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Add Fractions With Like Denominators

Key Concepts

  • Common Denominator
  • Addition
  • Numerator
  • Standard form or simplest form
  • Mixed fractions

Introduction: 

What is a common denominator? 

The denominator of a fraction is the number on the bottom. When we say that fractions have a common denominator, it means they have the same number on the bottom. 

What is a denominator? 

The denominator of a fraction is the number of equal parts that the whole has been split into.  

For example, 

When two or more fractions have a common denominator, that means the wholes have been divided into the same number of equal pieces, and each piece is the same size. 

For example,  

Here, the whole has been divided into 8 equal parts, and each part is the same size.  

Fractions with the same denominator are called like fractions. 

For example, 1/8, 2/8 , 3/8 , 4/8……… are like fractions. 

Addition of fractions with Like denominators: 

In order to add fractions, the fractions must have a common denominator. That means,  

we need the pieces of each fraction to be the same size to combine them together. 

For example, if we need to add 3/5 and 1/5  together we need to check the denominator. 

These two fractions have the same denominator. 

That means the equal parts that the whole has been split into are the same size. 

Since the pieces are all the same size, we can add these two fractions together. 

Let us check another example, 

If we have to add  1/9, 7/9 and 4/9  together, we can see that the denominators are the same.  

So, we can add these fractions together. 

1/9+7/9+4/9= 1+7+4/9= 12/9

If you check the answer, the numerator is greater than the denominator. 

Hence, 12/9  à Improper fractions  Which can be converted to a mixed fraction. 

We can show this calculation visually as below 

An easy way to add fractions with like denominators is that you can combine them together by adding the numerators together (the top numbers). The denominator will always stay the same because the size of the equal pieces does not change when you combine the two fractions together 

Steps to follow while adding the fractions with like denominators  

  • Add the numerators 
  • Keep the denominator the same 

Example:  

Add   6/10+ 1/10   

Solution: 

They have the same denominator, so they can be combined together. 

Add the numerators (1 + 6 = 7). Keep the denominator the same. 

Remember: The denominator does not change because the sizes of the pieces stay the same.  You’re just counting the total number of pieces between the two fractions. 

6/10+ 1/10 = 6+1/10= 7/10

Visually 

Example: 

The table shows the distance Shannon ran over a week. 

How far did Shannon run on Wednesday and Friday together? 

Solution:  

Distance ran on Wednesday = 62 miles

Distance ran on Friday = 42 miles

Total distance = 6/2+4/2= 6+4/2= 102

= 5 miles 

Exercise:

  1. Find 3/12+4/12 using a model.
  2. Robin bought a bamboo plant that was 4/5 feet high. After a month, it has grown another 7/5 feet. What was the total height of the plant after a month?
  3. On Monday, Tiffany spent 2 ⁄8 hours studying. On Tuesday, she spent another 1 ⁄8 hours studying. What is the combined length of time she spent studying?
  4. Emma likes chocolate. One day she bought a chocolate and ate 5/8 of it in the morning and 2/8 in the evening. What part of the chocolate did she eat?
  5. Sophia completed 2/5 of her homework before going out for play. She did 1/5 of her homework after the play. How much homework did she complete altogether?
  6. Mary read 2/9  of her book in the morning and 5/9  in the evening. What fraction of the book did she read?
  7. If Sarah’s friend Abby took  2/10   of Sarah’s cupcakes, and her friend Allison took 1/10 of the cupcakes, how much of the cupcakes did Abby and Allison take altogether? 
  8. You go out for a long walk. You walk 3/7 mile and then sit down to take a rest. Then you walk another 3/7 of a mile. How far did you walk altogether?
  9. Use the bar models to add
  1. Dora has 3/8 liters of juice. She gave 9/8 liters of juice to Doreen. How many liters of juice does both of them have together?

Concept Map:

What have we learned:

  • Fractions with same denominator
  • Like fractions
  • Addition of fractions with like denominators

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