How to Add Fractions With Unlike Denominators
Write down the beginning fractions., Find a common denominator., Multiply both numbers on the first fraction by the bottom number of the second fraction., Multiply both numbers on the second fraction by the bottom number of the first fraction., Line...
Step-by-Step Guide
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Step 1: Write down the beginning fractions.
Write them down side by side so that they're close to one another and easy to see.
We'll give you examples below for each step that you read.
Ex. 1: 1/2 + 1/4 Ex. 2: 1/3 + 3/4 Ex. 3: 6/5 + 4/3 -
Step 2: Find a common denominator.
Do this by finding a "multiple" of the two denominators.
An easy way to find one is to simply multiply the two denominators together.
Ex. 1: 2 x 4 =
8.
Both of our fractions will have a denominator of
8.
Ex. 2: 3 x 4 =
12.
Both of our fractions will have a denominator of
12.
Ex. 3: 5 x 3 =
15.
Both of our fractions will have a denominator of
15. , We're not changing the value of the fraction; we're just changing how the fraction looks.
It's still the same fraction.
Ex. 1: 1/2 x 4/4 = 4/8.
Ex. 2: 1/3 x 4/4 = 4/12.
Ex. 3: 6/5 x 3/3 = 18/15. , Again, we're not changing the value of the fraction; we're just changing how the fraction looks.
It's still the same fraction.
Ex. 1: 1/4 x 2/2 = 2/8.
Ex. 2: 3/4 x 3/3 = 9/12.
Ex. 3: 4/3 x 5/5 = 20/15. , We haven't added them yet, but that will come soon! What we've done is multiple each fraction by the number
1.
Ex. 1: instead of 1/2 + 1/4, we have 4/8 + 2/8 Ex. 2: instead of 1/3 + 3/4, we have 4/12 + 9/12 Ex. 3: instead of 6/5 + 4/3, we have 18/15 + 20/15 , The numerator is the top number of the fraction.
Ex. 1: 4 + 2 =
6. 6 will be our new numerator.
Ex. 2: 4 + 9 =
13. 13 will be our new numerator.
Ex. 3: 18 + 20 =
38. 38 will be our new numerator. , Ex. 1: 8 will be our new denominator.
Ex. 2: 12 will be our new denominator.
Ex. 3: 15 will be our new denominator. , Ex. 1: 6/8 is our answer to 1/2 + 1/4 = ? Ex. 2: 13/12 is our answer to 1/3 + 3/4 = ? Ex. 3: 38/15 is our answer to 6/5 + 4/3 = ? , Simplify by dividing both the numerator and the denominator in the fraction by each number's greatest common factor.
Ex. 1: 6/8 can be simplified to 3/4.
Ex. 2: 13/12 can be reduced to 1 1/12.
Ex. 3: 38/15 can be reduced to 2 8/15. -
Step 3: Multiply both numbers on the first fraction by the bottom number of the second fraction.
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Step 4: Multiply both numbers on the second fraction by the bottom number of the first fraction.
-
Step 5: Line both fractions up side by side with their new numbers.
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Step 6: Add together the numerators of the two fractions.
-
Step 7: Take the common denominator that you figured out in Step 2 and add it on the bottom of your new numerator.
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Step 8: Put the new numerator on top and the new denominator on bottom.
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Step 9: Simplify and reduce.
Detailed Guide
Write them down side by side so that they're close to one another and easy to see.
We'll give you examples below for each step that you read.
Ex. 1: 1/2 + 1/4 Ex. 2: 1/3 + 3/4 Ex. 3: 6/5 + 4/3
Do this by finding a "multiple" of the two denominators.
An easy way to find one is to simply multiply the two denominators together.
Ex. 1: 2 x 4 =
8.
Both of our fractions will have a denominator of
8.
Ex. 2: 3 x 4 =
12.
Both of our fractions will have a denominator of
12.
Ex. 3: 5 x 3 =
15.
Both of our fractions will have a denominator of
15. , We're not changing the value of the fraction; we're just changing how the fraction looks.
It's still the same fraction.
Ex. 1: 1/2 x 4/4 = 4/8.
Ex. 2: 1/3 x 4/4 = 4/12.
Ex. 3: 6/5 x 3/3 = 18/15. , Again, we're not changing the value of the fraction; we're just changing how the fraction looks.
It's still the same fraction.
Ex. 1: 1/4 x 2/2 = 2/8.
Ex. 2: 3/4 x 3/3 = 9/12.
Ex. 3: 4/3 x 5/5 = 20/15. , We haven't added them yet, but that will come soon! What we've done is multiple each fraction by the number
1.
Ex. 1: instead of 1/2 + 1/4, we have 4/8 + 2/8 Ex. 2: instead of 1/3 + 3/4, we have 4/12 + 9/12 Ex. 3: instead of 6/5 + 4/3, we have 18/15 + 20/15 , The numerator is the top number of the fraction.
Ex. 1: 4 + 2 =
6. 6 will be our new numerator.
Ex. 2: 4 + 9 =
13. 13 will be our new numerator.
Ex. 3: 18 + 20 =
38. 38 will be our new numerator. , Ex. 1: 8 will be our new denominator.
Ex. 2: 12 will be our new denominator.
Ex. 3: 15 will be our new denominator. , Ex. 1: 6/8 is our answer to 1/2 + 1/4 = ? Ex. 2: 13/12 is our answer to 1/3 + 3/4 = ? Ex. 3: 38/15 is our answer to 6/5 + 4/3 = ? , Simplify by dividing both the numerator and the denominator in the fraction by each number's greatest common factor.
Ex. 1: 6/8 can be simplified to 3/4.
Ex. 2: 13/12 can be reduced to 1 1/12.
Ex. 3: 38/15 can be reduced to 2 8/15.
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Matthew Baker
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