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Multiplying and Dividing Fractions

Master multiplication and division with fractions and mixed numbers

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Multiplying and Dividing Fractions

Multiplying Fractions

Steps:

  1. Multiply numerators
  2. Multiply denominators
  3. Simplify

ab×cd=a×cb×d\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

Example: 23×45=815\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}

With Mixed Numbers

Convert to improper fractions first!

213×112=73×32=216=72=3122\frac{1}{3} \times 1\frac{1}{2} = \frac{7}{3} \times \frac{3}{2} = \frac{21}{6} = \frac{7}{2} = 3\frac{1}{2}

Dividing Fractions

Rule: Multiply by the reciprocal (flip the second fraction)

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

Example: 34÷25=34×52=158=178\frac{3}{4} \div \frac{2}{5} = \frac{3}{4} \times \frac{5}{2} = \frac{15}{8} = 1\frac{7}{8}

Reciprocal

The reciprocal of a fraction is obtained by flipping it:

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

📚 Practice Problems

1Problem 1easy

❓ Question:

Calculate: 35×27\frac{3}{5} \times \frac{2}{7}

💡 Show Solution

Solution:

Multiply numerators and denominators: 3×25×7=635\frac{3 \times 2}{5 \times 7} = \frac{6}{35}

Already in simplest form.

Answer: 635\frac{6}{35}

2Problem 2easy

❓ Question:

Calculate: 35×27\frac{3}{5} \times \frac{2}{7}

💡 Show Solution

Solution:

Multiply numerators and denominators: 3×25×7=635\frac{3 \times 2}{5 \times 7} = \frac{6}{35}

Already in simplest form.

Answer: 635\frac{6}{35}

3Problem 3medium

❓ Question:

Calculate: 56÷23\frac{5}{6} \div \frac{2}{3}

💡 Show Solution

Solution:

Multiply by the reciprocal: 56÷23=56×32\frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2}

=5×36×2=1512= \frac{5 \times 3}{6 \times 2} = \frac{15}{12}

Simplify (divide by 3): 1512=54=114\frac{15}{12} = \frac{5}{4} = 1\frac{1}{4}

Answer: 1141\frac{1}{4}

4Problem 4medium

❓ Question:

Calculate: 56÷23\frac{5}{6} \div \frac{2}{3}

💡 Show Solution

Solution:

Multiply by the reciprocal: 56÷23=56×32\frac{5}{6} \div \frac{2}{3} = \frac{5}{6} \times \frac{3}{2}

=5×36×2=1512= \frac{5 \times 3}{6 \times 2} = \frac{15}{12}

Simplify (divide by 3): 1512=54=114\frac{15}{12} = \frac{5}{4} = 1\frac{1}{4}

Answer: 1141\frac{1}{4}

5Problem 5hard

❓ Question:

A recipe calls for 2232\frac{2}{3} cups of flour. If you want to make 34\frac{3}{4} of the recipe, how much flour do you need?

💡 Show Solution

Solution:

Multiply: 223×342\frac{2}{3} \times \frac{3}{4}

Convert to improper fraction: 223=832\frac{2}{3} = \frac{8}{3}

Multiply: 83×34=2412=2\frac{8}{3} \times \frac{3}{4} = \frac{24}{12} = 2

Answer: 2 cups of flour

6Problem 6hard

❓ Question:

A recipe calls for 2232\frac{2}{3} cups of flour. If you want to make 34\frac{3}{4} of the recipe, how much flour do you need?

💡 Show Solution

Solution:

Multiply: 223×342\frac{2}{3} \times \frac{3}{4}

Convert to improper fraction: 223=832\frac{2}{3} = \frac{8}{3}

Multiply: 83×34=2412=2\frac{8}{3} \times \frac{3}{4} = \frac{24}{12} = 2

Answer: 2 cups of flour

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📌 Related Topics in Rational Numbers

Operations with IntegersMultiplying and Dividing IntegersRational Number Operations

❓ Frequently Asked Questions

What is Multiplying and Dividing Fractions?▾
Master multiplication and division with fractions and mixed numbers
How can I study Multiplying and 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 Multiplying and Dividing Fractions study guide free?▾
Yes — all study notes, flashcards, and practice problems for Multiplying and Dividing Fractions on Study Mondo are free to access. No account is needed.
What course covers Multiplying and Dividing Fractions?▾
Multiplying and Dividing Fractions is part of the Grade 7 Math course on Study Mondo, specifically in the Rational Numbers section. You can explore the full course for more related topics and practice resources.
Are there practice problems for Multiplying and 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.