Lesson 14.2 · 25 min

Multiplying and Dividing Decimals

Knowing whether an answer will be bigger or smaller, multiplying decimals without a calculator, and dividing by making the divisor a whole number.

In this lesson you will learn to…

Predict whether multiplying or dividing by a number makes the answer bigger or smaller
Multiply decimals by working with whole numbers and placing the point
Divide by a decimal by first turning the divisor into a whole number
Handle negative decimals

Why this matters

It is a very common belief that multiplying always makes things bigger and dividing always makes them smaller. That is only true for numbers greater than 1 — and prices, measurements and rates are often decimals less than 1.

The rule in action

Calculation	Answer	Compared with 4
$4 \times 2.5$	10	bigger
$4 \times 0.1$	0.4	smaller
$4 \div 0.5$	8	bigger
$4 \div 2$	2	smaller

So $43.5 \times 0.986 = 45.891$ must be wrong without working it out: multiplying by a number less than 1 has to make 43.5 smaller.

Fatima’s fraction method also works: $6.24 \div 0.4 = \frac{624}{100} \div \frac{4}{10} = \frac{624}{100} \times \frac{10}{4} = 15.6$ .

Key rules and formulas

Bigger or smaller?
Multiplying by a number between 0 and 1 makes a positive number smaller; by more than 1, bigger. Dividing is the other way round: dividing by a number between 0 and 1 makes it bigger.
Multiplying decimals
Ignore the decimal points and multiply the whole numbers. Then count the total number of decimal places in the question — the answer has the same number. Check with an estimate.
Dividing by a decimal
$0.028 \div 0.04 = \frac{0.028 \times 100}{0.04 \times 100} = \frac{2.8}{4} = 0.7$
Multiply both numbers by 10, 100, … until the divisor is a whole number. The answer does not change.

Worked examples

Worked example 1

Multiplying

Work out

0.68 \times 0.045

Try it yourself first, then reveal the solution one step at a time.

Worked example 2

Dividing

Work out

17.37 \div 0.03

Try it yourself first, then reveal the solution one step at a time.

Worked example 3

Negatives

Work out

- 13.2 \div - 0.11

Try it yourself first, then reveal the solution one step at a time.

Practice: multiplying and dividing decimals

10 questions

Ten questions, no calculator.

Question 1 of 10Choose all that applyFoundation
Which calculations have answers less than 30?
Select every correct answer — there may be more than one.
$30 \times 0.5$ $30 \times \frac{1}{3}$ $30 \div 2.7$ $30 \times 1.8$ $30 \div 0.1$ $30 \div 0.8$
Question 2 of 10Quick-fire drill
Quick-fire: multiply.
8 questions · 75 seconds · answer as many as you can.
Question 3 of 10Type the answer
Work out $0.68 \times 0.045$ .
Your answer
Question 4 of 10Quick-fire drill
Quick-fire: divide.
8 questions · 75 seconds · answer as many as you can.
Question 5 of 10Step by step
Divide one step at a time.
Work out $0.028 \div 0.04$ .
1. What must you multiply both numbers by to make 0.04 a whole number?
  Step 1 answer
Question 6 of 10Choose all that apply
Which answers are clearly incorrect?
Select every correct answer — there may be more than one.
$3.8 \times 1.6 = 2.28$ $59 \div 2.5 = 23.6$ $47 \times 0.83 = 39.01$ $17 \div 0.32 = 5.44$
Question 7 of 10Type the answer
A ball of string contains 21.6 m. How many 0.16 m lengths can be cut from it?
Your answer
Question 8 of 10Type the answer
How many 0.3-litre bottles can be filled from an urn containing 45.9 litres?
Your answer
Question 9 of 10Type the answer
A field has area 100.8 m² and length 14.4 m. What is its width?
Your answerm
Question 10 of 10Type the answerChallenge
Work out $30 + 2.8 \div 0.04$ .
Your answer

In this lesson you will learn to…

Why this matters

The rule in action

Key rules and formulas

Bigger or smaller?

Multiplying decimals

Dividing by a decimal

Worked examples

Practice: multiplying and dividing decimals