{8} \times \cfrac{4}{1}=\cfrac{28}{8} \end{aligned}

You can simplify \cfrac{28}{8} to \cfrac{7}{2} and then 3 \cfrac{1}{2}.

Nia can make 3 \cfrac{1}{2} cup servings.

Teaching tips for fraction word problems

• Encourage students to look for key words to help determine the operation needed to solve the problem. For example, subtracting fractions word problems might ask students to find “how much is left” or “how much more” one fraction is than another.
• Provide students with an answer key to word problem worksheets to allow them to obtain immediate feedback on their solutions. Encourage students to attempt the problems independently first, then check their answers against the key to identify any mistakes and learn from them. This helps reinforce problem-solving skills and confidence.
• Be sure to incorporate real-world situations into your math lessons. Doing so allows students to better understand the relevance of fractions in everyday life.
• As students progress and build a strong foundational understanding of one-step fraction word problems, provide them with multi-step word problems that involve more than one operation to solve.
• Take note that students will not divide a fraction by a fraction as shown above until 6 th grade (middle school), but they will divide a unit fraction by a whole number and a whole number by a fraction in 5 th grade (elementary school), where the same mathematical rules apply to solving.
• There are many alternatives you can use in place of printable math worksheets to make practicing fraction word problems more engaging. Some examples are online math games and digital workbooks.

Easy mistakes to make

• Misinterpreting the problem Misreading or misunderstanding the word problem can lead to solving for the wrong quantity or using the wrong operation.
• Not finding common denominators When adding or subtracting fractions with unlike denominators, students may forget to find a common denominator, leading to an incorrect answer.
• Forgetting to simplify Unless a problem specifically says not to simplify, fractional answers should always be written in simplest form.

Related fractions operations lessons

• Fractions operations
• Multiplicative inverse
• Reciprocal math
• Fractions as divisions

Practice fraction word problem questions

1. Malia spent \cfrac{5}{6} of an hour studying for a math test. Then she spent \cfrac{1}{3} of an hour reading. How much longer did she spend studying for her math test than reading?

Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.

Malia spent \cfrac{5}{18} of an hour longer studying for her math test than reading.

Malia spent \cfrac{1}{2} of an hour longer reading than studying for her math test.

Malia spent 1 \cfrac{1}{6} of an hour longer studying for her math test than reading.

To find the difference between the amount of time Malia spent studying for her math test than reading, you need to subtract. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 6 as the common denominator, so \cfrac{1}{3} becomes \cfrac{3}{6}. Then you can subtract.

\cfrac{3}{6} can then be simplified to \cfrac{1}{2}.

Finally, you need to choose the answer that correctly answers the question within the context of the situation. Therefore, the correct answer is “Malia spent \cfrac{1}{2} of an hour longer studying for her math test than reading.”

2. A square garden is \cfrac{3}{4} of a meter wide and \cfrac{8}{9} of a meter long. What is its area?

The area of the garden is 1\cfrac{23}{36} square meters.

The area of the garden is \cfrac{27}{32} square meters.

The area of the garden is \cfrac{2}{3} square meters.

The perimeter of the garden is \cfrac{2}{3} meters.

To find the area of a square, you multiply the length and width. So to solve, you multiply the fractional lengths by mulitplying the numerators and multiplying the denominators.

\cfrac{24}{36} can be simplified to \cfrac{2}{3}. 

Therefore, the correct answer is “The area of the garden is \cfrac{2}{3} square meters.”

3. Zoe ate \cfrac{3}{8} of a small cake. Liam ate \cfrac{1}{8} of the same cake. How much more of the cake did Zoe eat than Liam?

Zoe ate \cfrac{3}{64} more of the cake than Liam.

Zoe ate \cfrac{1}{4} more of the cake than Liam.

Zoe ate \cfrac{1}{8} more of the cake than Liam.

Liam ate \cfrac{1}{4} more of the cake than Zoe.

To find how much more cake Zoe ate than Liam, you subtract. Since the fractions have the same denominator, you subtract the numerators and keep the denominator the same.

\cfrac{2}{8} can be simplified to \cfrac{1}{4}. 

Therefore, the correct answer is “Zoe ate \cfrac{1}{4} more of the cake than Liam.”

4. Lila poured \cfrac{11}{12} cup of pineapple and \cfrac{2}{3} cup of mango juice in a bottle. How many cups of juice did she pour into the bottle altogether?

Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.

Lila poured \cfrac{1}{4} cups of juice in the bottle altogether.

Lila poured \cfrac{11}{18} cups of juice in the bottle altogether.

Lila poured 1 \cfrac{3}{8} cups of juice in the bottle altogether.

To find the total amount of juice that Lila poured into the bottle, you need to add. Since the fractions have unlike denominators, you need to find a common denominator first.

You can use 12 as the common denominator, so \cfrac{2}{3} becomes \cfrac{8}{12}.  Then you can add.

\cfrac{19}{12} can be simplified to 1 \cfrac{7}{12}. 

Therefore, the correct answer is “Lila poured 1 \cfrac{7}{12} cups of juice in the bottle altogether.”

5. Killian used \cfrac{9}{10} of a gallon of paint to paint his living room and \cfrac{7}{10} of a gallon to paint his bedroom. How much paint did Killian use in all?

Killian used \cfrac{2}{10} gallons of paint in all.

