Multiplying & Dividing Decimals — KS3 Maths

Both of these turn into whole-number arithmetic, and each has one job to do with the point. Multiplying: count the decimal places in the question and put the same number back into the answer. Dividing: clear the bottom — scale both numbers up until the one you're dividing by is a whole number.

How do you multiply decimals?

Worked example

0.6 × 0.4 (the surprising one)

Ignore the points and multiply the digits: $6 \times 4 = 24$. Now count the decimal places — one in $0.6$ and one in $0.4$ makes two. So put the point two places in:

$0.6 \times 0.4 = 0.24$

It's $0.24$, not $2.4$ — because you're multiplying by less than one, the answer comes out smaller than what you started with.

Worked example

0.3 × 7

Ignore the point: $3 \times 7 = 21$. There is one decimal place in the question (in $0.3$), so one in the answer:

$0.3 \times 7 = 2.1$

How do you divide by a decimal?

Worked example

4.8 ÷ 0.6

Make the number you're dividing by ($0.6$) a whole number by multiplying both numbers by 10:

$4.8 \div 0.6 = 48 \div 6 = 8$

Multiplying both numbers by the same amount keeps the answer the same — but now it's an easy whole-number division.

Worked example

0.84 ÷ 0.4

Multiply both by 10 to clear the bottom, then divide:

$0.84 \div 0.4 = 8.4 \div 4 = 2.1$

Going further

Why does counting the places work? Because a decimal is a fraction in disguise. $0.6 \times 0.4$ is $\tfrac{6}{10} \times \tfrac{4}{10}$, and multiplying fractions multiplies the bottoms: $\tfrac{24}{100}$, which is $0.24$. One place plus one place makes two places because ten times ten makes a hundred. The multiplying fractions lesson is the same rule in the other notation.

Why is scaling both numbers allowed when dividing? A division is a fraction, and multiplying top and bottom by the same amount leaves a fraction unchanged — the same fact behind equivalent fractions. So $4.8 \div 0.6$ and $48 \div 6$ are genuinely the same question.

Where you'll use this next

• Best value and unit pricing — cost per 100 g is a decimal division.
• Area and volume of shapes with decimal measurements.
• Scaling recipes and conversions, where you multiply by a decimal factor.

Practice questions

Use the count-the-places method to multiply, and clear the bottom to divide. Then click to check.