## Key Concepts

- Finding least common multiple/Make the denominator same
- Add fractions with unlike denominators
- Subtracting fractions with unlike denominators(By finding least common multiple/Make the denominator same)

### Introduction:

In this chapter, we will learn about making the denominator of two fractions the same by finding the least common multiple and add fractions with unlike denominators.

**Example 1:**

Rose bought two copper pipes. The length of one pipe is 1/3 yard and the other is 1/6 yard. She joined both pipes to repair a water line in her house. What is the total length of the pipe? Solve this problem any way you choose. Write the answer in the lowest terms.

**Solution:**

Let us add the fractions by drawing a diagram,

To add, you need to use parts that are the same size.

**1/3 + 1/6 = 3/6**

Write the answer in the lowest terms.

**3/6 = 1/2**

### By Finding Least Common Multiple/Make the Denominator Same

**Example 1:**

Find the least common multiple for the fractions 1/3 + 1/6.

**Solution:**

The denominator of 1/6 is 3.

Multiples of 3 are 3, 6, 9, 12, …

The denominator of 1/6 is 6.

Multiples of 6 are 6, 12, 18, 24, …

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

### Add Fractions with Unlike Denominators

**Example 1:**

Add the fractions 1/3 + 1/6. Write the answer in the lowest terms.

**Solution:**

Since 6 is the common denominator of the fractions 1/3 and 1/6, write equivalent fractions with 6 as the denominator.

1/3+1/6 = 2/6+1/6

= 2+1/6 **Add the numerators**

= 3/6

= 1/2 **Write the answer in lowest terms**

## Subtract Fractions with Unlike Denominators

### Introduction

In this chapter, we will learn about the subtraction of fractions with unlike denominators.

### Subtracting Fractions with Unlike Denominators (By Finding Least Common Multiple/Make the Denominator Same)

**Example 1:**

Subtract 1/2 – 2/5

### Solution:

The denominator of is 2.

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

The denominator of 2/5 is 5.

Multiples of 5 are 5, **10**, 15, 20, …

The first multiple divisible by both 2 and 5 is 10.

A common denominator is 10.

Write equivalent fractions with 10 as the denominator.

1/2 – 2/5 = 5/10 – 4/10

=5-4/10 **Subtract the numerators**

=1/10

## Exercise

- Look at the diagram given, write an addition statement and then add.

- Look at the diagram given, write an addition statement and then add.

- Find the least common multiple of 2 and 3.
- Find the least common multiple of 6 and 4.
- Add the following fractions and write your answer in the lowest terms.

2/5 + 1/10

- Subtract the following fractions and write your answer in the lowest terms.

3/5-3/10

- Add the following fractions and write your answer in the lowest terms.

5/8+1/4

- Subtract the following fractions and write your answer in the lowest terms.

5/8-1/4

- The sum of each row, column, and diagonal in this magic square must equal 1. Copy the square and fill in the blanks.

5/12 | ||

7/12 | 1/12 | |

1/4 |

- John was leading in a swimming race by 5/8 of a length. He won the race by 1/2 a length. By how much did the second-place swimmer catch up by the end of the race?

### What have we Learned

- Finding least common multiple and make the denominators of two or more fractions same.
- Addition and subtraction of fractions with unlike denominators

### Concept Map

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