N1/E3.6
N1/E3.9
Division problems
Division problems can come in many different forms - some examples follow.
Sharing problems
Share out £1,500 equally between four people.
£1,500 ÷ 4 = £375
This could be done using written methods or by halving twice:
half of 1500 is 750, half of 750 is 375.
Grouping problems
Work out how many boxes that hold 6 eggs each are needed to pack
108 eggs.
108 ÷ 6 = 18 boxes.
This could be laid out as a written division calculation or by halving and
then dividing by three - half of 108 is 54, 54 divided by 3 is 18.
Rate problems
Workers produce 20 km of road markings
in 4 hours. How much is produced each
hour?
20 ÷ 4 = 5 km each hour
This could be done formally or by halving
twice: half of 20 is 10, half of 10 is 5.
Interpreting the answers
In the example problems above, the numbers have been chosen to work out exactly. If the
numbers don’t divide exactly, then there will be a remainder and an appropriate answer is needed
that depends on the situation.
For example:
In the first problem, the answer is an amount of money. If the answer wasn’t exact it would
be rounded to the nearest pence.
In the second problem, if the answer is not exact it would be usual to round down and have
the remainder left.
The third problem can have decimal or fractional answers.
These are examples and not patterns that are always repeated. Each problem needs to be
considered on its own.
© BBC 2011
N1/E3.6
N1/E3.9
Division: repeated subtraction
Different methods can be used for division. The repeated subtraction method is explained here.
Read through these examples and then try them yourself - this is the best way to find out which
method you prefer.
Example 1: what is 42 ÷ 7?
Step 1:
Subtract 7
Subtract 7 again
Subtract 7 again
Subtract 7 again
Subtract 7 again
Subtract 7 again
42 - 7 = 35
35 - 7 = 28
28 - 7 = 21
21 - 7 = 14
14 - 7 = 7
7-7=0
Step 2: count the number of times you subtracted 7. In this question it was 6 times.
Answer: 42 ÷ 7 = 6
Example 2: you have a box of 27 chocolates you want to share
between 5 people. How many chocolates will each person receive?
Step 1
Subtract 5
Subtract 5 again
Subtract 5 again
Subtract 5 again
Subtract 5 again
27 - 5 = 22
22 - 5 = 17
17 - 5 = 12
12 - 5 = 7
7-5=2
You can’t subtract 5 from 2 to leave a whole number. So 2 is the remainder.
Step 2: count the number of times you subtracted 5. In this
question it was 5 times, with a remainder 2.
Answer: 27 ÷ 5 = 5 remainder 2
Each person will get 5 chocolates, with 2 left over.
© BBC 2011
N1/E3.6
Division revision
Learn your times tables to help you with multiplication and division.
Division is a method of sharing or grouping a number into equal parts. When dividing numbers
use the division sign ÷.
Division can be thought of as repeated subtraction. 18 ÷ 6 is the same as saying:
18 - 6 = 12
12 - 6 = 6
6-6=0
6 was subtracted 3 times. So, 18 ÷ 6 = 3.
Sometimes when you divide you have an amount left over. This is called the remainder, r.
43 ÷ 3 = 14 r 1
There are lots of different ways of dividing numbers:
Subtract 4
14 - 4 = 10
Subtract 4
10 - 4 = 6
Subtract 4
6-4=1r2
4 was subtracted 3 times.
14 ÷ 4 = 3 r 2
Traditional method
Repeated subtraction 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
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N1/E3.6
Division tips
When dividing numbers you'll start to notice lots of patterns. Here are some common patterns
and ways of dividing that will soon help you get to grips with splitting up numbers. A number is
divisible by another number if there is no remainder when you divide.
Even numbers:
If a number is even it’s always divisible by 2.
Even numbers end in 0, 2, 4, 6, or 8.
Numbers that end in 0 or 5: If a number ends in 0 or 5 it’s always divisible by 5.
Numbers that end in 0:
If a number ends in 0 it’s always divisible by 2, 5 and 10.
What other division patterns can you find?
Dividing by 2:
Dividing by 2 is the same as halving a number. A quick method is
to split the number into tens and units and halve:
74 ÷ 2 is half of 70, which is 35 plus half of 4, which is 2.
If you add together 35 and 2 it gives you the answer: 37.
You can also split the numbers up to make it easier to halve. For
example:
74 is the same as 60 + 14. So:
74 ÷ 2 is half of 60, which is 30 plus half of 14, which is 7.
If you add together 30 and 7 it gives you the answer: 37.
Dividing by 4:
Remember that 2 × 2 = 4. Dividing by 4 is the same as halving
and halving again:
48 ÷ 4 is half of 48, which is 24 and half of 24, which is 12.
Dividing by 10:
To divide by 10 move all the numbers one place value to the right:
90 ÷ 10 = 9
tens units
9
Splitting into factors:
0
move the number one tens
place value to the right
units
9
.
0
You can split numbers into factors to make them easier to divide:
90 ÷ 6 = (90 ÷ 3) ÷ 2 = 30 ÷ 2 = 15
Checking your calculations
Multiplication and division are linked. They are the opposite action of each other:
10 × 5 = 50
. tenths
50 ÷ 5 = 10
or
50 ÷ 10 = 5
When you carry out a division you can check your answer using multiplication.
© BBC 2011
N1/E3.6
Introduction to division
Division can be seen as a way of sharing or grouping a number into equal parts. If you share
some sweets equally between 3 children, you’re dividing the number of sweets by 3.
For example: 20 ÷ 4 = 5
You can think of division as repeated subtraction. For example:
20 ÷ 4 is the same as saying 20 - 4 = 16, 16 - 4 = 12, 12 - 4 = 8, 8 - 4 = 4, 4 - 4 = 0
Here there are 5 lots of 4.
When you divide numbers you use the division sign: ÷
When you’re carrying out division calculations it’s important to keep the numbers in the correct
order.
For example:
10 ÷ 5 = 2
5 ÷ 10 = 0.5
is not the same as
Remainder
Sometimes when you divide you have an amount left over. This is called the remainder,
r = remainder.
For example: 23 ÷ 4 = 5 r 3
If you used a calculator to work out the answer you’d get the number 5.75. The 0.75 on the
calculator represents remainder 3. This is because the calculator has shown the remainder as a
decimal.
Different words can describe division. For example, 35 ÷ 5 = 7 can also be described as:
If you split 35 into 7 parts each part will contain 5.
35 shared between 5 = 7.
There are 7 groups of 5 in 35.
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 division you can check your answer by using multiplication.
© BBC 2011