N1/E3.4
N1/E3.5
Introduction to multiplication
Multiplication is a way of adding a number to itself a number of times. For example:
2 + 2 + 2 + 2 + 2 + 2 = 12
is the same as
6 × 2 = 12
5 + 5 + 5 + 5 + 5 = 25
is the same as
5 × 5 = 25
Multiplication is the same as repeated addition. When you multiply numbers you use the
multiplication sign (×)
When you’re multiplying numbers together it doesn’t matter what order you use. For example:
3 × 4 = 12
is the same as
4 × 3 = 12
2 × 8 = 16
is the same as
8 × 2 = 16
Multiplication is a quicker method of repeated addition. With repeated addition it doesn’t matter in
what order you add up the numbers. For example:
4 + 4 + 4 = 12
is the same as
4 + 4 + 4 = 12
8 + 8 = 16
is the same as
8 + 8 = 16
We use different words to describe multiplication. For example, 3 × 7 = 21 can also be described
as:
3 times 7 = 21
3 lots of 7 = 21
3 sets of 7 = 21
3 multiplied by 7 = 21
Checking your calculations
Multiplication and division are linked. They are the opposite action of each other:
10 × 5 = 50
50 ÷ 5 = 10
or
50 ÷ 10 = 5
When you carry out a multiplication you can check your answer using division.
You’ll recognise some of the calculations above from knowing your times tables. Knowing your
times tables helps you to work out multiplication questions far more quickly.
There are many different ways of multiplying numbers, read about them in the factsheets in this
topic. You can use some of these to help you do mental maths (ie working out the answers in
your head). You can use other methods when you need to write down calculations to work
answers out.
The important thing to remember is that everyone is different. Which multiplication method do you
prefer?
© BBC 2011
N1/E3.4
Multiplication revision
Learn your times tables to help you with multiplication and division.
Multiplication is a method of adding a number to itself a number of times.
2 + 2 + 2 + 2 + 2 + 2 = 12 is the same as 6 × 2 = 12
When you multiply numbers you use the multiplication sign: 6 × 2 = 12.
When you’re multiplying numbers together it doesn’t matter what order you use.
3 × 4 = 12 is the same as 4 × 3 = 12
There are many different ways of multiplying numbers:
Traditional
method
Lattice method
Grid or splitting method
Multiplication and division are linked. They are the opposite action of each other:
10 × 5 = 50 50 ÷ 5 = 10 or 50 ÷10 = 5
© BBC 2011
N1/E3.4
N1/E3.5
Multiplication: splitting method
There are many different ways of multiplying numbers. The method
described here is the splitting (or grid) method. You can use this
method to do mental multiplication.
Have a read through these examples and then try them yourself. The
best way to learn is to have a go.
Example 1: what is 32 × 3?
Steps:
1. Split 32 into tens and units: 32 = 30 + 2.
2. Multiply each number by 3: 30 × 3 = 90 and 2 × 3 = 6.
3. Add the numbers together: 90 + 6 = 96.
This method can also be shown using a grid. Have a look at the next example.
Example 2: you’re having a barbecue for your birthday and want to check how many vegetable
burgers you have in the freezer. You have 12 boxes of 4 burgers. How many burgers do you
have?
Steps:
×
10
2
1. Split 12 into tens and units and put these along the top of the
grid. Put the 4 down the side of the grid.
4
2. Multiply each number in the row by each number in the
column: 4 × 10 and 4 × 2.
×
10
2
4
40
8
3. Add each of the answers together: 40 + 8 = 48.
You have 48 burgers - enjoy the barbecue!
© BBC 2011
N1/E3.4
N1/E3.5
Multiplication tips
When multiplying numbers you’ll start to notice lots of patterns. Here are some common patterns
and other ways of multiplying that will help you become a multiplication wizard.
Multiplying by 2
Multiplying by 2 is the same as doubling a number. A quick method is to split the number into tens
and units and double: 2 × 13 is double 10, which is 20 plus double 3 which is 6 = 26.
