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# Add Fractions with Unlike Denominators

Sep 28, 2022

## 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

= 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.

2/5 + 1/10

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

3/5-3/10

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.
• 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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