Whole ÷ Fraction

Grade 5 · fractions · 77 practice problems · read aloud

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Dividing a Whole Number by a Fraction 🧮

What is it and Why is it Useful?

This operation asks: "How many parts of a fraction fit into a whole number?" It's super useful for real-life problems! For example, if you have 3 meters of ribbon and need pieces that are ¾ of a meter long, how many pieces can you cut? Dividing a whole by a fraction gives you the answer!

How to Solve: Step-by-Step

  1. Write the whole number as a fraction. Put the whole number over 1. (e.g., 5 becomes 5/1).
  2. Flip the divisor fraction. This is called finding the reciprocal. Flip the numerator and denominator of the fraction you are dividing by.
  3. Change the sign. Change the division sign (÷) to a multiplication sign (×).
  4. Multiply the fractions. Multiply the numerators together and the denominators together.
  5. Simplify your answer. Write the answer as a whole or mixed number if possible.

Visual Examples

Example 1: 4 ÷ ½

  1. 4 becomes 4/1
  2. Flip ½ to get 2/1
  3. Change to multiplication: (4/1) × (2/1)
  4. Multiply: (4 × 2) / (1 × 1) = 8/1
  5. Simplify: 8

Think: How many halves are in 4 wholes? There are 8 halves! ✅

Example 2: 3 ÷ ¾

  1. 3 becomes 3/1
  2. Flip ¾ to get 4/3
  3. Change to multiplication: (3/1) × (4/3)
  4. Multiply: (3 × 4) / (1 × 3) = 12/3
  5. Simplify: 12 ÷ 3 = 4

Think: How many three-quarter cups can you fill with 3 cups of juice? You can fill 4! ✅

Common Mistakes to Avoid ⚠️

Forgetting to Flip the Fraction: The biggest mistake is dividing straight across without finding the reciprocal. Remember: KEEP, CHANGE, FLIP!

Not Converting the Whole Number: Always write the whole number as a fraction over 1 first. This makes the multiplication step much easier.

Flipping the Wrong Number: Only flip the second fraction (the divisor), not the first one!

Tips & Tricks

Memory Aid: Use the phrase "Keep, Change, Flip!"

  • KEEP the first number the same.
  • CHANGE ÷ to ×.
  • FLIP the second fraction.

Real-World Connection: Imagine you are cutting a whole pizza into slices. The question "How many ¼-pizza slices are in 2 pizzas?" is 2 ÷ ¼. You'd get 8 slices!

How to Practice

  • Start with simple fractions like ½ and ¼ to build confidence.
  • Draw pictures! Use circles (like pizzas) or rectangles divided into parts to see the math in action.
  • Create your own word problems. For example, "I have 5 yards of fabric. Each bookmark uses ⅓ yard. How many bookmarks can I make?"
  • Practice with a friend and explain the "Keep, Change, Flip" rule to them. Teaching is a great way to learn!

Practice problems

6 of the 77, worked through step by step — try them before opening the answer.

1 8 ÷ 2/3 = ?

Hint: Think about how many groups of a certain size fit into the whole number.

Show the answer

Answer: 12

  1. Understand the problem We are dividing 8 by the fraction 2/3. The expression is: 8 ÷ 2/3
  2. Recall the rule for dividing by a fraction Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/3 is 3/2.
  3. Rewrite the division as multiplication So, 8 ÷ 2/3 becomes 8 × 3/2.
  4. Multiply First, multiply 8 by the numerator 3: 8 × 3 = 24
  5. Divide by the denominator Now divide 24 by the denominator 2: 24 ÷ 2 = 12
  6. Conclusion Therefore, 8 ÷ 2/3 = 12.

2 8 ÷ 1/4 = ?

Hint: Think about how many one-quarter pieces fit into a whole number. For example, how many one-half pieces fit into the number 2?

Show the answer

Answer: 32

  1. Understand the division by a fraction. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 1/4 is 4/1, which is just 4.
  2. Rewrite the division as multiplication. So, 8 ÷ 1/4 becomes 8 × 4.
  3. Perform the multiplication. 8 × 4 = 32
  4. Final answer. Therefore, 8 ÷ 1/4 = 32.

Step-by-step solution: We are solving: 8 ÷ 1/4

3 12 ÷ 2/3 = ?

Hint: When dividing a whole number by a fraction, think about how many of those fractional parts fit into the whole number.

Show the answer

Answer: 18

  1. Understand the division by a fraction. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 2/3 is 3/2.
  2. Rewrite the expression: 12 ÷ 2/3 = 12 × 3/2
  3. Multiply 12 by 3/2: First, multiply 12 by 3: 12 × 3 = 36
  4. Now divide 36 by 2: 36 ÷ 2 = 18
  5. Final answer: 12 ÷ 2/3 = 18

We are given: 12 ÷ 2/3

4 15 ÷ 3/4 = ?

Hint: Remember that dividing by a fraction is the same as multiplying by its reciprocal.

Show the answer

Answer: 20

  1. Start with 15 ÷ 3/4
  2. Dividing by a fraction is the same as multiplying by its reciprocal, so this becomes 15 × 4/3
  3. Multiply 15 by 4 to get 60
  4. Divide 60 by 3 to get 20
  5. The answer is 20

5 18 ÷ 2/3 = ?

Hint: Remember that dividing by a fraction is the same as multiplying by its reciprocal

Show the answer

Answer: 27

  1. Write the problem: 18 ÷ 2/3
  2. Dividing by a fraction is the same as multiplying by its reciprocal
  3. The reciprocal of 2/3 is 3/2
  4. Rewrite as multiplication: 18 × 3/2
  5. Multiply 18 by 3: 18 × 3 = 54
  6. Divide 54 by 2: 54 ÷ 2 = 27
  7. The answer is 27

6 24 ÷ 3/4 = ?

Hint: Remember that dividing by a fraction is the same as multiplying by its reciprocal. For example, 10 ÷ 1/2 = 20.

Show the answer

Answer: 32

  1. Write the division problem: 24 ÷ 3/4
  2. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 3/4 is 4/3.
  3. Rewrite the problem as multiplication: 24 × 4/3
  4. Multiply 24 by the numerator: 24 × 4 = 96
  5. Divide by the denominator: 96 ÷ 3 = 32
  6. The answer is 32.
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