Page 142 - MAT KS3 Y8 Cambridge CheckPoint

14 Ratio and proportion

Ratios are used to compare two or more numbers or quantities.
Key words
Every day, ratios are used in all sorts of ways for working out all
Make sure you learn and
sorts of things.
understand these key words:
For example, a builder uses ratios to work out the amounts of ratio
ingredients he needs to mix together, to make concrete or mortar. simplify
The ratio and ingredients vary, depending on what the builder direct proportion
will do with the concrete or mortar.
unitary method
To make the mortar for laying brickwork or block pavements, a
builder would use cement and sand in the ratio 1 : 4. This means that
every 1 kg of cement must be mixed with 4 kg of sand.
Builders often use a shovel or bucket to measure their ingredients.
For this mortar, they would need one shovel (or bucket) of cement
for every four shovels (or buckets) of sand.
To make a medium-strength concrete for a floor, a builder would
use three components, cement, sand and gravel, mixed in the ratio
1 : 2 : 4. This means that every 1 kg of cement must be mixed with
2 kg of sand and 4 kg of gravel.

It is important that a builder uses the correct ratio of ingredients
for the job, otherwise walls may fall down or floors may crack.

In many countries there are workplace rules and regulations
that use ratios. A good example of this is in childcare centres.
The table below shows an example of the legal child : staff
ratios in Australia.

Age of children Child : staff ratio
up to 24 months 4 : 1
24 months up to 3 years 5 : 1
3 years up to 5 years 11 : 1
The table shows that for children up to the age of 24 months, there
must be one member of staff for every four children. The ratio
changes as the children get older. By the time the children are aged
between 3 and 5 years, then there there must be one member of staff
for every 11 children.
In this unit you will learn how to simplify a ratio and how to share an amount in a given ratio. You will
also learn how to solve problems involving ratio and proportion.

140 14 Ratio and proportion