## Key Concepts

- Equivalent fractions and common denominators
- Finding common denominators

### Introduction

In this chapter, we will learn about common denominators, finding equivalent fractions and finding common denominators.

## Common denominator

If two or more fractions have the same number as the denominator, then we can say that the fractions have a common denominator.

Let us understand the common denominator in detail:

**In this pizza, there are 4 slices. Thus, it is represented ****as 1, that is, a whole.**

**If we take away one slice, we have 3 out of 4 slices ****remaining.**

**If we take away two slice, we have 2 out of 4 slices remaining.**

**If we take away three slices, we have 1 out of 4 slices, ****remaining.**

In the above examples, we can understand that the same number is used as denominator.

### Equivalent fractions and common denominators

Let us learn how to estimate the sum of two fractions.

**Example 1: **

Julie planted two 1-acre gardens. One had three sections of flowers, and the other had four sections of flowers. She plans to divide both gardens into more sections in order that they need an equivalent number of equal-sized sections. How many sections will each garden have?

**Solution:**

If you represent the gardens with pictures, they will be like,

*Garden 1* *Garden 2*

*Divide each* 1/3 *into fourths*

*Divide each* 1/4* into thirds*

Each of the wholes will be divided into the same size parts, twelfths.

**Garden 1**

**Garden 2**

**So, both garden will have 12 sections.**

### Finding common denominators

Let us learn how to determine a common denominator?

**Example 1: **

- Determine a common denominator for 2/3 and 1/2.

- Determine equivalent fractions for 2/3 and 1/2 using the common denominator from
*a*).

**Solution:**

**Method 1: Use Paper Folding or Diagrams**

**a) **Divide a rectangle into 3 equal parts. Either fold a piece of paper or draw a rectangle.

Fold the paper or divide the rectangle into 2 equal parts the other way.

There are 6 parts in the rectangle.

A common denominator for 2/3 and 1/2 is 6.

**b)** Shade 2/3 of the rectangle red.

4 of the 6 parts are red.

2/3 = 4/6

Turn the paper over, or draw another rectangle and divide it as in step *a*).

Shade 1/2 of this rectangle blue.

3 of the 6 parts are blue.

1/2 = 3/6

**Method 2: Use multiples**

**a) **The denominator of 1/2 is 2.

**Multiples **of 2 are 2, 4, **6**, 8, 10, 12, …

The denominator of 2/3 is 3.

Multiples of 3 are 3, **6**, 9, 12, 15, …

The first multiple divisible by both 2 and 3 is 6.

A common denominator is 6.

**b) **Write equivalent fractions using 6 as the denominator.

To determine equivalent fractions, multiply the numerator and denominator by the same number. This process does not change the value of the fraction.

## Exercise

- Ian says, “A common denominator for and 3 is 12”, Mike says,“ agree with lan or Mike? Why?
- Tina wanted to find a common denominator and equivalent fractions for 2 and 2. This is

what she did

a) Was she correct? If not, what was her error?

b) Draw diagrams to show what she should have done.

- Use multiples to find a common denominator for the fractions 2,2, and 2?
- Use the folded papers shown to determine a common denominator and equivalent fractions for the given pair of fractions.

- Use the folded papers shown to determine a common denominator and equivalent fractions for the given pair of fractions.

- Look at the diagrams to determine a common denominator and equivalent fractions for the given pair of fractions

- Look at the diagrams to determine a common denominator and equivalent fractions for

the given pair of fractions.

- Fill in the blanks to make equivalent fractions.
- 1/4 = ?/8 =?/12 = ?/16 = ?/20 = ?/24 = ?/28
- Fill in the blanks to make equivalent fractions
- 24/56 = 12/? = 6/? = 3/? = 48/? = 9/?
- A cookie recipe calls for > cup of brown sugar and = cup of walnuts. Find the least

common denominator of the fractions used in the recipe.

### Concept Map

### What have we learned

- Understand common denominator
- Find equivalent fractions
- Find common denominator for two or more fractions