Add Fractions with Unlike Denominators

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