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.
![Example 1:](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7174.png)
Solution:
Let us add the fractions by drawing a diagram,
![Solution:](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7175.png)
To add, you need to use parts that are the same size.
1/3 + 1/6 = 3/6
![1/3 + 1/6 = 3/6](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7176.png)
Write the answer in the lowest terms.
3/6 = 1/2
![](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7177.png)
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.
![common denominator](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7178.png)
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
![Solution:](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7180.png)
![Solution:](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7181.png)
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.
![exercise 1](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7182.png)
- Look at the diagram given, write an addition statement and then add.
![exercise 2](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7183.png)
- 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
![add fractions with unlike denominators](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-7184.png)
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