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Dividing Fractions

Use the "keep, change, flip" method to divide fractions

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Dividing Fractions

The "Keep, Change, Flip" Method

To divide fractions:

  1. Keep the first fraction the same
  2. Change division to multiplication
  3. Flip the second fraction (reciprocal)

ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

Example: 23÷45=23×54=1012=56\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}

What is a Reciprocal?

The reciprocal is the fraction flipped upside down:

  • Reciprocal of 34\frac{3}{4} is 43\frac{4}{3}
  • Reciprocal of 5=515 = \frac{5}{1} is 15\frac{1}{5}

Why Does This Work?

Dividing by a fraction is the same as multiplying by its reciprocal: 6÷2=36 \div 2 = 3 6×12=36 \times \frac{1}{2} = 3

Same idea with fractions!

Dividing by a Whole Number

Turn the whole number into a fraction first: 34÷2=34÷21=34×12=38\frac{3}{4} \div 2 = \frac{3}{4} \div \frac{2}{1} = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}

📚 Practice Problems

1Problem 1easy

❓ Question:

Calculate: 12÷14\frac{1}{2} \div \frac{1}{4}

💡 Show Solution

Solution:

Keep, Change, Flip: 12÷14=12×41=42=2\frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = \frac{4}{2} = 2

Answer: 2

2Problem 2easy

❓ Question:

Calculate: 12÷14\frac{1}{2} \div \frac{1}{4}

💡 Show Solution

Solution:

Keep, Change, Flip: 12÷14=12×41=42=2\frac{1}{2} \div \frac{1}{4} = \frac{1}{2} \times \frac{4}{1} = \frac{4}{2} = 2

Answer: 2

3Problem 3medium

❓ Question:

Calculate: 35÷23\frac{3}{5} \div \frac{2}{3}

💡 Show Solution

Solution:

Keep, Change, Flip: 35÷23=35×32\frac{3}{5} \div \frac{2}{3} = \frac{3}{5} \times \frac{3}{2}

Multiply: 3×35×2=910\frac{3 \times 3}{5 \times 2} = \frac{9}{10}

Answer: 910\frac{9}{10}

4Problem 4medium

❓ Question:

Calculate: 35÷23\frac{3}{5} \div \frac{2}{3}

💡 Show Solution

Solution:

Keep, Change, Flip: 35÷23=35×32\frac{3}{5} \div \frac{2}{3} = \frac{3}{5} \times \frac{3}{2}

Multiply: 3×35×2=910\frac{3 \times 3}{5 \times 2} = \frac{9}{10}

Answer: 910\frac{9}{10}

5Problem 5hard

❓ Question:

You have 34\frac{3}{4} of a pizza. You want to divide it equally among 3 people. What fraction does each person get?

💡 Show Solution

Solution:

Divide: 34÷3\frac{3}{4} \div 3

Turn 3 into a fraction: 34÷31\frac{3}{4} \div \frac{3}{1}

Keep, Change, Flip: 34×13=312=14\frac{3}{4} \times \frac{1}{3} = \frac{3}{12} = \frac{1}{4}

Answer: Each person gets 14\frac{1}{4} of the pizza

6Problem 6hard

❓ Question:

You have 34\frac{3}{4} of a pizza. You want to divide it equally among 3 people. What fraction does each person get?

💡 Show Solution

Solution:

Divide: 34÷3\frac{3}{4} \div 3

Turn 3 into a fraction: 34÷31\frac{3}{4} \div \frac{3}{1}

Keep, Change, Flip: 34×13=312=14\frac{3}{4} \times \frac{1}{3} = \frac{3}{12} = \frac{1}{4}

Answer: Each person gets 14\frac{1}{4} of the pizza

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❓ Frequently Asked Questions

What is Dividing Fractions?▾
Use the "keep, change, flip" method to divide fractions
How can I study Dividing Fractions effectively?▾
Start by reading the study notes and working through the examples on this page. Then use the flashcards to test your recall. Practice with the 6 problems provided, checking solutions as you go. Regular review and active practice are key to retention.
Is this Dividing Fractions study guide free?▾
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What course covers Dividing Fractions?▾
Dividing Fractions is part of the Grade 5 Math course on Study Mondo, specifically in the Fractions section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Dividing Fractions?▾
Yes, this page includes 6 practice problems with detailed solutions. Each problem includes a step-by-step explanation to help you understand the approach.