Adding & Subtracting

Find a Common Denominator before adding or subtracting numerators.

Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12

Multiplying Fractions

Multiply across (top-top, bottom-bottom).

Formula: a/b × c/d = ac/bd

Example: 2/3 × 4/5 = 8/15

Dividing Fractions

Keep the first, Change sign to multiply, Flip the second (KCF).

Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3

Simplifying

Divide top and bottom by their HCF.

Example: 10/25 = 2/5 (Divide by 5)

Mixed Numbers

Convert to improper fractions first.

Example: 1 ½ = 3/2 2 ¾ = 11/4

Complex Subtraction

Mixed number subtraction: borrow from the whole number or convert all to improper.

Example: 2 ¼ - 1 ¾ = 9/4 - 7/4 = 2/4 = 1/2

Algebraic Fractions

The rules are identical. Find common denominators using algebra.

Example: 1/x + 1/2x = 2/2x + 1/2x = 3/2x

Recurring Decimals

Convert recurring decimals to fractions using algebra (see specific topic).