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Multiplying Fractions

Learn to multiply fractions and whole numbers by fractions

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Multiplying Fractions

Multiplying Two Fractions

Three simple steps:

  1. Multiply the numerators (top numbers)
  2. Multiply the denominators (bottom numbers)
  3. Simplify if possible

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

Example: 23×45=2×43×5=815\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}

Multiplying a Whole Number by a Fraction

Turn the whole number into a fraction (put it over 1):

Example: 5×235 \times \frac{2}{3}

5×23=51×23=103=3135 \times \frac{2}{3} = \frac{5}{1} \times \frac{2}{3} = \frac{10}{3} = 3\frac{1}{3}

What Does It Mean?

Multiplying by a fraction means "taking a part of" something:

  • 12×10=5\frac{1}{2} \times 10 = 5 → Half of 10 is 5
  • 14×12=3\frac{1}{4} \times 12 = 3 → One-fourth of 12 is 3

Simplifying Before Multiplying

You can cross-cancel to make math easier:

45×58=4×55×8=48=12\frac{4}{5} \times \frac{5}{8} = \frac{4 \times \cancel{5}}{\cancel{5} \times 8} = \frac{4}{8} = \frac{1}{2}

📚 Practice Problems

1Problem 1easy

❓ Question:

Calculate: 13×25\frac{1}{3} \times \frac{2}{5}

💡 Show Solution

Solution:

Multiply numerators and denominators: 1×23×5=215\frac{1 \times 2}{3 \times 5} = \frac{2}{15}

Already in simplest form.

Answer: 215\frac{2}{15}

2Problem 2easy

❓ Question:

Calculate: 13×25\frac{1}{3} \times \frac{2}{5}

💡 Show Solution

Solution:

Multiply numerators and denominators: 1×23×5=215\frac{1 \times 2}{3 \times 5} = \frac{2}{15}

Already in simplest form.

Answer: 215\frac{2}{15}

3Problem 3medium

❓ Question:

What is 12\frac{1}{2} of 18?

💡 Show Solution

Solution:

"Of" means multiply: 12×18=12×181=182=9\frac{1}{2} \times 18 = \frac{1}{2} \times \frac{18}{1} = \frac{18}{2} = 9

Answer: 9

4Problem 4medium

❓ Question:

What is 12\frac{1}{2} of 18?

💡 Show Solution

Solution:

"Of" means multiply: 12×18=12×181=182=9\frac{1}{2} \times 18 = \frac{1}{2} \times \frac{18}{1} = \frac{18}{2} = 9

Answer: 9

5Problem 5hard

❓ Question:

A recipe needs 34\frac{3}{4} cup of sugar. If you want to make 23\frac{2}{3} of the recipe, how much sugar do you need?

💡 Show Solution

Solution:

Multiply the fractions: 23×34=2×33×4=612\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12}

Simplify (divide by 6): 612=12\frac{6}{12} = \frac{1}{2}

Answer: 12\frac{1}{2} cup of sugar

6Problem 6hard

❓ Question:

A recipe needs 34\frac{3}{4} cup of sugar. If you want to make 23\frac{2}{3} of the recipe, how much sugar do you need?

💡 Show Solution

Solution:

Multiply the fractions: 23×34=2×33×4=612\frac{2}{3} \times \frac{3}{4} = \frac{2 \times 3}{3 \times 4} = \frac{6}{12}

Simplify (divide by 6): 612=12\frac{6}{12} = \frac{1}{2}

Answer: 12\frac{1}{2} cup of sugar

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Dividing Fractions
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❓ Frequently Asked Questions

What is Multiplying Fractions?▾
Learn to multiply fractions and whole numbers by fractions
How can I study Multiplying 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 Fractions study guide free?▾
Yes — all study notes, flashcards, and practice problems for Multiplying Fractions on Study Mondo are free to access. No account is needed.
What course covers Multiplying Fractions?▾
Multiplying 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 Multiplying 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.