Mixed Number Multiplication

Grade 5 · mathematics · 63 practice problems · read aloud

🔊 Listen to this explanation

Multiplying Mixed Numbers 🧮

This operation helps us find a part of a part! It's super useful for real-life problems like cooking (doubling a recipe), measuring for crafts, or figuring out areas of rooms and gardens.

How to Solve: Step-by-Step

  1. Convert to Improper Fractions: Change each mixed number into a fraction where the numerator is larger than the denominator.
  2. Multiply the Fractions: Multiply the numerators together and the denominators together.
  3. Simplify: Reduce your answer to its simplest form. If it's an improper fraction, convert it back to a mixed number.

Let's Look at Some Examples

Example 1: 2 ½ × 1 ⅓

  1. Convert: 2 ½ = 5/2 and 1 ⅓ = 4/3
  2. Multiply: (5 × 4) / (2 × 3) = 20/6
  3. Simplify: 20/6 = 10/3 = 3 ⅓

Example 2: 1 ¾ × 2 ⅖

  1. Convert: 1 ¾ = 7/4 and 2 ⅖ = 12/5
  2. Multiply: (7 × 12) / (4 × 5) = 84/20
  3. Simplify: 84/20 = 21/5 = 4 ⅕

⚠️ Common Mistakes to Avoid

  • Don't multiply the whole numbers and fractions separately. You must convert to improper fractions first!
  • Forgetting to simplify your final answer. Always check if the numerator and denominator can be divided by the same number.
  • Mixing up multiplication rules with addition rules. We don't need a common denominator for multiplication!

🌟 Tips & Tricks

  • Use the "FO" method: Fractions Only! Remember to convert first.
  • Cancel early: Before multiplying, see if any numerator and denominator share a common factor you can divide by. This makes the numbers smaller and easier!
  • Double-check your conversion from a mixed number. A quick way is: (Whole Number × Denominator) + Numerator.

How to Practice

  • Start with simple problems, like a mixed number times a whole number.
  • Create your own word problems about pizza, chocolate bars, or lengths of ribbon.
  • Use online math games or flashcards to build speed and accuracy.
  • Practice with a friend and explain the steps to each other—teaching is a great way to learn!

Practice problems

6 of the 63, worked through step by step — try them before opening the answer.

1 2 1/4 × 3 1/3 = ?

Hint: Convert mixed numbers to improper fractions before multiplying. Remember to simplify your answer.

Show the answer

Answer: 7 1/2

  1. Convert each mixed number to an improper fraction. 2 1/4 = (2 × 4 + 1)/4 = (8 + 1)/4 = 9/4 3 1/3 = (3 × 3 + 1)/3 = (9 + 1)/3 = 10/3
  2. Multiply the improper fractions. (9/4) × (10/3) = (9 × 10) / (4 × 3) = 90 / 12
  3. Simplify the fraction 90/12. First, divide numerator and denominator by 6: (90 ÷ 6) / (12 ÷ 6) = 15/2
  4. Convert the improper fraction 15/2 back to a mixed number. 15 ÷ 2 = 7 remainder 1, so 15/2 = 7 1/2 Final Answer: 7 1/2

Let's solve 2 1/4 × 3 1/3 step by step.

2 3 1/2 × 2 2/3 = ?

Hint: Convert mixed numbers to improper fractions before multiplying, then simplify your answer

Show the answer

Answer: 9 1/3

  1. Convert 3 1/2 to an improper fraction: (3 × 2 + 1)/2 = 7/2
  2. Convert 2 2/3 to an improper fraction: (2 × 3 + 2)/3 = 8/3
  3. Multiply the fractions: 7/2 × 8/3 = (7 × 8)/(2 × 3) = 56/6
  4. Simplify 56/6 by dividing numerator and denominator by 2: 28/3
  5. Convert 28/3 to a mixed number: 28 ÷ 3 = 9 with remainder 1, so 9 1/3

The answer is 9 1/3.

3 2 3/4 × 1 1/2 = ?

Hint: Convert mixed numbers to improper fractions before multiplying. Remember to simplify your answer.

Show the answer

Answer: 4 1/8

  1. Convert 2 3/4 to an improper fraction: 2 × 4 + 3 = 11/4
  2. Convert 1 1/2 to an improper fraction: 1 × 2 + 1 = 3/2
  3. Multiply the fractions: 11/4 × 3/2 = 33/8
  4. Convert back to a mixed number: 33 ÷ 8 = 4 with remainder 1, so 4 1/8

The answer is 4 1/8.

4 2 1/2 × 3 3/4 = ?

Hint: Convert mixed numbers to improper fractions before multiplying, then simplify the result

Show the answer

Answer: 9 3/8

  1. Convert 2 1/2 to an improper fraction: (2 × 2 + 1)/2 = 5/2
  2. Convert 3 3/4 to an improper fraction: (3 × 4 + 3)/4 = 15/4
  3. Multiply the fractions: 5/2 × 15/4 = (5 × 15)/(2 × 4) = 75/8
  4. Convert 75/8 to a mixed number: 75 ÷ 8 = 9 with remainder 3, so 9 3/8

The answer is 9 3/8.

5 3 1/4 × 2 2/3 = ?

Hint: Convert mixed numbers to improper fractions before multiplying, then simplify your answer.

Show the answer

Answer: 8 2/3

  1. Convert 3 1/4 to an improper fraction: (3 × 4 + 1)/4 = (12 + 1)/4 = 13/4
  2. Convert 2 2/3 to an improper fraction: (2 × 3 + 2)/3 = (6 + 2)/3 = 8/3
  3. Multiply the fractions: 13/4 × 8/3 = (13 × 8)/(4 × 3) = 104/12
  4. Simplify 104/12 by dividing numerator and denominator by 4: 104 ÷ 4 = 26, 12 ÷ 4 = 3, so 26/3
  5. Convert 26/3 to a mixed number: 26 ÷ 3 = 8 with remainder 2, so 8 2/3

The answer is 8 2/3.

6 2 1/2 × 3 1/4 = ?

Hint: Convert mixed numbers to improper fractions before multiplying, then simplify the result.

Show the answer

Answer: 8 1/8

  1. Convert 2 1/2 to an improper fraction: 2 × 2 + 1 = 5, so 2 1/2 = 5/2
  2. Convert 3 1/4 to an improper fraction: 3 × 4 + 1 = 13, so 3 1/4 = 13/4
  3. Multiply the fractions: 5/2 × 13/4 = (5 × 13)/(2 × 4) = 65/8
  4. Convert 65/8 to a mixed number: 65 ÷ 8 = 8 with remainder 1, so 65/8 = 8 1/8
  5. The final answer is 8 1/8
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