Fractions: Multiplying and Dividing
Multiplying fractions is actually simpler than adding them — no common denominator needed. Just multiply numerators and multiply denominators. Dividing fractions uses the 'keep-change-flip' rule: keep the first fraction, change ÷ to ×, flip the second.
Key Concepts
Multiplying Fractions
2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. Always simplify your answer. You can also cross-cancel before multiplying: if a numerator and a different denominator share a common factor, divide both by it first. This keeps numbers small.
Dividing Fractions — Keep-Change-Flip
2/3 ÷ 1/4 → Keep 2/3, Change ÷ to ×, Flip 1/4 to 4/1 → 2/3 × 4/1 = 8/3 = 2⅔. Why does this work? Dividing by 1/4 is the same as asking 'how many fourths fit in 2/3?' Flipping and multiplying gives the correct count.
Fraction Word Problems
'A recipe needs 3/4 cup of flour. You want to make 2/3 of the recipe. How much flour?' 3/4 × 2/3 = 6/12 = 1/2 cup. Always read carefully: 'of' usually means multiply, 'split into' usually means divide.
🆕 Multiply & Divide Fractions
See keep-change-flip and cross-cancellation in action!
✅ Check Your Understanding
1. To divide fractions, you keep-change-flip. What gets flipped?
2. What is 3/4 × 2/3?
3. 'Of' in a fraction word problem usually means...