Mathfinity · §2.3 Fractions

Theory A

Adding and subtracting fractions

Like fractions have the same denominator. Add or subtract the numerators; keep the denominator the same.

2/7 + 3/7 = 5/7
6/8 − 3/8 = 3/8

First convert the fractions to like fractions. Use the LCM of the denominators as the new denominator.

1/4 + 1/5 = 5/20 + 4/20 = 9/20
3/10 + 1/15 = 9/30 + 2/30 = 11/30

Convert mixed numbers to improper fractions when necessary, then calculate.

2 1/3 = 7/3
2 1/3 − 1/2 = 14/6 − 3/6 = 11/6 = 1 5/6

Agreement: Simplify your answer as much as possible.

Theory B

Multiply the numerators. Multiply the denominators. Simplify the result.

2/3 × 3/5 = 6/15 = 2/5

Write a whole number as a fraction over 1. Convert mixed numbers to improper fractions first.

3 × 2/7 = 6/7
1 1/4 × 2 2/5 = 5/4 × 12/5 = 60/20 = 3

Multiplication comes before addition and subtraction.

1/2 + 1/3 × 2/5 = 1/2 + 2/15 = 15/30 + 4/30 = 19/30

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