Dividing a fraction by a fraction runs on two feeder skills: multiplying fractions (multiply tops, multiply bottoms) and the reciprocal (flip) idea. Warm both up and "keep–flip–multiply" becomes easy to follow.
Answer these 3, then press Show my path. No grade — this just points you to the right level.
1. What is 1/2 × 1/3? (multiply tops, multiply bottoms)
2. What is the reciprocal (flip) of 2/3?
3. Which fraction is equivalent to 1/2?
To multiply fractions: multiply the tops, multiply the bottoms. The reciprocal of a fraction is that fraction flipped upside down — swap top and bottom. These two moves are the engine of fraction division.
Your quick check picks one for you, but you can switch any time:
Level 0 One small multiply step at a time.
A. Multiply the tops: 1 × 1 = ___
1 × 1 = 1.
B. Multiply the bottoms: 2 × 3 = ___
2 × 3 = 6.
C. So 1/2 × 1/3 = ___?
Top 1×1 = 1 over bottom 2×3 = 6 → 1/6.
Level 1 Multiply and find flips.
A. What is 2/3 × 1/2? (simplify)
2×1 = 2 over 3×2 = 6 → 2/6 = 1/3.
B. What is the reciprocal of 1/4?
Flip top and bottom: 1/4 → 4/1 (which equals 4).
Level 2 Stretch into keep–flip–multiply.
A. 1/2 ÷ 1/4: keep 1/2, flip 1/4 to 4/1, multiply. What is 1/2 × 4/1?
1×4 = 4 over 2×1 = 2 → 4/2 = 2. (Two 1/4s fit in 1/2.)
B. What is the reciprocal of 3/4?
Swap top and bottom: 3/4 → 4/3.
1. What is 1/3 × 1/2?
1×1 = 1 over 3×2 = 6 → 1/6.
2. What is the reciprocal (flip) of 2/5?
Swap top and bottom: 2/5 → 5/2.
You've practiced exactly what Lesson 2-3 uses. Time to dive in.
Start Lesson 2-3 →