Ever wondered what half of three-quarters of a cake is?
Kemi has 34 of a birthday cake left. She gives half of it to her brother Tunde. Tunde's piece is "12 of 34" — and working that out is exactly what multiplying fractions does.
Revision notes
Multiply fractions straight across, understand why "of" means ×, and handle whole and mixed numbers.
Kemi has 34 of a birthday cake left. She gives half of it to her brother Tunde. Tunde's piece is "12 of 34" — and working that out is exactly what multiplying fractions does.
To multiply fractions, multiply the numerators together and the denominators together: 23 × 45 = 815.
You do not need a common denominator — that is only for adding and subtracting.
Simplify at the end: 34 × 29 = 636 = 16.
🔑 Key idea: Top × top, bottom × bottom, then simplify.
12 of 34: cut each of the 3 quarters in half. Each quarter becomes 2 eighths, and half of 6 eighths is 3 eighths.
And 12 × 34 = 38 — the same answer. So "of" means multiply.
Multiplying by a proper fraction takes only part of a number, so the answer is smaller: 23 × 12 = 8.
🔑 Key idea: "Of" means ×. Multiplying by a fraction less than 1 makes a number smaller.
Write a whole number over 1: 35 × 4 = 35 × 41 = 125 = 225.
Change mixed numbers into improper fractions first: 112 × 213 = 32 × 73 = 216 = 312.
Do NOT multiply the wholes and the fractions separately — 1 × 2 and 12 × 13 gives 216, which is wrong.
🔑 Key idea: Mixed numbers → improper fractions → multiply.
Work out 29 × 12.
Step 1: Multiply tops and bottoms
29 × 12 = 218
Why? No common denominator is needed for multiplying.
Step 2: Simplify
= 19
Answer: 19
Ready to check you've got it? Scroll up and work through the lesson: the interactive visuals, practice questions and mastery check are all there.