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Lesson · Grade 8 · Mathematics

Adding and Subtracting Fractions with Different Denominators

  • Grade 8
  • Mathematics
  • 2 min 9 s
  • British Columbia
  • BC8-MA-13

Fraction strips show why 2/3 + 3/4 is not 5/7, then find the common denominator 12 by counting in threes and fours, and cut both strips into twelfths to get 8/12 + 9/12 = 17/12 = 1 5/12. The same twelfths solve 3 1/4 − 1 2/3 = 39/12 − 20/12 = 19/12 = 1 7/12, and the video ends on the recap: find a common denominator, then add or subtract the numerators.

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In one sentence

The question this lesson answers

How do we add two thirds and three quarters?

The top number is the numerator. The bottom number is the denominator: how many equal parts make a whole.

Transcript

What the lesson says

How do we add two thirds and three quarters?

The top number is the numerator. The bottom number is the denominator: how many equal parts make a whole.

Thirds and quarters are different sizes, so we cannot just count the pieces.

A common mistake is to add the tops and the bottoms, giving five sevenths.

But five sevenths is less than three quarters alone, so it is wrong.

Instead, use a common denominator: the lowest common multiple of 3 and 4.

Count in threes: 3, 6, 9, 12. Count in fours: 4, 8, 12. 12 is first in both lists.

Cut both strips into twelfths: a third is 4 twelfths, a quarter is 3.

Multiply the top and bottom of two thirds by 4: eight twelfths, an equivalent fraction worth the same.

For three quarters, multiply by 3 to get nine twelfths.

Now the pieces match, so add the numerators: 8 plus 9 is 17. The denominator stays 12.

17 twelfths is an improper fraction, because its top is bigger than its bottom. 12 twelfths make 1 whole, and 5 are left.

So the answer is the mixed number 1 and five twelfths: a whole number and a fraction.

Subtraction works the same way: 3 and one quarter minus 1 and two thirds.

In twelfths, 3 and one quarter is 36 plus 3, or 39. 1 and two thirds is 12 plus 8, or 20.

Subtract the numerators: 39 minus 20 is 19. 19 twelfths is 1 and seven twelfths.

Recap: find a common denominator, then add or subtract the numerators.

Curriculum

Where this fits

British Columbia, Grade 8

Mathematics, Number: operations with fractions (addition, subtraction, multiplication, division, and order of operations)BC8-MA-13

Previous: Sharing an Amount in a RatioNext: Multiplying Fractions: A Fraction of a Fraction

The outcomes and strands follow the British Columbia curriculum.

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