Adding and Subtracting Fractions with Unlike Denominators

Contributor: Erika Wargo. Lesson ID: 12536

When you get a pizza for lunch, you add. When you eat it, you subtract. Is math that much fun? Interactive quizzes and online games help make finding common denominators for fractions more digestible!

categories

Elementary

subject
Math
learning style
Visual
personality style
All
Grade Level
Intermediate (3-5)
Lesson Type
Skill Sharpener

Lesson Plan - Get It!

Audio:

Two pizzas are delivered to your house. One is divided into fourths and the other is divided into eighths. If you eat one slice from each pizza, what fraction of the pizzas did you eat?

Fractions show part of a whole.

Fractions have common denominators (the bottom number) if their denominators are equal. The top number of a fraction is the numerator. When adding and subtracting fractions, they need to have the same denominator.

Watch a short video to review adding and subtracting fractions with unlike denominators and write down the answers to these questions:

  • What does “least common denominator” mean?
  • What is a multiple?
  • How do you find the least common multiple of two numbers?
  • When adding and subtracting fractions, which part of the fraction is added or subtracted? Explain.

Discuss the questions above after you have watched Math Antics - Common Denominator LCD:

 

There are a two ways you can find a common denominator for fractions:

  1. Multiply the current denominators together and use the product as the new denominator.
  2. List the multiples of each number and find the first number they have in common.

Example 1

 1  +  5  =
6 12

When fractions have unlike denominators, find the least common multiple (LCM) of the denominators.

The denominators are 6 and 12. Since 12 is a multiple of 6, the LCM of 6 and 12 is 12.

Multiples of 6: 6, 12, 18, 24

Multiples of 12: 12, 24, 36

Since 512 already has a denominator of 12, leave the fraction as is.

16 does not have a denominator of 12. Since 6 x 2 = 12, multiply the numerator and denominator by 2.

Important: If you multiply the denominator by a number, you must also multiply the numerator by the same number to create an equivalent fraction.

 1  x  2  =  2 
6 2 12

Replace the new fraction, 2/12  and add.

 5  +  2  =  7 
12 12 12

 

Example 2

 1  -  1  =
4 10

 

When fractions have unlike denominators, find the LCM of the fractions, then subtract the numerators and keep the denominator the same. Be sure to subtract the smaller number from the larger number.

Multiples of 4: 4, 8, 12, 16, 20

Multiples of 10: 10, 20, 30, 40

 1  x  5  =  5 
4 5 20

 

 1  x  2  =  2 
10 2 20

 

 1  -  1  becomes  5   2 
4 10 20 20

 

 5  -  2  =  3 
20 20 20

 

Example 3 Tommy ate 38 of a pizza and Henry ate ¼ of the same pizza. Who ate more pizza? How much more did that person eat?

Since the fractions have uncommon denominators, you need to find the LCM of the fractions before you can solve the problem. The question asks, "Who ate more pizza?", so you will compare the fractions and then subtract them to find how much more pizza was eaten.

Multiples of 4: 4, 8, 12

Multiplies of 8: 8, 16, 24

¼ = 28 as a fraction.

Tommy ate 38. Henry ate 28. Since the denominators are the same, you can compare the numerators. Tommy ate 3 out of the 8 slices. Henry ate 2 out of the 8 slices.

Tommy ate more slices of pizza. To find out how many more slices, subtract the fractions:

38 - 28 = 18

Discuss with a parent or teacher:

  • Why do fractions need to have a common denominator before adding or subtracting? Draw a model to show an example.
  • How do you find the least common multiple (LCM) of two numbers?
  • In what ways could this skill be applied to real-life activities such as cooking?

Now, you will move on to the Got It? section to complete some practice activities with adding and subtracting fractions with unlike denominators.

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