Dividing Fractions by Whole Numbers KS2

Dividing a fraction by a whole number (like 3/4 ÷ 2) is a key KS2 maths skill. The rule is simple: keep the fraction the same, change ÷ to ×, and flip the whole number into a fraction (e.g., 2 becomes 1/2), then multiply across. This page explains the method step by step, with worked examples, common mistakes, and practice questions.

Formula

To divide a fraction by a whole number, use this formula:

a/b ÷ w = a / (b × w)

Where:

• a = numerator (top number of the fraction)
• b = denominator (bottom number of the fraction)
• w = whole number (the number you are dividing by)

So you keep the numerator the same, multiply the denominator by the whole number, and simplify if possible.

Worked Example

Using the calculator defaults: 3/4 ÷ 2

1. Keep the numerator: 3
2. Multiply the denominator by the whole number: 4 × 2 = 8
3. Write the result: 3/8
4. Simplify: 3/8 is already in simplest form (3 and 8 share no common factor other than 1).

So 3/4 ÷ 2 = 3/8. In decimal, that is 0.375. The calculator shows the same: a/(b×w) = 3/(4×2) = 3/8.

Why This Works: The Visual Idea

Think of a fraction as a part of a whole. Dividing by a whole number splits that part into smaller equal pieces. For example, 3/4 of a pizza divided among 2 people means each person gets half of 3/4, which is 3/8 of the whole pizza. The denominator doubles because you are cutting each quarter into two smaller pieces.

Another way to see it: dividing by 2 is the same as multiplying by 1/2. So 3/4 ÷ 2 = 3/4 × 1/2 = (3×1)/(4×2) = 3/8.

Step-by-Step Method for KS2

Here is the standard method taught in Key Stage 2 (ages 7–11):

1. Write the whole number as a fraction with denominator 1 (e.g., 2 becomes 2/1).
2. Change the division sign to multiplication.
3. Flip the second fraction (the whole number fraction) upside down. So 2/1 becomes 1/2.
4. Multiply the numerators together and the denominators together.
5. Simplify the answer if possible (find the greatest common factor).

Example: 5/6 ÷ 3

• 3 as a fraction = 3/1
• 5/6 ÷ 3/1 = 5/6 × 1/3
• Multiply: (5×1)/(6×3) = 5/18
• 5/18 is already in simplest form.

Common Mistakes and How to Avoid Them

• Forgetting to flip the whole number: Some students multiply by the whole number instead of its reciprocal. Remember: division by a number is the same as multiplication by its reciprocal.
• Multiplying the numerator by the whole number: The correct rule is to multiply the denominator only. For example, 3/4 ÷ 2 = 3/8, not 6/4.
• Not simplifying: Always check if the final fraction can be reduced. For instance, 2/4 ÷ 2 = 2/8, which simplifies to 1/4.
• Mixed numbers: If you have a mixed number (like 1 1/2), convert it to an improper fraction first (3/2) before dividing.

When to Use This in Real Life

This skill appears in many everyday situations:

• Sharing food: If you have 3/4 of a cake and want to share it equally among 3 people, each gets 3/4 ÷ 3 = 1/4 of the whole cake.
• Cutting lengths: A 2/3 metre ribbon cut into 4 equal pieces gives each piece 2/3 ÷ 4 = 1/6 metre.
• Scaling recipes: Halving a recipe that uses 1/2 cup of sugar means you need 1/2 ÷ 2 = 1/4 cup.

Understanding this also builds a foundation for algebra and more advanced fraction work in secondary school.

Practice Questions

Try these (answers at the end):

1. 1/2 ÷ 3
2. 2/5 ÷ 4
3. 7/8 ÷ 2
4. 3/10 ÷ 5

Answers: 1) 1/6, 2) 1/10, 3) 7/16, 4) 3/50

Frequently Asked Questions

What is the rule for dividing a fraction by a whole number?
Keep the fraction, change ÷ to ×, flip the whole number to its reciprocal (e.g., 2 becomes 1/2), then multiply across. Simplify if needed.

Why do we flip the whole number?
Because dividing by a number is the same as multiplying by its reciprocal. For example, dividing by 2 is the same as multiplying by 1/2. This works for any number, including fractions.

What if the whole number is 0?
You cannot divide by zero. Division by 0 is undefined in maths. So a fraction divided by 0 has no answer.

Do I need to simplify the answer?
Yes, it is good practice to give the fraction in its simplest form. For example, 4/8 should be written as 1/2. If the numerator is larger than the denominator, you can also write it as a mixed number.

How is this different from dividing a whole number by a fraction?
When dividing a whole number by a fraction, you flip the fraction and multiply. For example, 2 ÷ 3/4 = 2 × 4/3 = 8/3. The key difference is which number is the divisor.

Can I use a calculator for this?
Yes, but it is important to understand the method. The calculator above shows the result as a fraction and a decimal, but you should still be able to do it by hand for tests and homework.

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in a | Numerator | - | 3 | 0
in b | Denominator | - | 4 | 0
in w | Whole number | - | 2 | 0
out frac | Result (fraction) | - | a / (b * w) | 4
out dec | Result (decimal) | - | a / (b * w) | 4