Download Fraction Wall

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
O
D
M
A
S
Brackets
Of or Powers e.g. 22
Division
Multiplication
Addition
Subtraction
(20 ÷ 2) + (3 x 2) = 10 + 6 = 16
32 - 22 = 3 x 3 - 2 x 2 = 9 – 4 = 5
25 ÷ 5 – 4 = 5 – 4 = 1
5 x 5 + 1 = 25 + 1 = 26
(20 – 10) + (5 + 5) = 10 + 10 = 20
(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
Jim Tyrrell
Fraction Wall
Support for fractions
1/1
ONE WHOLE
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
ONE TWELFTH
ONE
TWENTIETH
1
1/10
1/12
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 numerator and tells us the number of parts or fractions we have.
Jim Tyrrell
Support for fraction, decimal and percentage equivalences
Fraction
ONE WHOLE
1/1
ONE HALF
1/2
ONE THIRD
1/3
ONE FOURTH
1/4
ONE FIFTH
1/5
ONE SIXTH
1/6
1.0
0.5
0.33’
0.25
0.2
0.166’
ONE SEVENTH 1/7
ONE EIGHTH
0.143
1/8
0.125
ONE NINETH 1/9
0.11
ONE TENTH 1/10
ONE TWELFTH
1/12
ONE
TWENTIETH
1/20
Wall of equivalences between
Decimal
Percentage
100%
50%
33.33%
25%
20%
16.67%
14.3%
12.5%
11%
0.1
10%
0.083
8%
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.
Jim Tyrrell
Ratio and Direct Proportion
Support for ratio calculations
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.