Whole numbers
Addition
When doing addition problems, it is very important that you follow a few
basic rules to ensure that you get the answer right every time.
We are going to work out 47 + 39
1st step
When writing out the sum, make sure
that the numbers are in the correct columns
2nd step Always start in the end column, in this case
the units column, then move along to the left
TU
47
+39
86
7 + 9 = 16
The answer is 86
Now try questions 1 and 2 in your booklet.
4+3+1=8
Whole numbers
Subtraction
When doing subtraction problems, it is very important that you follow a
few basic rules to ensure that you get the answer right every time.
We are going to work out 147 – 59
1st step
When writing out the sum, make sure
that the numbers are in the correct columns
2nd step Always start in the end column, in this case
the units column, then move along to the left
H0 T1 3 U
1 47
-59
88
7 – 9 you can’t do, so borrow one from the next column along: 17 – 9 = 8
3 – 5 you can’t do, so borrow one from the next column along: 13 – 5 = 8
The answer is 88
Now try questions 3 and 4 in your booklet.
Whole numbers
When solving problems in maths, you have to decide what the
correct operation is to use.
When addition is required to solve the problem, there are a few key words
that you can look out for:
altogether
total
sum
combined
1. Hamish played two rounds of golf in 1 week and recorded his scores,
which were 75 and 74. What was his total score over the 2 days?
75
+74
1 49
His total score was 149.
Whole numbers
2. Ben bought a second-hand car. In order to get it on the road, he had to
buy insurance for £450, road tax for £110 and petrol for £40. How
much did it cost to get the car on the road?
475
110
+ 40
625
It cost Ben £625 to get his car on the road.
3. Stacie spent £30 on make-up, £45 on a hair cut and £85 on a dress for
a night out. How much did she spend in total?
30
45
+85
160
Stacie spent £160.
Now try question 5 in your booklet.
Whole numbers
When subtraction is required to solve the problem, there are a few key
words that you can look out for:
difference
slower
fallen
less than
1. Angela got 86% for her maths test and 55% for her English test. What
is the difference between the two marks?
86
– 55
3 1
The difference is 31%.
Whole numbers
2. Sam has saved up £400. He spends £365 on a new iPhone. How
much money does he have left?
400
–365
35
Sam has £35 left.
3. There are 135 people in 3rd year. Last week the attendance was 108.
How many students were absent last week?
135
–108
27
There were 27 people absent.
Now try question 6 in your booklet.
Whole numbers
Sometimes there are two parts to a question that might involve both
addition and subtraction.
1. Marshall earned £350 last week and his wife Karen earned £375.
How much did they earn altogether last week?
How much more did Karen earn than Marshall?
350
+375
725
They earned £725 last week.
375
–350
25
Karen earned £25 more than Marshall.
Whole numbers
2. Sarah drove from Aberdeen to Birmingham, a total of 620 kilometres.
She stops to refuel after 435 kilometres. How many kilometres does
she still have to travel?
620
–435
185
Sarah has 185 kilometres still to travel.
3. Derek has to save up £420 for a new laptop. For his birthday he is
given £205, which he adds to his savings of £162. How much more
does he still have to save?
205
420
+162
–367
367
53
Derek still has £53 to save up.
Now try question 7 in your booklet.
Multiplying
When doing multiplication problems, it is very important that you follow the
same basic rules that were highlighted when adding and subtracting.
We are going to work out 37 × 6
1st step
When writing out the sum, make sure
that the numbers are in the correct columns
2nd step Always start in the end column, in this case
the units column, then move along to the left
TU
37
× 6
222
6 × 7 = 42
Put the 2 in and carry the 4
The answer is 222
Now try questions 8 and 9 in your booklet.
6 × 3 = 18
18 + 4 = 22
Multiplying
1. George stays at a hotel for £65 per night. How much will it cost him to
stay at the hotel for 5 nights ?
65
×5
325
It will cost £325.
2. Anna has downloaded eight albums on her iPod. Each album has 14
tracks on it. How many tracks does she have on her iPod?
14
×8
112
Anna has 112 tracks.
Now try question 10 in your booklet.
Multiplying
When multiplying by numbers that have two or more digits, it can be much
faster to use a calculator.
To go and watch his local football team play, Josh has to pay £13 for a
ticket. If 2300 people go to the game, how much money will the club get
for the game?
2300
×13
29900
The club will get £29,900 in gate receipts.
Now try question 11 in your booklet.
