year 8 maths

302 Chapter 5 Ratios and rates
5F Ratios and rates and the unitary method
The concept of solving problems using the unitary method was introduced in Chapter 4. The unitary
method involves finding the value of ‘one unit’. This is done by dividing the amount by the given quantity.
Once the value of ‘one unit’ is known, multiplying will find the value of the number of units required.
Let’s start: Finding the value of ‘1 unit’
For each of the following, find the value of one unit or one item.
• eight basketballs cost $200 .
• four cricket bats cost $316 .
• 5 kg of watermelon cost $7.50 .
For each of the following, find the rate per one unit.
• Car travelled 140 km in 2 hours.
• 1000 L of water leaked out of the tank in 8 hours.
• $51 was the price paid for 3 kg of John Dory fish.
For each of the following, find the value of one ‘part’.
• Ratio of books to magazines read was 2 : 5 . Milli has read 14 books.
• Ratio of pink to red flowers is 7 : 11 . A total of 330 red flowers are in bloom.
• Ratio of girls to boys is 8 : 5 . There are 40 girls in a group.
Key ideas
■ The unitary method involves finding the value of ‘one unit’ and then using this information to
solve the problem.
■ When dealing with ratios , find the value of one ‘part’ of the ratio.
For example: Ratio of cars to motorbikes is 35 : 2 and there are six motorbikes.
2 parts = 6 motorbikes
÷2 ÷2
1 part = 3 motorbikes
■ When dealing with rates , find the value of the rate per one ‘unit’.
For example: Pedro earned $64 for a 4 -hour shift at work.
Therefore, wage rate = $64 per 4 hours = $16 per hour = $16/h .
■ Once the value of one ‘part’ or the rate per one ‘unit’ is known, the value of any number of
parts or units can be found by multiplying.
■ The technique of dividing and/or multiplying values in successive one-step calculations can be
applied to the concept of converting rates from a set of given units to a different set of units.
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
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