Free How to Pass Numerical Reasoning by Heidi Smith

both sides by 20:
    Ratio = 1 : 6.
    Worked example
    What is the ratio of 25 grammes (g) to 5 kilogrammes (kg)?
    Convert the larger unit (kg) to the equivalent measure of the smaller unit (g): 1 kg = 1,000 g so 5 kg = (5 × 1,000 g) = 5,000 g Therefore the ratio of 25 g : 5 kg = 25 : 5,000
    Divide both sides by 25 to express the ratio in its lowest terms.
    The ratio of 25 g : 5 kg in its lowest terms is 1 : 200.
    Ratios converter drill 1
    Set a stopwatch and aim to complete the following drill in two minutes. Express the following ratios in their simplest forms, in the format x : y.
Q1

Q2
Q3

Q4
Q5

Q6
Q7

Q8
Q9

Q10
    Ratios converter drill 2
    Set a stopwatch and aim to complete the following drill in 1 minute. Express the following ratios, given in the format x : y, as fractions in their lowest form.
Q1
22 : 3
Q2
19 : 20
Q3
3 : 15
Q4
35 : 45
Q5
3 : 4
Q6
325 : 375
Q7
105 : 120
Q8
7 : 22
Q9
2 : 56
Q10
268 : 335
    Types of ratio
    Two types of ratio are typically tested in numeracy tests. These are ‘part to part’ ratios and ‘part to whole’ ratios. When you think about the ‘whole’ and the ‘part’ with ratios, think of the ‘whole’ as the complete set (or the ‘parent set’) and the ‘part’ as a subset of the parent set. For example, players in a football squad are the complete set (the whole) and those players picked for the starting line-up are the subset (the part). Once you understand how these ratios work, you can use ratios to determine actual values, for example the exact number of players in the squad.
    ‘Part to part’ ratios
    Worked example
    There are four oak trees for every two willow trees. What is the ratio of willows to oaks?
    ‘Types of trees’ is the parent set, and consists of two subsets, ‘willows’ and ‘oaks’.
Willows to Oaks = 2 : 4
    Divide both sides by 2 to express the ratio in its simplest form:
Willows to Oaks = 1 : 2
    ‘Part to whole’ ratios
    If you know the ratio of subsets to the complete set, you can work out the number of parts in the whole. You can also convert the ‘part to part’ ratio to a ‘part to whole’ ratio only when you are sure that there are no missing parts.
    Worked example
    A filing cabinet in Whitehall contains only files classified as ‘secret’ or ‘top secret’. The ratio of ‘secret’ to ‘top secret’ files in the filing cabinet is 3 : 2. What is the ratio of ‘top secret’ files to all files in the cabinet?
    The parent set is ‘all files in the filing cabinet’ and consists of two subsets, ‘secret files’ and ‘top secret files’. You are given a ‘part to part’ ratio and asked to express one part as a subset of the whole. As there are only ‘secret’ and ‘top secret’ files in the filing cabinet, you can convert the ‘part to part’ ratio to a ‘part to whole’ ratio:
Part (secret)
+
Part (top secret)
=
Whole
3
+
2
=
5
    This tells you that for every five files, three are classified as ‘secret’ and two are classified as ‘top secret’. The ratio of top secret files to all files is therefore:
    Note that this does not give you actual values (the number of files), just the ratio between quantities.
    Worked example
    A software company decides to expand its floor area by building additional floors underground for the software testers. When the construction is finished, one in four of the total floors in the building will be underground. What is the ratio of floors above ground to floors underground?
    The floors can only be underground or above ground, so you can be sure to know all the subsets of the parent set. Therefore you can determine the part to whole ratio. The question tells you that for every floor underground, three are above ground. If ¼ of all floors are below ground, then ¾ must be above ground. The ratio of floors above ground to floors below is ¾ to ¼. Both quantities are expressed as quarters, so you can form a ratio with the numerators: Floors above ground to floors below ground = 3 :