Divide Fractions by Fractions

How the lesson starts: Divide Fractions by Fractions

Kiki's Smoothie Cart
Welcome to Kiki's Smoothie Cart! Kiki has 3/4 of a jug of mango juice. Each smoothie cup takes 1/8 of a jug. How many cups can she pour? That's 3/4 ÷ 1/8. Dividing fractions asks one friendly question: how many pieces fit?
How many fit?
The top bar shows 3/4 of a jug. Cut every fourth in half to make eighths. The bottom bar shows the same juice as 6 eighths. Count them: 6 pieces of 1/8 fit. So 3/4 ÷ 1/8 = 6 cups!
Times the bottom number
Why does this work? A whole jug holds 3 cups of 1/3. So 2/5 of a jug holds 2/5 of 3 cups. That's 2/5 × 3 = 6/5. So 2/5 ÷ 1/3 = 6/5. Check by multiplying back: 6/5 × 1/3 = 6/15, which is 2/5. It works!