Mixed Number Division

Grade 6 · mathematics · 73 practice problems · read aloud

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Dividing Mixed Numbers 🧮

What is Mixed Number Division?

It's a way to split a whole number with a fraction by another whole number with a fraction. We use this when sharing things like pizza, measuring ingredients for a recipe, or dividing up lengths of ribbon.

How to Solve: Step-by-Step

  1. Convert to Improper Fractions: Change each mixed number to a fraction where the numerator is larger than the denominator.
  2. Keep, Change, Flip: Keep the first fraction, change the division sign (÷) to multiplication (×), and flip the second fraction (find its reciprocal).
  3. Multiply the Fractions: Multiply the numerators together and the denominators together.
  4. Simplify: Simplify your answer. If it's an improper fraction, convert it back to a mixed number.

Worked Examples

Example 1: 2 ½ ÷ 1 ¼

  1. Convert: 2 ½ = 5/2, 1 ¼ = 5/4
  2. Keep, Change, Flip: 5/2 × 4/5
  3. Multiply: (5 × 4) / (2 × 5) = 20/10
  4. Simplify: 20/10 = 2

Example 2: 3 ⅓ ÷ 1 ½

  1. Convert: 3 ⅓ = 10/3, 1 ½ = 3/2
  2. Keep, Change, Flip: 10/3 × 2/3
  3. Multiply: (10 × 2) / (3 × 3) = 20/9
  4. Simplify: 20/9 = 2 2/9

⚠️ Common Mistakes to Avoid

  • Forgetting to convert: Never try to divide the whole numbers and fractions separately. Always convert to improper fractions first!
  • Skipping the flip: Remember, you must find the reciprocal of the second fraction only.
  • Not simplifying: Always give your final answer in simplest form.

🌟 Tips & Tricks

  • Memory Aid: Use the phrase "Keep, Change, Flip" to remember the steps.
  • Cross-Cancel: Before multiplying, see if you can simplify diagonally across the multiplication sign.
  • Check your work: Does your answer make sense? If you're dividing by a number greater than 1, your answer should be smaller than what you started with.

How to Practice

Start with simple problems like 2 ½ ÷ 2. Create your own problems using measuring cups or a pizza! Ask a friend to solve a problem, then you check their work. Use online math games focused on fraction division for extra fun practice.

Practice problems

6 of the 73, worked through step by step — try them before opening the answer.

1 4 2/3 ÷ 1 1/6 = ?

Hint: Convert mixed numbers to improper fractions before dividing. Remember that dividing by a fraction is the same as multiplying by its reciprocal.

Show the answer

Answer: 4

  1. Convert 4 2/3 to an improper fraction: (4 × 3 + 2)/3 = (12 + 2)/3 = 14/3
  2. Convert 1 1/6 to an improper fraction: (1 × 6 + 1)/6 = (6 + 1)/6 = 7/6
  3. Rewrite the division as multiplication by the reciprocal: 14/3 ÷ 7/6 = 14/3 × 6/7
  4. Multiply the fractions: (14 × 6)/(3 × 7) = 84/21
  5. Simplify the fraction: 84 ÷ 21 = 4

The answer is 4.

2 3 1/2 ÷ 2 1/4 = ?

Hint: Convert mixed numbers to improper fractions before dividing, then multiply by the reciprocal of the divisor.

Show the answer

Answer: 1 5/9

  1. Convert 3 1/2 to an improper fraction: 3 1/2 = (3 × 2 + 1)/2 = 7/2
  2. Convert 2 1/4 to an improper fraction: 2 1/4 = (2 × 4 + 1)/4 = 9/4
  3. Rewrite the division as multiplication by the reciprocal: 7/2 ÷ 9/4 = 7/2 × 4/9
  4. Multiply the fractions: (7 × 4)/(2 × 9) = 28/18
  5. Simplify the fraction: 28/18 = 14/9
  6. Convert to a mixed number: 14/9 = 1 5/9

The answer is 1 5/9.

3 3 1/3 ÷ 2 1/2 = ?

Hint: Convert mixed numbers to improper fractions before dividing, then multiply by the reciprocal of the divisor.

Show the answer

Answer: 1 1/3

  1. Convert 3 1/3 to an improper fraction: 3 1/3 = (3 × 3 + 1)/3 = (9 + 1)/3 = 10/3
  2. Convert 2 1/2 to an improper fraction: 2 1/2 = (2 × 2 + 1)/2 = (4 + 1)/2 = 5/2
  3. Rewrite the division as multiplication by the reciprocal: 10/3 ÷ 5/2 = 10/3 × 2/5
  4. Multiply the fractions: (10 × 2)/(3 × 5) = 20/15
  5. Simplify the fraction: 20/15 = 4/3
  6. Convert to a mixed number: 4/3 = 1 1/3

The answer is 1 1/3.

4 3 1/3 ÷ 1 2/5 = ?

Hint: Convert mixed numbers to improper fractions before dividing, then multiply by the reciprocal of the divisor.

Show the answer

Answer: 2 2/7

  1. Convert 3 1/3 to an improper fraction: (3 × 3 + 1)/3 = 10/3
  2. Convert 1 2/5 to an improper fraction: (1 × 5 + 2)/5 = 7/5
  3. Rewrite the division as multiplication by the reciprocal: 10/3 ÷ 7/5 = 10/3 × 5/7
  4. Multiply the fractions: (10 × 5)/(3 × 7) = 50/21
  5. Convert 50/21 to a mixed number: 50 ÷ 21 = 2 with remainder 8, so 2 8/21
  6. Simplify 8/21: The fraction 8/21 is already in simplest form since 8 and 21 share no common factors
  7. The final answer is 2 8/21

5 3 1/2 ÷ 1 3/4 = ?

Hint: Convert mixed numbers to improper fractions before dividing. Remember that dividing by a fraction is the same as multiplying by its reciprocal.

Show the answer

Answer: 2

  1. Convert 3 1/2 to an improper fraction: 3 1/2 = (3 × 2 + 1)/2 = 7/2
  2. Convert 1 3/4 to an improper fraction: 1 3/4 = (1 × 4 + 3)/4 = 7/4
  3. Rewrite the division: 7/2 ÷ 7/4
  4. Change division to multiplication by the reciprocal: 7/2 × 4/7
  5. Multiply the fractions: (7 × 4)/(2 × 7) = 28/14
  6. Simplify the fraction: 28 ÷ 14 = 2

The answer is 2.

6 3 1/3 ÷ 1 1/4 = ?

Hint: Convert mixed numbers to improper fractions before dividing, then multiply by the reciprocal of the divisor.

Show the answer

Answer: 2 2/3

  1. Convert 3 1/3 to an improper fraction: (3 × 3 + 1)/3 = (9 + 1)/3 = 10/3
  2. Convert 1 1/4 to an improper fraction: (1 × 4 + 1)/4 = (4 + 1)/4 = 5/4
  3. Rewrite the division as multiplication by the reciprocal: 10/3 ÷ 5/4 = 10/3 × 4/5
  4. Multiply the fractions: (10 × 4)/(3 × 5) = 40/15
  5. Simplify the fraction: 40 ÷ 5 = 8, 15 ÷ 5 = 3, so 40/15 = 8/3
  6. Convert back to a mixed number: 8 ÷ 3 = 2 with remainder 2, so 8/3 = 2 2/3

The answer is 2 2/3.

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