The document discusses the basic arithmetic operations of addition, subtraction, multiplication, and division. It provides examples and explanations of how to perform each operation with both whole numbers and decimals. For each operation, it gives practice problems working through the steps and calculating the answers.

1. Arithmetic
Addition, Subtraction,
Multiplication and Division

2. Arithmetic
• Arithmetic refers to the basic mathematical operations from
which all other mathematics is derived.
• The most basic operation is addition. This is where you add
one value to another.
• The opposite of addition is subtraction. This is where you take
one value from another.
• Next we have multiplication, where you have a number of
values which are all the same and you work out the total
value.
• And finally division, where you have one value which you wish
to split into a number of portions, each of equal value.

3. Addition
• The most basic of operations, addition, simply involves
taking the total of two or more values.
• The simplest way to do this is to count on from one
value a number of spaces equal to the first.
• All mathematics is built upon the principle that 1 + 1
= 2. (Or 1 + 1 = 10, same thing).
• When working with particularly large or particularly
small numbers addition can be quite tricky.
• When adding large pools of numbers together it can
be quite easily to make a simple clerical error.

4. Addition
• The process of addition means you can simply
count upwards a number of places to reach a final
answer.
• When dealing with larger numbers it can help to
split the addition into component parts.
• First you add the units, carrying over any tens,
then you add the tens carrying over any hundreds,
etc.
1234
345
43
7
11
1629

5. Addition
• See if you can perform these simple additions.
 17 + 8
 23 + 15
 9 + 14
 41 + 34
 12 + 5
 18 + 33
 19 + 47
 35 + 21
 25 + 6
 5041 + 897
 4327 + 421
 5674 + 672
 3997 + 212
 0.034 + 0.4
 0.5 + 0.21
 0.04 + 0.07
 325.7 + 3.4
 0.1 + 0.01

6. Addition
• See if you can perform these simple additions.
 17 + 8
 23 + 15
 9 + 14
 41 + 34
 12 + 5
 18 + 33
 19 + 47
 35 + 21
 25 + 6
 25
 38
 23
 75
 17
 51
 66
 56
 31
 5041 + 897
 4327 + 421
 5674 + 672
 3997 + 212
 0.034 + 0.4
 0.5 + 0.21
 0.04 + 0.07
 325.7 + 3.4
 0.1 + 0.01
 5938
 4748
 6346
 4209
 0.434
 0.71
 0.11
 329.1
 0.11

7. Addition
• You had five days until your brother was due to be
coming over to stay. Unfortunately he has had to
postpone for another full week. How many days
will it be before he arrives?
• You receive a £60 fine in the post. You decide to
take the matter to court but things go badly. You
are asked to pay the original fine plus £125 in
court costs. How much are you required to pay?
y

8. Addition
• You had five days until your brother was due to be
coming over to stay. Unfortunately he has had to
postpone for another full week. How many days
will it be before he arrives?
• 5 + 7 = 12 days
• You receive a £60 fine in the post. You decide to
take the matter to court but things go badly. You
are asked to pay the original fine plus £125 in
court costs. How much are you required to pay?
• £185

9. Subtraction
• Subtraction simply involves counting one number
off of another.
• Subtraction is literally the reverse of addition.
• Like addition, when dealing with large pools of
numbers, clerical errors can easily occur.
• Subtraction can be tricky if the number you are
subtracting from is smaller than the number you
are using to do the subtraction.
• Subtraction is something you are likely to use on
regular basis when trying to budget.

10. Subtraction
• The process of subtraction means you can simply
count downwards a number of places to reach a
final answer.
• When dealing with larger numbers it can help to
split the subtraction into component parts.
• First you subtract the units, pulling in any extra
tens you need, then you subtract the tens pulling
in any extra hundreds, etc.
1234
345
-1-1-1
889

11. Subtraction
• See if you can perform these simple subtractions.
 17 - 8
 23 - 15
 14 - 9
 41 - 34
 12 - 5
 33 - 18
 47 - 19
 35 - 21
 25 - 6
 5041 - 897
 4327 - 421
 5674 - 672
 3997 - 212
 0.4 - 0.034
 0.5 - 0.21
 0.07 - 0.04
 325.7 - 3.4
 0.1 - 0.01

