Converting compatible units | Year 8

01 / LEARN

The idea, step by step

A rate contains two units

A rate such as 72 km/h has a distance unit and a time unit. Replace both with equivalent quantities: 72 km is 72,000 m and 1 hour is 3,600 seconds. Then divide.

A larger unit in the numerator and a larger unit in the denominator affect the number differently. Work with equivalent quantities rather than trying to remember an unlabelled multiplication rule.

Useful conversion checks

For speed, dividing km/h by 3.6 gives m/s, and multiplying m/s by 3.6 gives km/h. The conversion follows from $1000 / 3600 = 1 / 3.6$ .

For price per 100 g to price per kilogram, ten groups of 100 g make 1 kg, so multiply the price by 10. Check that the converted rate represents the same total for a test quantity.

1 m/s = 3.6 km/h

A common trap

To convert km/h to m/s, multiply by 1,000 and stop.

Instead: That changes only the distance unit. You must also replace one hour with 3,600 seconds before dividing.

02 / WORKED EXAMPLES

See the thinking

Example 1

Kilometres per hour to metres per second

Convert 72 km/h to m/s.

Write 72,000 metres per 3,600 seconds.
Divide: $72000 \div 3600 = 20$ .
Reverse check: $20 \times 3.6 = 72$ km/h.

20 m/s.

Example 2

Metres per minute to metres per second

Convert 450 m/min to m/s.

One minute contains 60 seconds.
The same 450 m is covered in 60 s.
$450 \div 60 = 7.5$ .

7.5 m/s.

Check your understanding

Convert 10 m/s to km/h.

Show answer

36 km/h.

In one hour the distance is $10 \times 3600 = 36000$ m, or 36 km.

03 / WORKSHEET

Your turn

6 questions · 14 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Convert 36 km/h to m/s.
2 marks
Convert 15 m/s to km/h.
2 marks
Convert 3.5 L/min to mL/min.
2 marks
Convert 240 cm/min to m/s.
3 marks
A food costs AUD 0.80 per 100 g. Find its cost per kilogram.
2 marks
A runner covers 2.7 km in 15 minutes. Find the average speed in m/s.
3 marks

Read the worked solutions

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

Convert 36 km/h to m/s.
2 marks
$36 \div 3.6 = 10$ .
10 m/s.
Convert 15 m/s to km/h.
2 marks
$15 \times 3.6 = 54$ .
54 km/h.
Convert 3.5 L/min to mL/min.
2 marks
Each litre is 1,000 mL.
$3.5 \times 1000 = 3500$ .
3,500 mL/min.
Convert 240 cm/min to m/s.
3 marks
240 cm is 2.4 m.
$2.4 \div 60 = 0.04$ m/s.
0.04 m/s.
A food costs AUD 0.80 per 100 g. Find its cost per kilogram.
2 marks
1 kg contains ten lots of 100 g.
$0.80 \times 10 = 8$ .
AUD 8/kg.
A runner covers 2.7 km in 15 minutes. Find the average speed in m/s.
3 marks
2.7 km is 2,700 m; 15 min is 900 s.
$2700 \div 900 = 3$ .
3 m/s.

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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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