Arithmetic

Addition, Subtraction, Multiplication and Division

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.

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.

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

34543

7

162911

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

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

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

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

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.

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.

1234345

889-1-1-1

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

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

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

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

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.

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

1414000

2800420

56

17276=x =

+

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

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

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?

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

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.

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.

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

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

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

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

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.

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?

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

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?

Functional Skills Example

• (22 + 2) ÷ 4 = 6• 6 x 3 = 18• 18 ÷ 6 = 3

• (3 ÷ 3) x 2 = 2• 2 x 0.63 = £1.26

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?