Jim Tyrrell

Support for number calculations using BODMAS

BODMAS

BODMAS is an abbreviation (using letters that represent or stand for words) that refers to a mathematical method or general rule to follow when working out equations or formula.

The basic operations of calculating numbers are addition, subtraction, multiplication and division. The basic rule when brackets (or when there is one calculating method using different operations) are used in calculations is:

B Brackets (20 ÷2) + (3 x 2) = 10 + 6 = 16

O Of or Powers e.g. 22 32 - 22 = 3 x 3 - 2 x 2 = 9 – 4 = 5

D Division 25 ÷ 5 – 4 = 5 – 4 = 1

M Multiplication 5 x 5 + 1 = 25 + 1 = 26

A Addition (20 – 10) + (5 + 5) = 10 + 10 = 20

S Subtraction (15 + 5) – (10 -5) = 20 – 5 = 15

When there is a number and then a bracket this means that the number multiplies the sum of the bracket:

5(20-15) = 5 x (20 – 15) = 5 x 5 = 25

Use brackets to help you with sums:

A group of 20 people want £10 seat tickets for a theatre show. They qualify for a £1 reduction per person. How much is the total cost for the seats?

20 x 10 – 20 x 1 (use brackets to help you calculate the total cost) = (20 x 10) – (20 x 1) = 200 -20 = £180

Support for fractions Fraction Wall

ONE WHOLE 1/1 1
ONE HALF / 1/2
ONE THIRD / 1/3
ONE FOURTH / 1/4
ONE FIFTH / 1/5
ONE SIXTH / 1/6
ONE SEVENTH / 1/7
ONE EIGHTH / 1/8
ONE NINETH / 1/9
ONE TENTH / 1/10
ONE TWELFTH / 1/12
ONE TWENTIETH / 1/20

A fraction is part of something. This wall has being divided into different fractions or parts. The bottom of a fraction is called the denominator and tells us the total parts or fractions of the wall (or whole thing) we can have; the top of the fraction is called the numeratorand tells us the number of parts or fractions we have.

Support for fraction, decimal and percentage equivalences Wall of equivalences between

Fraction Decimal Percentage

ONE WHOLE 1/1 1.0 100%
ONE HALF 1/2 / 0.5 50%
ONE THIRD 1/3 / 0.33’ / 33.33%
ONE FOURTH 1/4 / 0.25 / 25%
ONE FIFTH 1/5 / 0.2 / 20%
ONE SIXTH 1/6 / 0.166’ / 16.67%
ONE SEVENTH 1/7 / 0.143 / 14.3%
ONE EIGHTH 1/8 / 0.125 / 12.5%
ONE NINETH 1/9 / 0.11 / 11%
ONE TENTH 1/10 / 0.1 / 10%
ONE TWELFTH 1/12 / 0.083 / 8%
ONE TWENTIETH
1/20 / 0.05 / 5%

When we split a whole thing into parts we can represent the amount of parts we have as fractions, decimals or percentages.

Support for ratio calculations Ratio and Direct Proportion

Ratio refers to different amounts or parts that are related by making up a whole thing. This could be:

Mixing concentrated juice to water:

Mix 1 part orange to 4 parts water

Direct proportion refers to the increase (or decrease) in the ratio parts as the size or quantity of the whole thing increases (or decreases). That is, the ratios must stay the same.

When working out ratios, keep the ratios in the order they appear in the question:

You mix orange concentrate to water for a party in a ratio of 1 to 4. How much water must you add to 4 litres of orange concentrate?

Ratio

Orange : Water

1 : 4

4 Litres of orange : (4 parts water x ?)

(1 x 4 = 4) : (4 x 4 = 16)

4 Litres of orange : 16 litres of water

When given a total amount and the task is to find the proportion of one of the ratios, simply add the ratios and divide the total. Using the same example above:

Ratio Order

Orange: Water

1 :4

Total orange drink = 20 litres

20

1+4 = 5 = 20 ÷ 5 = 4 which is 1 ratio’s value

Multiply ratio order by the value of one ratio to get the correct proportions

1 x 4 = 4 : 16 = 4x4

4 litres of orange concentrate : 16 litres of water (4 + 16 = 20 litres)

Use the methods to work out other ratio and proportion questions.