Multiplying Fractions by Fractions and Whole Numbers Worksheet

Complete practice worksheet with 20 problems covering fraction multiplication by fractions and whole numbers.

MULTIPLYING FRACTIONS WORKSHEET
Grade 4 Mathematics - Multiplying Fractions by Fractions and Whole Numbers

Name: _________________ Date: _________________ Score: _______/20

Part A: Multiplying Fractions by Fractions (10 problems)
1
\(\frac{2}{3} \times \frac{4}{5}\)
2
\(\frac{3}{4} \times \frac{1}{2}\)
3
\(\frac{5}{6} \times \frac{2}{3}\)
4
\(\frac{1}{4} \times \frac{3}{8}\)
5
\(\frac{7}{8} \times \frac{4}{7}\)
6
\(\frac{2}{9} \times \frac{3}{5}\)
7
\(\frac{5}{12} \times \frac{6}{7}\)
8
\(\frac{3}{10} \times \frac{5}{9}\)
9
\(\frac{4}{15} \times \frac{5}{8}\)
10
\(\frac{7}{12} \times \frac{8}{21}\)
Part B: Multiplying Fractions by Whole Numbers (10 problems)
11
\(3 \times \frac{2}{5}\)
12
\(4 \times \frac{3}{7}\)
13
\(5 \times \frac{1}{4}\)
14
\(6 \times \frac{2}{9}\)
15
\(7 \times \frac{3}{8}\)
16
\(8 \times \frac{5}{12}\)
17
\(9 \times \frac{4}{15}\)
18
\(10 \times \frac{7}{20}\)
19
\(12 \times \frac{5}{18}\)
20
\(15 \times \frac{2}{25}\)
ANSWER KEY
1. \(\frac{2}{3} \times \frac{4}{5}\)
\(\frac{8}{15}\)
2. \(\frac{3}{4} \times \frac{1}{2}\)
\(\frac{3}{8}\)
3. \(\frac{5}{6} \times \frac{2}{3}\)
\(\frac{5}{9}\)
4. \(\frac{1}{4} \times \frac{3}{8}\)
\(\frac{3}{32}\)
5. \(\frac{7}{8} \times \frac{4}{7}\)
\(\frac{1}{2}\)
6. \(\frac{2}{9} \times \frac{3}{5}\)
\(\frac{2}{15}\)
7. \(\frac{5}{12} \times \frac{6}{7}\)
\(\frac{5}{14}\)
8. \(\frac{3}{10} \times \frac{5}{9}\)
\(\frac{1}{6}\)
9. \(\frac{4}{15} \times \frac{5}{8}\)
\(\frac{1}{6}\)
10. \(\frac{7}{12} \times \frac{8}{21}\)
\(\frac{2}{9}\)
11. \(3 \times \frac{2}{5}\)
\(\frac{6}{5}\) or \(1\frac{1}{5}\)
12. \(4 \times \frac{3}{7}\)
\(\frac{12}{7}\) or \(1\frac{5}{7}\)
13. \(5 \times \frac{1}{4}\)
\(\frac{5}{4}\) or \(1\frac{1}{4}\)
14. \(6 \times \frac{2}{9}\)
\(\frac{4}{3}\) or \(1\frac{1}{3}\)
15. \(7 \times \frac{3}{8}\)
\(\frac{21}{8}\) or \(2\frac{5}{8}\)
16. \(8 \times \frac{5}{12}\)
\(\frac{10}{3}\) or \(3\frac{1}{3}\)
17. \(9 \times \frac{4}{15}\)
\(\frac{12}{5}\) or \(2\frac{2}{5}\)
18. \(10 \times \frac{7}{20}\)
\(\frac{7}{2}\) or \(3\frac{1}{2}\)
19. \(12 \times \frac{5}{18}\)
\(\frac{10}{3}\) or \(3\frac{1}{3}\)
20. \(15 \times \frac{2}{25}\)
\(\frac{6}{5}\) or \(1\frac{1}{5}\)
Solution Guide and Key Concepts
\(\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}\)
\(n \times \frac{a}{b} = \frac{na}{b}\)
Multiplication Rules
Key definitions:

