Adding Fractions. By looking at the model below, we can easily see that 1 / / 3 = 2 / 3 Notice that we added only the numerators. Since the denominator of both fractions was already 3, we just rewrite it as the denominator of our sum =

3 / / 16 In this problem, the denominators are different. We can't add until we rename one of the fractions so it has the same denominator as the other fraction. The LCM of 8 and 16 is / 8 needs to be renamed so its denominator becomes / 8 × 2 / 2 = 6 / 16 Now the problem can be rewritten and solved. 6 / / 16 = 11 / 16

1 / / 10 In this problem, we need to rename both fractions to find a common denominator. The LCM of 6 and 10 is 30. Both fractions need to be renamed so their denominators become / 6 × 5 / 5 = 5 / 30 Now the problem can be rewritten and solved. 5 / / 30 = 14 / 30 3 / 10 × 3 / 3 = 9 / 30

Always simplify your answer. In the last problem, the sum was 14 / 30. This answer is not in its simplest form. To simplify a fraction, divide the numerator and denominator by the greatest common factor of both numbers. The GCF of 14 and 30 is / 30 ÷ 2 / 2 = 7 / / 30 = 7 / 15

Subtracting Fractions. 10 / / 8 To subtract fractions, follow the same procedures used when adding fractions. Rename one or both fractions to obtain common denominators. 2 / 8 × 2 / 2 = 4 / 16 Rewrite and solve. 10 / / 16 = 6 / 16 Simplify the answer. 6 / 16 ÷ 2 / 2 = 3 / 8

1) Fractions must have common denominators before you add or subtract. (The LCM will tell you how to rename the fractions.) 2) Add or subtract only the numerators. 3) Always simplify your answer. (The GCF will tell you how to simplify the answer.)