Multiplication and Division
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Revision notes for Edexcel GCSE Maths Multiplication and Division. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.

Multiplication and Division

What you'll learn

  • How to multiply whole numbers using place value.
  • How to divide by a one-digit number.
  • How to multiply and divide decimals carefully.
  • How to check whether your answer is sensible.

The basics: digits and place value

A digit is one symbol in a number, such as 0, 1, 2, 3, and so on.

Definition

Place value

Place value means the value of a digit depending on where it is in the number: hundreds, tens, ones, tenths, hundredths, and so on.

For example, in 463, the 4 means 400, the 6 means 60, and the 3 means 3.

A place value chart showing how each digit in 463 represents hundreds, tens and ones.

Example

Breaking a number into place value parts

Break 572 into hundreds, tens, and ones.

Place value chart showing that 572 is made from 5 hundreds, 7 tens and 2 ones.

  1. Look at the hundreds digit: 5 hundreds means 500.

  2. Look at the tens digit: 7 tens means 70.

  3. Look at the ones digit: 2 ones means 2.

  4. Write the number as a sum:

    572=500+70+2572 = 500 + 70 + 2572=500+70+2
Key Idea

Use place value

Harder multiplications and divisions become easier when you split numbers into hundreds, tens, and ones.

Multiplication

Definition

Multiplication

Multiplication means finding the total when you have equal groups. The answer to a multiplication is called the product.

For example, 6 groups of 4 gives a total of 24.

Multiplying by a one-digit number

When multiplying a 3-digit number by a 1-digit number, split the bigger number into place value parts.

Example

Multiplying by a one-digit number

Work out 246 multiplied by 7.

An area model splitting 246 into place value parts before multiplying each part by 7.

Area model splitting 246 into 200, 40 and 6 before multiplying each part by 7.

  1. Split 246 into hundreds, tens, and ones:

    246=200+40+6246 = 200 + 40 + 6246=200+40+6

  2. Multiply each part by 7:

    200×7=140040×7=2806×7=42\begin{aligned} 200 \times 7 &= 1400\\ 40 \times 7 &= 280\\ 6 \times 7 &= 42 \end{aligned}200×740×76×7​=1400=280=42​

  3. Add the three answers:

    1400+280+42=17221400 + 280 + 42 = 17221400+280+42=1722

  4. So 246 multiplied by 7 is 1722.

Common Mistake

Forgetting one part

If you split a number into parts, make sure every part is used. For 246, you need 200, 40, and 6.

Division

Definition

Division

Division means sharing into equal groups. The answer to a division is called the quotient.

In a division, the number being divided is the dividend. The number you divide by is the divisor.

Dividing by a one-digit number

For Grade 1 questions, try to split the number into parts that divide easily.

Example

Dividing by a one-digit number

Work out 936 divided by 8.

A bar model showing 936 split into parts that are easy to divide by 8.

Bar model showing 936 split into parts that divide exactly by 8.

  1. Split 936 into parts that divide by 8:

    936=800+80+56936 = 800 + 80 + 56936=800+80+56

  2. Divide each part by 8:

    800÷8=10080÷8=1056÷8=7\begin{aligned} 800 \div 8 &= 100\\ 80 \div 8 &= 10\\ 56 \div 8 &= 7 \end{aligned}800÷880÷856÷8​=100=10=7​

  3. Add the answers:

    100+10+7=117100 + 10 + 7 = 117100+10+7=117

  4. So 936 divided by 8 is 117.

Common Mistake

Never divide by zero

You cannot divide by 0. A calculation such as 12 divided by 0 has no ordinary GCSE answer.

Multiplying by a two-digit number

A two-digit number has tens and ones, like 34 or 58.

To multiply by a two-digit number, split it into tens and ones.

Example

Multiplying by tens and ones

Work out 62 multiplied by 34.

A grid method diagram showing 62 multiplied by the tens and ones parts of 34.

Grid method showing 62 multiplied by the tens and ones parts of 34.

  1. Split 34 into 30 and 4:

    34=30+434 = 30 + 434=30+4

  2. Multiply 62 by each part:

    62×30=186062×4=248\begin{aligned} 62 \times 30 &= 1860\\ 62 \times 4 &= 248 \end{aligned}62×3062×4​=1860=248​

  3. Add the two answers:

    1860+248=21081860 + 248 = 21081860+248=2108

  4. So 62 multiplied by 34 is 2108.

Tip

Remember the tens row

Multiplying by 30 means multiplying by 3 tens, so the answer is ten times bigger than multiplying by 3.

