Multiplying a Fraction by a Whole Number KS2

Multiplying a fraction by a whole number at KS2 (Key Stage 2, ages 7–11) means finding a fraction of a whole number, such as working out 2/3 of 12. You do this by multiplying the numerator (top number) by the whole number, keeping the denominator (bottom number) the same, then simplifying if needed.

Formula

The rule is simple: multiply the numerator by the whole number, then divide by the denominator. In symbols:

Result = (whole number × numerator) ÷ denominator

Or as a single fraction:

(a × b) / c

Where:

• a = the whole number (e.g., 12)
• b = the numerator of the fraction (e.g., 2 in 2/3)
• c = the denominator of the fraction (e.g., 3 in 2/3)

The answer is a number (which may be an integer, a decimal, or a mixed number). For example, 2/3 × 12 = 8.

Worked Example

Using the calculator defaults: a = 12, b = 2, c = 3.

1. Multiply the whole number by the numerator: 12 × 2 = 24
2. Divide by the denominator: 24 ÷ 3 = 8

So 2/3 × 12 = 8. The calculator shows 8.00 (rounded to 2 decimal places).

Why This Works

Think of “2/3 of 12” as splitting 12 into 3 equal parts (each part is 4) and then taking 2 of those parts (2 × 4 = 8). That is exactly what the formula does: divide by the denominator first, then multiply by the numerator. The order doesn’t matter – you can multiply first then divide (as above) or divide first then multiply. Both give the same answer.

This is a key KS2 concept because it connects fractions to division and multiplication. It appears in real contexts like recipes (e.g., “use 2/3 of a 12-egg box”), measurements, and sharing amounts fairly.

Common Mistakes and How to Avoid Them

• Multiplying the denominator too. Many children multiply both top and bottom by the whole number. Only the numerator changes. The denominator stays the same unless you simplify later.
• Forgetting to simplify. If the answer is an improper fraction (e.g., 9/4), convert it to a mixed number (2 1/4) or simplify if possible. For example, 4/6 simplifies to 2/3.
• Confusing “of” with multiplication. In word problems, “of” means multiply. “Find 3/4 of 20” is the same as 3/4 × 20.
• Not reducing before multiplying. You can cancel common factors between the whole number and the denominator first. For example, 5/6 × 12: cancel 6 and 12 to get 5/1 × 2 = 10. This makes the arithmetic easier.

How to Read the Result

The result is the exact value of the fraction of the whole number. If the result is a whole number (like 8), that means the fraction divides the whole number evenly. If it is a decimal (like 2.5), you can also write it as a mixed number (2 1/2). In KS2, children are expected to give answers as fractions or mixed numbers, not always decimals.

For example, 3/4 × 10 = 7.5. As a fraction, that is 7 1/2 or 15/2. Both are correct, but the context may require one form.

When to Use This in Real Life

This skill is used whenever you need a part of a quantity:

• Cooking: halving a recipe that uses 3/4 cup of sugar (3/4 × 2 = 1 1/2 cups for double).
• Money: finding 1/4 of £20 to work out a quarter.
• Measurement: 2/3 of a metre of ribbon.
• Time: 3/4 of an hour (3/4 × 60 = 45 minutes).

It also builds the foundation for multiplying fractions by each other (which you learn later) and for understanding percentages (which are fractions out of 100).

Frequently Asked Questions

What is the rule for multiplying a fraction by a whole number?

Multiply the numerator (top number) by the whole number, keep the denominator the same, then simplify if possible. For example, 2/5 × 3 = (2×3)/5 = 6/5 = 1 1/5.

Why do we not multiply the denominator?

The denominator tells you how many equal parts the whole is divided into. Multiplying the whole number only changes how many parts you have (the numerator), not the size of each part. If you multiplied the denominator, you would change the size of the parts, which would give a wrong answer.

How do you multiply a mixed number by a whole number?

First convert the mixed number to an improper fraction. For example, 1 1/2 becomes 3/2. Then multiply the numerator by the whole number: 3/2 × 4 = 12/2 = 6. Or you can multiply the whole part and the fraction separately and add: (1×4) + (1/2×4) = 4 + 2 = 6.

What if the fraction is more than one whole, like 5/3?

That is fine. Multiply as usual: 5/3 × 6 = 30/3 = 10. The answer can be larger than the original whole number when the fraction is greater than 1.

Should the answer be a fraction or a decimal?

In KS2, both are acceptable, but the question usually asks for a specific form. If it says “give your answer as a fraction,” use a fraction or mixed number. If it says “give your answer as a decimal,” convert. For example, 3/4 × 5 = 15/4 = 3.75.

How can I check my answer?

Use the inverse operation: divide your answer by the whole number and see if you get the original fraction. For example, if 2/3 × 12 = 8, then 8 ÷ 12 = 2/3, which is correct. Or use a calculator to verify.

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in a | Whole number | - | 12 | 0
in b | Numerator | - | 2 | 0
in c | Denominator | - | 3 | 0
out result | Fraction × whole number | - | (a * b) / c | 2