Unit rates | Year 8 | Ascent Library

01 / LEARN

The idea, step by step

What per means

A unit rate states how much of one quantity corresponds to one unit of another. A cost of AUD 24 for 8 L is $24 \div 8 = 3$ dollars per litre. The units tell you the direction of the division.

The reciprocal rate can also be useful, but it answers a different question. Litres per minute describes filling speed; minutes per litre describes time needed for each litre.

Divide, then scale

First divide the total quantity by the number of units to get the rate per one. Then multiply by a new number of units. Keep an exact value until money needs rounding to cents.

Check by multiplying the unit rate by the original number of units. It should reproduce the given total. A label such as dollars/kg prevents a correct number being used in the wrong way.

unit rate = \frac{total quantity}{number of units}

A common trap

A rate of 6 L/min is the same number as 6 min/L.

Instead: These are reciprocal units. At 6 L/min, each litre takes $1 / 6$ minute, not 6 minutes.

02 / WORKED EXAMPLES

See the thinking

Example 1

Cost per litre

Eight litres of paint cost AUD 24. Find the unit price and the cost of 5 L at the same rate.

Divide the cost by the litres: $24 \div 8 = 3$ .
The unit price is AUD 3 per litre.
Five litres cost $5 \times 3 = 15$ dollars.

AUD 3/L; AUD 15 for 5 L.

Example 2

Words per minute

A speaker reads 375 words in 5 minutes. Find the average rate.

The denominator must be time in minutes.
Calculate $375 \div 5 = 75$ .
At this average rate, 2 minutes would correspond to $2 \times 75 = 150$ words.

75 words/minute.

Check your understanding

A tap fills 28 L in 4 minutes. What is its rate?

Show answer

7 L/min.

Divide 28 litres by 4 minutes; $7 \times 4 = 28$ checks the result.

03 / WORKSHEET

Your turn

6 questions · 10 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Six kilograms cost AUD 18. Find the cost per kilogram.
1 mark
A car travels 240 km in 3 hours. Find its average speed.
1 mark
A pump moves 42 L in 7 minutes. Find its rate.
1 mark
Three litres of juice cost AUD 8.40. Find the unit price.
2 marks
A machine makes 150 items in 12 seconds. Find the average rate.
2 marks
A 0.6 kg bag costs AUD 5.40. Find the price per kilogram and per 100 g.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Six kilograms cost AUD 18. Find the cost per kilogram.
1 mark
$18 \div 6 = 3$ .
AUD 3/kg.
A car travels 240 km in 3 hours. Find its average speed.
1 mark
$240 \div 3 = 80$ .
80 km/h.
A pump moves 42 L in 7 minutes. Find its rate.
1 mark
$42 \div 7 = 6$ .
6 L/min.
Three litres of juice cost AUD 8.40. Find the unit price.
2 marks
$8.40 \div 3 = 2.80$ .
AUD 2.80/L.
A machine makes 150 items in 12 seconds. Find the average rate.
2 marks
$150 \div 12 = 12.5$ .
Check: $12.5 \times 12 = 150$ .
12.5 items/s.
A 0.6 kg bag costs AUD 5.40. Find the price per kilogram and per 100 g.
3 marks
$5.40 \div 0.6 = 9$ .
100 g is one tenth of a kilogram, so divide 9 by 10.
AUD 9/kg; AUD 0.90 per 100 g.

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Curriculum reference & lesson scope

Australian Curriculum v9 / SA Curriculum Mathematics

Ratio scaling and division review; unit rates; comparing rates and best buys; speed, distance and time; converting compatible units; direct-proportion tables and graphs; modelling practical rate problems and checking assumptions.

Official curriculum source ↗

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