Dividing
It’s easier to divide numbers if you know your times tables.
We are going to work out 531 ÷ 3.
1st step
When writing out the sum, take the number you are dividing by
outside the division
2nd step The number you are dividing goes into the division
3rd step Move along the division one number at a time, dividing each
one by the number outside the division
1 7 7
3
2
2
5 3 1
3 into 5 is 1 remainder 2
3 into 23 is 7 remainder 2
The answer is 177
3 into 21 is 7
Now try questions 12 and 13 in your booklet.
Dividing
1. Nine people share a lottery win of £2972. How much does each
person win ?
0 3 31
9
2
2
2979
They each get £331
2. Batteries are packed in boxes of six. How many boxes of batteries
would be required for 4324 batteries?
0 7 21
6
4
721 boxes will be required
1
4326
Now try question 14 in your booklet.
Dividing
When dividing by numbers that have two or more digits, it can be much
faster to use a calculator.
The cost of a school trip for 33 students is £1452. The children share the
cost equally. How much does each child pay?
44
33
1452
It costs £44 per child for the trip.
Now try question 15 in your booklet.
Fractions
A fraction of something can be described as a part of something, for
example a half.
If something is divided into fractions, each part must be the same size or
the same number.
This shape has been divided into four equal bits .
One of the four bits has been shaded
blue.
1
This can be written as a fraction:
4
This shape has been divided into four
bits.
This shape has not been divided equally, so
cannot be described as 1
4
Fractions
These 8 circles represent the number 8.
If you divide the number 8 by ½ , you get 2 sets of 4.
The number is the same in each group, 4.
8 has been divided by ½.
If you divide the number 8 into sets of 2 and 6, it is not divided into equal
fractions.
The number is not the same in each group so each group is not ½ of 8.
Fractions
To calculate a fraction of a number, you follow these simple rules.
To calculate
of a number, you divide the number by 2
To calculate
of a number, you divide the number by 3
To calculate
of a number, you divide the number by 4
To calculate
of a number, you divide the number by 5
To calculate
of a number, you divide the number by 10
of 18 = 18 ÷ 2 = 9
of 36 = 36 ÷ 3 = 12
Dividing
1. In February 2010, snow fell for
did it snow for?
of the month . How many days
There are 28 days in February.
of 28 = 28 ÷ 4 = 7
2. In a group of 240 school students,
of them were left-handed.
How many of the students were right-handed?
of 240 = 240 ÷ 8 = 30 were left-handed
240 – 30 = 180 were right-handed
Now try question 16 in your booklet.
Finding remainders
A greengrocer is packing oranges into bags of 6. He has ordered 50
oranges. How many bags of oranges will he have, and how many of the
oranges will be left over?
Step 1 Divide 50 by 6 on a calculator.
50 ÷ 6 = 8.333333….
Step 2 This answer shows you can fill 8 bags full.
The 0.33333…. is a remainder, which means
that there are some oranges left over.
Step 3 To work out how many are left over, multiply 8 by 6
8 × 6 = 48
48 oranges were used to fill the bags.
Step 4 Take 48 from 50 to find how many were left over.
50 – 48 = 2
There are 2 oranges left over.
Finding remainders
It costs £3.50 for a salad at a café. How many salads can be bought for
£20 and how much money will be left over?
Step 1 On your calculator, 20 ÷ 3.5 = 5.714285….
Step 2 This answer shows you can only buy 5 full salads.
The 0.714285…. is a remainder, which means
that there is some change left over.
Step 3 To work out how much money is left over, multiply 5 by £3.50
5 × 3.50 = £17.50. The 5 salads cost £17.50.
Step 4 Take £17.50 from £20 to find how much money is left over.
20 – 17.50 = 2.50
There is £2.50 left over
Now try question 17 in your booklet.
Writing numbers
You will often come across numbers written in words.
Sometimes it is necessary to write numbers out in words rather than in
figures, particularly when writing cheques.
It is important to know the column headings that each number falls under
to do this.
1. Gregg buys a second-hand car for £2540. He writes a cheque to pay
for his purchase. Write the cost in words.
Th H T U
2 5 4 0
Two thousand, five hundred and forty.
2. Gregg writes a second cheque to his insurance company for £588.
Write this in words.
H T U
5 8 8
Five hundred and eighty eight.
Now try question 18 in your booklet.
Test yourself
You are now ready to tackle the end-of-topic test in your booklet.
GOOD LUCK!!