Tip: when you multiply by 2 you always end up with an even number.
Multiplying by 4
Remember that 2 × 2 = 4. Multiplying by 4 is the same as doubling and doubling again: 4 × 15
is double 15 which is 30 and double 30 = 60.
Multiplying by 10
To multiply by 10 move all the numbers one place value to the left: 10 × 8 = 80
Tens
units
8
move the number one
place value to the left
tens
units
8
0
Tip: when you multiply a whole number by 10 it always ends in 0.
Multiplying by 5
To multiply by 5, multiply by 10 and then halve: 5 × 62 is half of 10 × 62 which is half of 620 = 310
Tip: when you multiply a number by 5 it always ends in 0 or 5.
Adjusting numbers
You can round numbers up or down and then adjust to make them easier to multiply:
4 × 29 = (4 × 30) - 4 = 120 - 4 = 116
3 × 22 = (3 × 20) + 6 = 60 + 6 = 66
Splitting into factors
You can split numbers into factors to make them easier to multiply:
17 × 6 = 17 × 2 × 3 = 34 × 3 = 102
Splitting into the numbers added together
You can split numbers into addition facts and then multiply:
7 × 52 = 7 × (50 + 2) = (7 × 50) + (7 × 2) = 350 + 14 = 364
Checking your calculations
Multiplication and division are linked. They are the opposite action of each other:
10 x 5 = 50
50 ÷ 5 = 10
or
50 ÷ 10 = 5
After multiplying you can check your answer using division.
© BBC 2011
N1/L1.3
Multiplication glossary
Here are some of the words that will crop up when you do multiplication sums:
Have a look below to see how they can be used in the simple sum 2 x 2 = 4.
Factors
2 is a factor of 4. One number is a factor of another number if it divides or goes into it exactly.
Groups of
2 groups of 2 make 4.
Lots of
2 lots of 2 make 4.
Multiple
4 is a multiple of 2.
Multiply
If you multiply 2 by 2 you get 4.
Product
The product of 2 and 2 is 4.
Sets of
2 sets of 2 make 4.
Times
2 times 2 is 4.
To find out more about maths words look in the Skillswise Glossary.
© BBC 2011
N1/L1.4
Multiplication shortcuts
When multiplying by 10, 100 and 1,000 there’s a pattern that can help you get the right answer
very quickly. This method moves the decimal point rather than the digits.
Multiplying number
Number of places to
move the decimal point
10
1
100
2
1,000
3
10,000
4
The zeros in the multiplying number tell you how many places to move the decimal point.
Remember you’re making the number bigger.
Make sure you move the digits (or the decimal point) in the correct direction!
When multiplying by 10, 100, 1,000 etc count the zeros
to find out how much bigger your number must be.
Example
Multiply 2.341 by 100:
100 has two zeros. Make 2.341 bigger by moving the decimal point two places.
© BBC 2011
N1/L1.4
Multiplying by 10, 100 and 1,000
Multiplying by 10
When you multiply a decimal number by 10 you move all the digits one place to the left. The
number becomes 10 times bigger.
Example: 2.63 × 10 = 26.3
You can see from the answer that the digits move to the left - units move to tens and the others
follow like this:
H
T
U
2
1
10
1
100
3
2
.
6
6
.
3
H = hundreds
T = tens
U = units
Multiplying by 100
When you multiply a decimal number by 100 you move all the digits two places to the left. The
number becomes 100 times bigger.
Example: 2.63 × 100 = 263
Th
H
T
U
2
2
6
.
1
10
1
100
6
3
Th = thousands
H = hundreds
T = tens
U = units
3
Multiplying by 1,000
When you multiply a decimal number by 1,000 you move all the digits three places to the left.
The number becomes 1,000 times bigger.
Example: 2.63 × 1,000 = 2,630
TTh
Th
H
T
U
2
2
6
3
.
1
10
1
100
6
3
TTh = tens of thousands
Th = thousands
H = hundreds
T = tens
U = units
0
© BBC 2011