How to Pass Numerical Reasoning (35 page)

For example, what is the ratio of black cats to white cats?

Reduce the fraction to its lowest terms.

Worked example

Express the following ratios (1) in words (2) with a colon separating the quantities and (3) as a fraction.

Q1 What is the ratio of shoes to feet?

(1) Shoes to Feet

(2) Shoes : Feet

(3)

Q2 What is the ratio of flowers to stems?

(1) Flowers to Stems

(2) Flowers : Stems

(3)

Q3 What is the ratio of guitarists to bandmembers?

(1) Guitarists to Bandmembers

(2) Guitarists : Bandmembers

(3)

Ratios and common units of measure

In order to compare two quantities, they must be expressed in terms of the same unit. To set up a ratio when the original units of measure are in different units, simplify the calculation by converting the larger unit to the smaller unit of measure. This method ensures that you work with common units throughout your calculation.

Worked example

What is the ratio of 20 minutes to 2 hours?

Convert the larger unit (2 hours) into the smaller unit (minutes): 2 hours = 120 minutes.

The ratio of 20 minutes to 120 minutes = 20 : 120.

Divide 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.