Fraction ÷ Whole

Grade 5 · fractions · 41 practice problems · read aloud

🔊 Listen to this explanation

Dividing a Fraction by a Whole Number 🧮

What is it and why is it useful?

Dividing a fraction by a whole number is like splitting a part of something into even smaller, equal parts. You use this when you need to share a fraction of a pizza among friends or divide part of a bag of candy equally.

How to Solve It: Step-by-Step

  1. Write the whole number as a fraction. Put it over 1. For example, 3 becomes 3/1.
  2. Find the reciprocal of the whole number fraction. Flip the numerator and denominator (e.g., the reciprocal of 3/1 is 1/3).
  3. Multiply the first fraction by this reciprocal.
  4. Simplify your answer if possible.

Visual Examples

Example 1: 1/2 ÷ 3

  1. Whole number as fraction: 3 = 3/1
  2. Reciprocal of 3/1 is 1/3
  3. Multiply: 1/2 × 1/3 = (1×1)/(2×3) = 1/6
  4. Answer: 1/6

Imagine half a pizza divided among 3 people. Each person gets 1/6 of the whole pizza.

Example 2: 3/4 ÷ 2

  1. Whole number as fraction: 2 = 2/1
  2. Reciprocal of 2/1 is 1/2
  3. Multiply: 3/4 × 1/2 = (3×1)/(4×2) = 3/8
  4. Answer: 3/8

Common Mistakes to Avoid 🚫

Don't just divide the numerator by the whole number. For 1/2 ÷ 2, the answer is NOT 1/4 by dividing the numerator. You must follow the reciprocal rule!

Don't forget to simplify your final answer. For 2/6 ÷ 2, the calculation gives you 2/12, which simplifies to 1/6.

Tips & Tricks

Memory Aid: "Dividing fractions, as easy as pie, flip the second and multiply!" 🔄

Shortcut: You can also think of it as multiplying the denominator by the whole number. 1/2 ÷ 3 = 1/(2×3) = 1/6. This only works when the numerator is 1!

How to Practice

  • Start with simple fractions with a numerator of 1 (e.g., 1/3 ÷ 2, 1/5 ÷ 4).
  • Use visual models like drawing circles or rectangles and splitting them into parts.
  • Create your own word problems about sharing food or dividing lengths of ribbon.
  • Practice with a friend and explain the steps to each other—teaching is a great way to learn!

Practice problems

6 of the 41, worked through step by step — try them before opening the answer.

1 3/4 ÷ 2 = ?

Hint: When dividing a fraction by a whole number, think about what happens when you split the fraction into equal parts.

Show the answer

Answer: 3/8

  1. Understand the problem. We are dividing the fraction 3/4 by the whole number 2. Division by a number is the same as multiplication by its reciprocal. The reciprocal of 2 is 1/2.
  2. Rewrite the division as multiplication. So, 3/4 ÷ 2 becomes 3/4 × 1/2.
  3. Multiply the fractions. To multiply fractions, multiply the numerators together and multiply the denominators together. Numerator: 3 × 1 = 3 Denominator: 4 × 2 = 8 This gives us the new fraction: 3/8.
  4. Check if the fraction can be simplified. The numbers 3 and 8 have no common factors other than 1, so 3/8 is already in its simplest form. Therefore, the final answer is 3/8.

Let's solve 3/4 ÷ 2 step-by-step.

2 3/4 ÷ 5 = ?

Hint: Remember that dividing by a whole number is the same as multiplying by its reciprocal. For example, 2/3 ÷ 4 = 2/3 × 1/4.

Show the answer

Answer: 3/20

  1. Write the division as a multiplication by the reciprocal: 3/4 ÷ 5 = 3/4 × 1/5
  2. Multiply the numerators: 3 × 1 = 3
  3. Multiply the denominators: 4 × 5 = 20
  4. Combine the results: 3/20

The answer is 3/20.

3 2/3 ÷ 4 = ?

Hint: Remember that dividing a fraction by a whole number is the same as multiplying by the reciprocal of that number.

Show the answer

Answer: 1/6

  1. Write the problem as a fraction division: 2/3 ÷ 4
  2. Write the whole number as a fraction: 2/3 ÷ 4/1
  3. Change division to multiplication by the reciprocal: 2/3 × 1/4
  4. Multiply the numerators: 2 × 1 = 2
  5. Multiply the denominators: 3 × 4 = 12
  6. Simplify the fraction: 2/12 = 1/6

The answer is 1/6.

4 5/6 ÷ 4 = ?

Hint: Remember that dividing a fraction by a whole number is the same as multiplying by the reciprocal of that number.

Show the answer

Answer: 5/24

  1. Write the division as a fraction: 5/6 ÷ 4 = (5/6) ÷ (4/1)
  2. Change division to multiplication by the reciprocal: (5/6) × (1/4)
  3. Multiply the numerators: 5 × 1 = 5
  4. Multiply the denominators: 6 × 4 = 24
  5. Write the result: 5/24

The answer is 5/24.

5 3/4 ÷ 6 = ?

Hint: Remember that dividing a fraction by a whole number is the same as multiplying by the reciprocal of that whole number.

Show the answer

Answer: 1/8

  1. Write the problem: 3/4 ÷ 6
  2. Dividing by 6 is the same as multiplying by 1/6, so rewrite as: 3/4 × 1/6
  3. Multiply the numerators: 3 × 1 = 3
  4. Multiply the denominators: 4 × 6 = 24
  5. The result is 3/24
  6. Simplify the fraction by dividing numerator and denominator by 3: 3 ÷ 3 = 1, 24 ÷ 3 = 8
  7. The simplified fraction is 1/8

The answer is 1/8.

6 7/8 ÷ 5 = ?

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

Show the answer

Answer: 7/40

  1. Write the problem: 7/8 ÷ 5
  2. Write the whole number as a fraction: 7/8 ÷ 5/1
  3. Change division to multiplication by the reciprocal: 7/8 × 1/5
  4. Multiply the numerators: 7 × 1 = 7
  5. Multiply the denominators: 8 × 5 = 40
  6. Write the result: 7/40

The answer is 7/40.

Practise this topic — 10 free problems, no signup →