Decomposing fractions to show equivalence

Decomposing Fractions to Show Equivalence 

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Decomposing fractions is one of the most interesting and fun lessons to teach in 4th grade, thanks to the many games and fun activities that math teachers can enrich their lessons with.

Yet, it’s not infrequent that educators and homeschooling parents struggle with teaching this topic, especially in cases where children have gaps in foundational knowledge of fractions. After all, to be able to decompose a fraction requires an understanding of what fractions are and what parts they’re composed of.

To help out, we’ve compiled a list of tips on how to teach this topic to fourth graders. Follow these simple and engaging tips and never worry about teaching decomposing fractions again!

What Is Decomposing Fractions?

By now, fourth graders should have an idea of what a fraction is. So you could start your lesson by asking students to provide a definition of fractions. They should be able to define a fraction as a number representing equal parts of a whole.

You can also point out that fractions are composed of two parts – a denominator and a numerator. The denominator is above the division line in a given fraction and the numerator is below it.

In other words, the denominator represents the bottom number in a fraction, indicating the number of equal parts an item is divided into; whereas the numerator is the top number in a fraction, showing how many parts we have.

Once everyone is clear on what fractions are and what parts they consist of, you can explain that decomposing a fraction means dividing it into smaller parts, i.e. smaller fractions. One caveat though: by adding these smaller fractions, we must be able to obtain the initial fraction.

If you’d like to review adding fractions with your students, you can check out our article on this topic. It contains a bunch of free resources, worksheets, and activities that you could use as bell-work warm-ups for your lesson on decomposing fractions.

How to Teach Decomposing Fractions (4th Grade)


To get children to think in the direction of decomposing fractions, you can begin with an easier example with visualization. For instance, you can draw a pizza on the whiteboard and cut it into 8 slices (or even better, create a colorful pizza out of cardboard and bring it to class!)

Ask students to tell you how we can divide the pizza between two students equally. How many slices of pizza would each person get? Students should easily tell you that each person should get four slices of pizza.

Why? The answer is simple, because 4 + 4 = 8. So by decomposing the number 8, we’re dividing it into smaller parts (4 and 4) such that by adding all these smaller parts, we’ll obtain the initial number, i.e. 8.

Point out that we use the same logic in decomposing fractions. Then, ask them to express the slices that each person got in fractions. Since 8 is the number of equal parts an item is divided into and 4 shows how many parts each person obtained, we’ll get: 4⁄8(4⁄8+ 4⁄8= 8⁄8)

Ways of Decomposing Fractions (4th Grade)

Sum of Unit Fractions

Explain to students that there are several ways of decomposing fractions. The easiest method is probably breaking into unit fractions. Tell children that we’ll try to decompose the fraction from earlier, that is, 4⁄8. You can use a circle or a rectangle to first present this fraction.

Point out that a unit fraction is a fraction in which the numerator is always 1. Examples of unit fractions are 1⁄3, 1⁄9, 1⁄5, ½, etc.

Remind students that our aim in decomposing 4⁄8 is to show this quantity as a sum of its component parts. How can we break 4⁄8 into unit fractions? We can simply present the initial fraction as four times of the unit fraction 1⁄8:

1⁄8+ 1⁄8+ 1⁄8+ 1⁄8= 4⁄8

Sum of Smaller Fractions That Aren’t All Unit Fractions

Another way of decomposing a fraction is by breaking it into smaller fractions that aren’t all unit fractions, and then adding these smaller fractions together. For example, the fraction 4⁄8 can be decomposed as a sum of 1⁄8 (which is a unit fraction) and 3⁄8 (not a unit fraction):

1⁄8+3⁄8= 4⁄8

Use the above drawing again to illustrate this visually. You can shade 1⁄8 first and then shade 3⁄8 to show that the sum of these two smaller fractions does form four parts of the whole circle (or rectangle, depending on which drawing you’re using).

You can also ask students to think of any other way of decomposing this fraction, such as:

2⁄8+2⁄8= 4⁄8

Additional Resources:

You can also decide to complement your lesson by using videos in your classroom. For example, you can use this video containing step-by-step instructions on how to decompose fractions for fourth graders.

In addition, this video contains simple guidelines on the different ways of decomposing fractions, as well as this video that shows how we can decompose fractions with the help of manipulatives (blocks).

Activities to Practice Decomposing Fractions (4th Grade)

Decompose Fractions Battle

This game will help students practice decomposing fractions, by decomposing a fraction as a sum of unit fractions, as well as by decomposing a fraction as a sum of smaller fractions that aren’t all unit fractions.

To implement the ‘Decompose Fractions Battle’ in your classroom, you’ll need to print out this Interactive Notebook Worksheet (Members Only). Pair students up and hand out one copy per student.

Provide the instructions of the game to the students. Students are required to decompose a fraction into a sum of fractions with the same denominator in more than one way and be prepared to justify the decompositions they’ve made.

The student that manages to finish the fraction decompositions first, wins the game. They must then present their work in front of the class and explain why they decided to decompose the fractions the way they did.

Decompose Fractions Game

This fun online game will help your students sharpen their skills of decomposing fractions. Children can play the game individually. The only thing you’ll need is a sufficient number of devices in your classroom.

The game shows different fractions that the student must decompose as quickly as possible. The student is shown multiple boxes with smaller fractions as answers from which they can select a few, keeping in mind that the sum of these smaller fractions must equal the initial fraction.

At the end of the game, they get a final score of how many answers they answered correctly. As there are no winners or losers, students can play the game as long as they enjoy it or as long as time allows it.

Before You Leave…

If you enjoyed these tips and activities, you’ll want to check out our lesson that’s dedicated to teaching decomposing fractions to show equivalence! So if you need guidance to structure your class and teach it, sign up for our emails to receive loads of free content!

Feel free to also check out our blog – you’ll find plenty of awesome resources that you can use in your class! And if you’re ready to become a member, simply join our Math Teacher Coach community!

This article is based on:

Unit 5 – Fractions

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