Subtracting Like and Unlike Fractions

Rewrite the problem with equivalent fractions List the multiples of both denominators. Find the least common multiple (LCM). Write new fractions with the LCM as the new denominator. Find the factor you multiply by to get from your original denominator to your new denominator. Use that same factor, and multiply it by your original numerator to get a new numerator.

WHAT DOES THAT MEAN? Let’s illustrate the steps with an example. 3 1 - 4 6

3 1 - 4 6 9 2 x 3 x 2 - 12 12 7 Multiples of 4: 4, 8, 12, 16, 20 12 Multiples of 6: 6, 12, 18, 24, 30

Example 2 9 2 10 10

Example 2 9 2 10 10 7 = 10

We need a common denominator to add these fractions. -

- We need a common denominator to add these fractions. - Count by 2's 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 Count by 7's 7, 14, 21, 28, 35…

- 7 6 1 = = + 7 - 6 = 1 x 7 X 7 x 2 x 2 Make equivalent fractions. Add the numerators = + 7 - 6 = 1 x 2 1

- We need a common denominator to subtract a fraction from another. Count by 5's 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 Count by 11's 11, 22, 33, 44, 55, 66, 77…

15 11 4 15 - 11 = 4 = = - x 5 x 5 x 11 x 11 Make equivalent fractions. Subtract. = 15 - 11 = 4 - x 11 4

- We need a common denominator to subtract one fraction from another. Count by 2's 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 … Count by 10's 10, 20, 30…

5 3 2 5 – 3 = 2 = - = x 5 x 5 x 1 x 1 Make equivalent fractions. Subtract. - = 5 – 3 = 2 x 1 2