The Number System
GradesSixth GradeThe Number SystemDividing Fractions by Fractions

Dividing Fractions by Fractions

🔢 The Number System

Dividing Fractions by Fractions

Keep, change, flip — then multiply straight across.

To divide any fraction by any fraction, use the Keep-Change-Flip (KCF) algorithm: keep the first fraction as-is, change the division sign to multiplication, and flip the second fraction (take its reciprocal). Then multiply normally.

ab÷cd=ab×dc=a×db×c\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{a \times d}{b \times c}
🍕Real-World Context
You have ¾ of a pizza. Each serving is ½ of a pizza. How many servings? ¾ ÷ ½ = ¾ × 2/1 = 6/4 = 3/2 = 1½ servings. There are one and a half servings — which makes sense since ¾ > ½.

Full Example: ⅔ ÷ ⅘

1Keep: ⅔
2Change: ÷ becomes ×
3Flip: ⅘ becomes 5/4
4Multiply: ⅔ × 5/4 = (2×5)/(3×4) = 10/12
5Simplify: 10/12 = 5/6
💡

Remember This!

Check your answer's reasonableness. If you divide by a fraction less than 1, your quotient should be larger than the dividend. If you divide by a fraction greater than 1, the quotient is smaller.

✏️ Try It!

What is ¾ ÷ ½?

Take Quiz 📝 — 25 Questions