Grade 5 Fractions: Dividing Fractions

A grade 6 preview: divide fractions using reciprocals

What You'll Learn

Find reciprocals
Keep-Change-Flip

📖Dividing

Keep, Change, Flip!

💡Where this fits

Common Core teaches dividing a fraction by a fraction in grade 6 (6.NS.A.1), so this lesson is a stretch for this grade. Grade 5 divides unit fractions by whole numbers (5.NF.B.7) — the sharing stories in Word Problems. Try this once multiplying fractions is solid.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
3/4 ÷ 5/8 = ?
1. Keep the first fraction, change ÷ to ×, and flip the second: 5/8 becomes 8/5.
2. 3/4 ÷ 5/8 = 3/4 × 8/5.
3. Multiply the numerators: 3 × 8 = 24. Multiply the denominators: 4 × 5 = 20.
4. That gives 24/20.
5. The greatest number that divides both 24 and 20 is 4.
6. Divide the top and bottom by 4: 24 ÷ 4 = 6 and 20 ÷ 4 = 5, so 24/20 = 6/5.
7. So 3/4 ÷ 5/8 = 6/5.
Answer: 6/5
Example 2
1/2 ÷ 3/5 = ?
1. Keep the first fraction, change ÷ to ×, and flip the second: 3/5 becomes 5/3.
2. 1/2 ÷ 3/5 = 1/2 × 5/3.
3. Multiply the numerators: 1 × 5 = 5. Multiply the denominators: 2 × 3 = 6.
4. That gives 5/6.
5. So 1/2 ÷ 3/5 = 5/6.
Answer: 5/6
Example 3
1/5 ÷ 1/2 = ?
1. Keep the first fraction, change ÷ to ×, and flip the second: 1/2 becomes 2/1.
2. 1/5 ÷ 1/2 = 1/5 × 2/1.
3. Multiply the numerators: 1 × 2 = 2. Multiply the denominators: 5 × 1 = 5.
4. That gives 2/5.
5. So 1/5 ÷ 1/2 = 2/5.
Answer: 2/5