12. Subtraction
• See if you can perform these simple subtractions.
 17 - 8
 23 - 15
 14 - 9
 41 - 34
 12 - 5
 33 - 18
 47 - 19
 35 - 21
 25 - 6
 9
 8
 5
 7
 7
 15
 28
 14
 19
 5041 - 897
 4327 - 421
 5674 - 672
 3997 - 212
 0.4 - 0.034
 0.5 - 0.21
 0.07 - 0.04
 325.7 - 3.4
 0.1 - 0.01
 4144
 3906
 5002
 3785
 0.366
 0.29
 0.03
 322.3
 0.09

13. Subtraction
• You are cooking yourself dinner and following the
recipe you placed the casserole dish in the oven at
150oC. The recipe says to leave the dish in the
oven for 2 hours. If it has been in the oven
already for 25 minutes how long is left?
• You are at the swimming pool doing lengths. You
have set yourself a target of 50 lengths and have
so far completed 36. How many more lengths
must you complete to reach your target?
y

14. Subtraction
• You are cooking yourself dinner and following the
recipe you placed the casserole dish in the oven at
150oC. The recipe says to leave the dish in the
oven for 2 hours. If it has been in the oven
already for 25 minutes how long is left?
• 120 – 25 = 95 minutes, or 1h 35mins
• You are at the swimming pool doing lengths. You
have set yourself a target of 50 lengths and have
so far completed 36. How many more lengths
must you complete to reach your target?
• 50 – 36 = 14 lengths

15. Multiplication
• Multiplication can be described as performing a
number of additions simultaneously when all the
values being added together are the same.
• Another way to look at multiplication is to imagine
you have a number of groups of equal value and
that you are trying to find the collective total
value.
• When performing multiplication it doesn’t matter
which way you look at it, the total value of six
groups of four is the same as the total value of
four groups of six.

16. Multiplication
• As a process multiplication is simply a matter of
carrying out a repeated addition. If you have
seven groups of five, then five plus five is ten.
Plus five is fifteen. Plus five is twenty. Plus five is
twenty five. Plus five is thirty. Plus five is thirty
five.
• When performing large multiplications we can
break down the number into component parts and
add the results together.
1234
14
14000
2800
420
56
= 17276
x
=
+

17. Multiplication
• See if you can perform these simple multiplications.
 2 x 8
 3 x 5
 4 x 7
 2 x 9
 6 x 8
 12 x 9
 11 x 7
 10 x 5
 12 x 8
 324 x 3
 432 x 5
 567 x 7
 399 x 6
 14 x 13
 21 x 11
 32 x 14
 2341 x 3
 5298 x 7

18. Multiplication
• See if you can perform these simple multiplications.
 2 x 8
 3 x 5
 4 x 7
 2 x 9
 6 x 8
 12 x 9
 11 x 7
 10 x 5
 12 x 8
 16
 15
 28
 18
 48
 108
 77
 50
 96
 324 x 3
 432 x 5
 567 x 7
 399 x 6
 14 x 13
 21 x 11
 32 x 14
 2341 x 3
 5298 x 7
 972
 2160
 3969
 2394
 182
 231
 448
 7023
 37086

19. Multiplication
• You need to buy three packs of soft white rolls for a
barbeque you are having. Each pack costs £1.56, what
is the total cost?
• Each pack contains twelve rolls. How many rolls would
have in total?
• You are making the rolls and then cutting them into
four and putting them out on plates so people can
help themselves. How many portions are available?

20. Multiplication
• You need to buy three packs of soft white rolls for a
barbeque you are having. Each pack costs £1.56, what
is the total cost?
• 1.56 x 3 = £4.68
• Each pack contains twelve rolls. How many rolls would
have in total?
• 12 x 3 = 36 rolls
• You are making the rolls and then cutting them into
four and putting them out on plates so people can
help themselves. How many portions are available?
• 36 x 4 = 144 portions

21. Division
• Division is the reverse of multiplication, when you
try to establish what number would be required to
be added together x number of times to arrive at
your answer.
• Another way to look at division is to imagine you
are trying to split a large value into a number of
groups of equal value.
• When performing division it does matter which
way you look at it, splitting twenty four into six
groups is not the same as splitting six into twenty
four groups.