Decimals and the decimal point

Definition

Decimal point

The decimal point separates the whole number part from the decimal part. For example, in 18.7, the whole number part is 18 and the decimal part is 7 tenths.

Definition

Decimal places

The number of decimal places is how many digits are to the right of the decimal point. For example, 4.25 has 2 decimal places.

Multiplying decimals by a whole number

A helpful method is:

  • Ignore the decimal point for a moment.
  • Multiply as whole numbers.
  • Put the decimal point back by counting decimal places.
Example

Multiplying a decimal by a whole number

Work out 18.7 multiplied by 6.

A decimal-place diagram showing how 18.7 is multiplied as 187 and then one decimal place is restored.

Decimal-place diagram showing 18.7 changed to 187 for multiplication, then one decimal place restored.

  1. Ignore the decimal point and multiply 187 by 6:

    187×6=1122187 \times 6 = 1122187×6=1122

  2. The number 18.7 has 1 decimal place.

  3. Put 1 decimal place into the answer:

    1122→112.21122 \to 112.21122→112.2

  4. So 18.7 multiplied by 6 is 112.2.

Multiplying one decimal by another decimal

When both numbers have decimals, count the total number of decimal places in both numbers.

Example

Multiplying two decimals

Work out 42.1 multiplied by 6.3.

A decimal-place count showing that multiplying 42.1 by 6.3 gives an answer with two decimal places.

Decimal-place count showing that the final product must have two decimal places.

  1. Ignore the decimal points:

    421×63=26523421 \times 63 = 26523421×63=26523

  2. Count the decimal places: 42.1 has 1 decimal place and 6.3 has 1 decimal place.

  3. The answer needs 2 decimal places in total:

    26523→265.2326523 \to 265.2326523→265.23

  4. So 42.1 multiplied by 6.3 is 265.23.

Common Mistake

Putting the decimal point in the wrong place

Do not just copy the decimal point from the question. Count the decimal places in the numbers you multiplied.

Tip

Estimate first

Round the numbers to check your answer. For example, 42.1 multiplied by 6.3 is about 40 multiplied by 6, which is about 240, so 265.23 is sensible.

Dividing decimals by a whole number

When dividing a decimal by a whole number, keep the decimal places carefully.

Example

Dividing a decimal by a whole number

Work out 45.36 divided by 9.

A place value diagram showing 45.36 as 4536 hundredths before dividing by 9.

Place value diagram showing 45.36 as 4536 hundredths before division.

  1. Think of 45.36 as 4536 hundredths.

  2. Divide 4536 by 9:

    4536÷9=5044536 \div 9 = 5044536÷9=504

  3. 504 hundredths is 5.04.

  4. So 45.36 divided by 9 is 5.04.

Dividing by a decimal

If the divisor is a decimal, make it a whole number first.

The important rule is: multiply both numbers by the same amount.

Example

Dividing by a decimal

Work out 52.8 divided by 0.4.

A scaling diagram showing both numbers multiplied by 10 so the divisor becomes a whole number.

Scaling diagram showing both numbers multiplied by 10 so the divisor becomes a whole number.

  1. The divisor is 0.4, which is a decimal.

  2. Multiply both numbers by 10 so that 0.4 becomes 4:

    52.8÷0.4=528÷452.8 \div 0.4 = 528 \div 452.8÷0.4=528÷4

  3. Now divide:

    528÷4=132528 \div 4 = 132528÷4=132

  4. So 52.8 divided by 0.4 is 132.

Common Mistake

Only changing one number

If you multiply the divisor by 10, you must multiply the dividend by 10 as well. Otherwise, you have changed the question.

Exam technique

In the exam

  1. For 2-mark questions, show your method, not just the final answer.

  2. Line up digits carefully and keep decimal points clear.

  3. Use an estimate to check whether your answer is much too big or much too small.

Self review

Check yourself

  • Can you multiply a 3-digit number by a 1-digit number using place value?

  • When multiplying decimals, how do you decide where the decimal point goes?

  • Can you turn a division by 0.6 into a division by 6?

Recap questions

Test yourself with 5 quick questions on this guide. Answer them all correctly to complete it.

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Multiplication and Division Revision Guide

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