Numerator: Top number in a fraction (represents parts taken)

Denominator: Bottom number in a fraction (represents total equal parts)

Proper Fraction: Numerator < Denominator (value < 1)

Improper Fraction: Numerator ≥ Denominator (value ≥ 1)

Mixed Number: Whole number + Proper fraction

Greatest Common Divisor (GCD): Largest number that divides both numbers evenly

Simplification: Reducing a fraction to lowest terms

Multiplication process:
  1. Identify fractions: Recognize numerators and denominators
  2. Multiply numerators: Calculate \(a \times c\) (or \(n \times a\) for whole number)
  3. Multiply denominators: Calculate \(b \times d\) (or keep \(b\) for whole number)
  4. Write as fraction: Form \(\frac{ac}{bd}\) or \(\frac{na}{b}\)
  5. Simplify: Find GCD and divide both by it
  6. Convert if needed: Change improper to mixed number
  7. Verify: Check reasonableness and arithmetic
Tip 1: Always multiply numerators together and denominators together.
Tip 2: Simplify before multiplying when possible by canceling common factors.
Tip 3: When multiplying by whole numbers, write the whole number as a fraction over 1.
Tip 4: Remember that multiplying two fractions less than 1 gives a result even smaller than both.
Common errors: Adding instead of multiplying, forgetting to multiply denominators, not simplifying final answers, incorrectly converting improper fractions.
Exam preparation: Practice GCD calculation, master improper to mixed conversions, work on word problems, memorize the multiplication rule.
Essential formulas:

• Fraction by fraction: \(\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}\)

• Fraction by whole: \(n \times \frac{a}{b} = \frac{na}{b}\)

• Simplification: \(\frac{a}{b} = \frac{a ÷ \text{GCD}}{b ÷ \text{GCD}}\)

• Conversion: \(\frac{a}{b} = q + \frac{r}{b}\) where \(a = bq + r\)

• GCD calculation: Find largest number that divides both evenly

Worksheet Help & Solutions

Question: How do I multiply a fraction by a whole number? Is it different from multiplying two fractions?

Answer: Multiplying a fraction by a whole number is actually quite similar to multiplying two fractions:

  • Convert the whole number to a fraction: \(n = \frac{n}{1}\)
  • Then multiply: \(n \times \frac{a}{b} = \frac{n}{1} \times \frac{a}{b} = \frac{na}{b}\)

For example: \(3 \times \frac{2}{5} = \frac{3}{1} \times \frac{2}{5} = \frac{6}{5}\)

You can think of it as: "What is 3 groups of \(\frac{2}{5}\)?"

Question: When do I need to convert an improper fraction to a mixed number?

Answer: You should convert an improper fraction to a mixed number:

  • When the problem asks for the answer in mixed number form
  • When the answer represents a real-world measurement (like cups of flour)
  • When the numerator is greater than the denominator (as a general practice)

To convert: Divide the numerator by the denominator. The quotient is the whole number, and the remainder over the denominator is the fraction.

Example: \(\frac{7}{3} = 7 ÷ 3 = 2\) remainder \(1\), so \(\frac{7}{3} = 2\frac{1}{3}\)

Question: How do I know if I should simplify my answer?

Answer: You should ALWAYS simplify your fraction answers unless specifically told otherwise:

  • Find the Greatest Common Divisor (GCD) of the numerator and denominator
  • Divide both the numerator and denominator by the GCD
  • The result is the fraction in its simplest form

Example: \(\frac{8}{12}\) has GCD = 4, so \(\frac{8 ÷ 4}{12 ÷ 4} = \frac{2}{3}\)

A fraction is in simplest form when the only common factor of numerator and denominator is 1.

Question: What if I get stuck on a problem during the worksheet?

Answer: Here's what to do when you're stuck:

  • Read the problem again carefully
  • Look at the examples in the solution guide above
  • Try a simpler version of the problem first
  • Check if you can cancel common factors before multiplying
  • Ask for help from your teacher or a classmate

Remember: It's better to show your work and attempt the problem than to leave it blank. Even partial credit shows effort and understanding.