22. Division
• The process of division involves splitting the number
into equal groups. Checking how many times one
number can fit inside another will tell you how many
groups you can have. e.g. 4 fits inside 8 twice, so you
could have 4 groups of 2.
• When performing division with larger numbers it is
easiest to work from the largest component of the
number to the smallest.
• Often when performing division you will be left with a
remainder. In maths this can be expressed as a
fraction or a decimal but sometimes in practical terms
it is not possible to make use of the remainder.

23. Division
• See if you can perform these simple divisions.
 8 ÷ 2
 15 ÷ 3
 28 ÷ 7
 18 ÷ 2
 48 ÷ 6
 108 ÷ 9
 77 ÷ 11
 50 ÷ 5
 96 ÷ 12
 324 ÷ 3
 435 ÷ 5
 567 ÷ 7
 396 ÷ 6
 147 ÷ 7
 209 ÷ 11
 322 ÷ 14
 2340 ÷ 3
 5299 ÷ 7

24. Division
• See if you can perform these simple divisions.
 8 ÷ 2
 15 ÷ 3
 28 ÷ 7
 18 ÷ 2
 48 ÷ 6
 108 ÷ 9
 77 ÷ 11
 50 ÷ 5
 96 ÷ 12
 4
 5
 4
 9
 8
 12
 7
 10
 8
 324 ÷ 3
 435 ÷ 5
 567 ÷ 7
 396 ÷ 6
 147 ÷ 7
 209 ÷ 11
 322 ÷ 14
 2340 ÷ 3
 5299 ÷ 7
 108
 87
 81
 66
 21
 19
 23
 780
 757

25. Division
• You are hosting a children’s birthday party for 32
children and have 4 cakes. How many portions should
each cake be split into?
• Your lottery syndicate of 12 members wins £96.12.
How much should each member receive?
• You are trying to work out how much you would have
to put aside each week to raise £1400 in three years.
What is the correct amount?
r

26. Division
• You are hosting a children’s birthday party for 32
children and have 4 cakes. How many portions should
each cake be split into?
• 32 ÷ 4 = 8 portions
• Your lottery syndicate of 12 members wins £96.12.
How much should each member receive?
• 96.12 ÷ 12 = £8.01
• You are trying to work out how much you would have
to put aside each week to raise £1400 in three years.
What is the correct amount?
• 1400 ÷ 156 = £8.98

27. Arithmetic and Functional Skills
• We have already seen some examples of how
arithmetic is used in simple scenarios.
• When dealing with real life activities it may
be necessary to perform several successive
arithmetic operations to calculate the
information we need.
• This is reflected in the functional skills
questions you are likely to receive.
• Many different terms can be used in the
questions to mean the same thing.

28. Functional Skills Example
• You have been working all week for £6.80 an hour.
You work five days a week, nine hours a day. You
need to use a third of your paycheque to cover
bills. Another £100 comes out for rent. If you spend
£16 getting to and from work and another £63 at
the weekend then how much do you have to spend
on your lunches at work?

29. Functional Skills Example
• You have been working all week for £6.80 an hour.
You work five days a week, nine hours a day. You
need to use a third of your paycheque to cover
bills. Another £100 comes out for rent. If you spend
£16 getting to and from work and another £63 at
the weekend then how much do you have to spend
on your lunches at work?
 6.8 x 9 = £61.20
 61.2 x 5 = £306
 306 ÷ 3 = £102
 Either 306 – 102 or 102 x 2
= £204
 204 – 16 = £188
 £188 – 63 = £125
 £125 ÷ 5 = £25

30. Functional Skills Example
 You are baking for a party and you want to make sure you
have enough cake for everyone. Their will be 22 people
attending plus you and your partner. Each cake serves four
people and requires 3 eggs to make. Eggs are sold at the local
shop by the half dozen with a buy 2 get 1 free offer. If a
carton of eggs costs 63 pence then how much will you have
to spend on eggs to ensure you have enough?

31. Functional Skills Example
 You are baking for a party and you want to make sure you
have enough cake for everyone. Their will be 22 people
attending plus you and your partner. Each cake serves four
people and requires 3 eggs to make. Eggs are sold at the local
shop by the half dozen with a buy 2 get 1 free offer. If a
carton of eggs costs 63 pence then how much will you have
to spend on eggs to ensure you have enough?
• (22 + 2) ÷ 4 = 6
• 6 x 3 = 18
• 18 ÷ 6 = 3
• (3 ÷ 3) x 2 = 2
• 2 x 0.63 = £1.26