Killian used \cfrac{1}{5} gallons of paint in all.

Killian used \cfrac{63}{100} gallons of paint in all.

Killian used 1 \cfrac{3}{5} gallons of paint in all.

To find the total amount of paint Killian used, you add the amount he used for the living room and the amount he used for the kitchen. Since the fractions have the same denominator, you add the numerators and keep the denominators the same.

\cfrac{16}{10} can be simplified to 1 \cfrac{6}{10} and then further simplified to 1 \cfrac{3}{5}.

Therefore, the correct answer is “Killian used 1 \cfrac{3}{5} gallons of paint in all.”

6. Evan pours \cfrac{4}{5} of a liter of orange juice evenly among some cups.

He put \cfrac{1}{10} of a liter into each cup. How many cups did Evan fill?

Evan filled \cfrac{2}{25} cups.

Evan filled 8 cups.

Evan filled \cfrac{9}{10} cups.

Evan filled 7 cups.

To find the number of cups Evan filled, you need to divide the total amount of orange juice by the amount being poured into each cup. To divide fractions, you mulitply the first fraction (the dividend) by the reciprocal of the second fraction (the divisor).

\cfrac{40}{5} can be simplifed to 8.

Therefore, the correct answer is “Evan filled 8 cups.”

Fraction word problems FAQs

Fraction word problems are math word problems involving fractions that require students to use problem-solving skills within the context of a real-world situation. Fraction word problems may involve addition, subtraction, multiplication, or division of fractions.

To solve fraction word problems, first you need to determine the operation. Then you can write an equation and solve the equation based on the arithmetic rules for that operation.

Fraction word problems and decimal word problems are similar because they both involve solving math problems within real-world contexts. Both types of problems require understanding the problem, determining the operation needed to solve it (addition, subtraction, multiplication, division), and solving it based on the arithmetic rules for that operation.

The next lessons are

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Word Problems with Fractions

Today we are going to look at some examples of word problems with fractions.

Although they may seem more difficult, in reality, word problems involving fractions are just as easy as those involving whole numbers. The only thing we have to do is:

• Read the problem carefully.
• Think about what it is asking us to do.
• Think about the information we need.
• Simplify, if necessary.
• Think about whether our solution makes sense (in order to check it).

As you can see, the only difference in fraction word problems is step 5 (simplify) .

There are some word problems which, depending on the information provided, we should express as a fraction.  For example:

In my fruit basket, there are 13 pieces of fruit, 5 of which are apples. 

How can we express the number of apples as a fraction?

5 – The number of apples (5) corresponds to the numerator (the number which expresses the number of parts that we wish to represent).

13 – The total number of fruits (13) corresponds to the denominator (the number which expresses the number of total possible parts).

The solution to this problem is an irreducible fraction (a fraction which cannot be simplified). Therefore, there is nothing left to do.

Word problems with fractions: involving two fractions

In these problems, we should remember how to carry out operations with fractions.

Carefully read the following problem and the steps we have taken to solve it:

What fraction of the payment has Maria spent?

We find the common denominator:

We calculate:

Word problems with fractions: involving a fraction and a whole number

Finally, we are going to look at an example of a word problem with a fraction and a whole number. Now we will have to convert all the information into a fraction with the same denominator (as we did in the example above) in order to calculate

  We convert 1 into a fraction with the same denominator:

What do you think of this post? Do you see how easy it is to solve word problems with fractions?

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Learn More:

• Understand What a Fraction Is and When It Is Used
• Fraction Word Problems: Addition, Subtraction, and Mixed Numbers
• Learn and Practice How to Subtract or Add Fractions
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• Review and Practice the Two Methods of Dividing Fractions
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41 Comments

I loved the word problem

Thanks for your help

it simplifies the teaching and learning process

Thanks for the explanation… really grateful 🙏

Thank you for such good explanations, it helped me a lot

It is really good it helped me improve my math a lot.

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Good exercises

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Hi can you not show the answer till the bottom of the page or your giving away the answer so if you solved number one problem the number one aware to the question will be there at the bottom of the page because it is way to easy if it is right there

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Hi Letlhogonolo,

Thank you very much for your comment. If you want to learn more content like this and practice elementary school math, just sign up at Smartick . You have a free trial period with no strings attached. If you have any additional questions or doubts you can write to my colleagues of the pedagogical team at [email protected] .

Best regards!

I like it… but you can level up please 🙄

Roll two dices, the first dice is the numerator, the second is the denominator, this is the first fraction. Roll both dices again and repeat the process to generate the second fraction. Write a division story problem that incorporates these two fractions.

Seems easy of the examples but when I have fraction word promblems in front of me then its still hard for me to figure it out.The examples on this site still is helpful.I will use the site that you give on here to get further practice.Thank you for the examples on here

Interesting and very helpful. I’m going to continue using this site and tell others about it too.

I really like it

Hey I am in grade five and it is super helpful for my exams thanks and maybe if you could make more it would be appriciated thx 🙂

Good efforts

i kinda like it pls write some more problems

I think it was really good how you are helping fellow students! But I think you can improve if there were more problems for solving! Thanks

Cool, it helps a lot.

it is helpfull

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• The matrices section contains commands for the arithmetic manipulation of matrices.
• The graphs section contains commands for plotting equations and inequalities.
• The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

Math Topics

More solvers.

• Add Fractions
• Simplify Fractions