# Convert Compound Units

In this worksheet, students will practise converting compound speed values into alternative units to find equivalents.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Difficulty level:

### QUESTION 1 of 10

Compound units are made up of more than 1 unit of measurement e.g.

Speed (made up of distance and time);

Density (mass and volume);

Pressure (force and area).

While technically we need to be able to convert values between any of these units of measurement, in practice, we will probably only have to convert speeds in exams.

If you get asked to convert one of the others, just follow the concepts here and you shouldn't go far wrong.

Let's follow some examples through to learn how to convert speed values into alternative measurements.

e.g. Change 10 m/s into km/h.

Step 1: Write as a proportion.

10 m/s means 10 metres covered in 1 second.

To write this as a proportion, we need to create an equation with an equals sign, like this:

10 metres = 1 second

Step 2: Convert the time unit.

It's easier to change the seconds into hours first.

1 hr = 3600 seconds, so we can multiply both sides by 3600 to get:

36000 metres = 3600 seconds

36000 metres = 1 hour

Step 3: Convert the speed unit.

We know that 1 km = 1000 m.

We can now change the distance travelled into kilometres by dividing by 1000 to reach:

36 km = 1 hour

Since we now have our units expressed in kilometres and hours, we can say that 10 m/s = 36 km/h.

Let's try another to check that we have this process clear.

e.g. Change 20 km/h into m/s.

Step 1: Write as a proportion.

20 km/hr means 20 kilometres covered in 1 hour.

20 kilometres = 1 hour

Step 2: Convert both units to their equivalents.

We know that 1 hr = 3600 seconds and 1 km = 1000, so we can convert both sides into these alternative units:

20 kilometres = 1 hour  -->  20000 m = 3600 seconds

Step 3: Convert the time to 1 second.

We currently know how many metres we travel in 3600 seconds, but we want to know how many we travel in just 1 second.

To find this, we need to divide both sides by 3600:

5.56 m = 1 second

Since we now have our expressed in metres and seconds, we can say that 20 km/h = 5.56 m/s.

In this activity, we will convert compound speed values into alternative units to find equivalents using variations of the method shown above.

If Lucy travels 20 metres in 1 second, how many metres will she travel in 1 hour?

Mohamed travelled 75000 m in 1 hour.

How many kilometres has he travelled in this time?

Complete the sentence below by filling the gaps.

You should write your answers using numbers only, or you may be marked incorrectly.

Complete the sentence below by filling the gaps.

You should write your answers using numbers only, or you may be marked incorrectly.

What is 25 m/s expressed in km/h?

6.95 km/h

90 km/h

9 km/h

What is 12 km/h expressed in m/s?

43.2 m/s

33.34 m/s

3.34 m/s

Find the speed pairs below which are equivalents

All conversions have been rounded to one decimal place

## Column B

10 m/s
36 km/h
14 m/s
15.6 m/s
22 km/h
6.1 m/s
56 km/h
50.4 km/h

To convert from m/s into km/h, which option below summarises the correct order of operation?

× 3600 then ÷ 1000

÷ 1000 then × 3600

Either, it doesn't matter

Change 32 m/s into km/h.

Just write your answer as a number without any units as the correct unit has been provided for you.

Write your answer to one decimal place

× 3600 then ÷ 1000

÷ 1000 then × 3600

Either, it doesn't matter

Change 42 km/h into m/s.

Just write your answer as a number without any units as the correct unit has been provided for you.

Write your answer to two decimal places

× 3600 then ÷ 1000

÷ 1000 then × 3600

Either, it doesn't matter

• Question 1

If Lucy travels 20 metres in 1 second, how many metres will she travel in 1 hour?

CORRECT ANSWER
EDDIE SAYS
This question asks for the answer in metres, so we don't need to change the distance units on this occasion. Therefore, we just need to convert the time units. There are 3600 seconds in 1 hour, so to convert between seconds and hours, we need to multiply by 3600: 20 × 3600 = 7200 m/h How did you get on with this first challenge? Review the Introduction examples before you move on if you found it challenging.
• Question 2

Mohamed travelled 75000 m in 1 hour.

How many kilometres has he travelled in this time?

CORRECT ANSWER
EDDIE SAYS
Now the unit of time is remaining the same, and we just need to convert the units of distance. There are 1000 metres in 1 kilometre, so to convert between metres and kilometres, we need to divide by 1000: 75000 ÷ 1000 = 75 km/h
• Question 3

Complete the sentence below by filling the gaps.

You should write your answers using numbers only, or you may be marked incorrectly.

CORRECT ANSWER
EDDIE SAYS
As we discussed in the Introduction, our first step should be to convert the time unit and then the distance unit. The time unit has a scale factor of 3600, as there are 3600 seconds in an hour. The distance unit has a scale factor of 1000, as there are 1000 metres in a kilometre. Does that make sense?
• Question 4

Complete the sentence below by filling the gaps.

You should write your answers using numbers only, or you may be marked incorrectly.

CORRECT ANSWER
EDDIE SAYS
To convert the other way around, we just need to switch the order of our actions! This time, our first step should be to convert the distance unit and then the time unit. Simple! Let's practise applying these processes now.
• Question 5

What is 25 m/s expressed in km/h?

CORRECT ANSWER
90 km/h
EDDIE SAYS
Did you remember that to convert from m/s to km/h, we need to multiply to convert the time unit, then divide to convert the distance unit? 25 × 3600 ÷ 1000 = 90 km/h
• Question 6

What is 12 km/h expressed in m/s?

CORRECT ANSWER
3.34 m/s
EDDIE SAYS
Did you remember that to convert from km/h to m/s, we need to switch the order of operations from the previous question? 12 × 1000 ÷ 3600 = 3.34 m/s
• Question 7

Find the speed pairs below which are equivalents

All conversions have been rounded to one decimal place

CORRECT ANSWER

## Column B

10 m/s
36 km/h
14 m/s
50.4 km/h
22 km/h
6.1 m/s
56 km/h
15.6 m/s
EDDIE SAYS
Do we even need to calculate the conversions here? We know that each m/s measurement must match with a km/h, and we can then just say that the slowest speed in m/s is the slowest speed in km/h - a sneaky possible shortcut here! If you worked through each conversion, then your working should look something like this: 10 m/s × 3600 ÷ 1000 = 36 km/h 14 m/s × 3600 ÷ 1000 = 50.4 km/h 22 km/h × 1000 ÷ 3600 = 6.1 m/s 56 km/h × 1000 ÷ 3600 = 15.6 m/s
• Question 8

To convert from m/s into km/h, which option below summarises the correct order of operation?

CORRECT ANSWER
Either, it doesn't matter
EDDIE SAYS
This was a bit of a trick question - sorry! It actually doesn't matter which order we use; you can do it any order you want. The reason that we normally multiply first, is so we don't have to deal with complex decimals. However, you will still get the same answer either way, which is important to remember!
• Question 9

Change 32 m/s into km/h.

Just write your answer as a number without any units as the correct unit has been provided for you.

Write your answer to one decimal place

CORRECT ANSWER
EDDIE SAYS
Let's just follow our simple rule again: × 3600 then ÷ 1000 32 × 3600 ÷ 1000 = 115.2 km/h
• Question 10

Change 42 km/h into m/s.

Just write your answer as a number without any units as the correct unit has been provided for you.

Write your answer to two decimal places

CORRECT ANSWER
EDDIE SAYS
This time, let's just flip the order of our process: × 1000 then ÷ 3600 42 × 1000 ÷ 3600 = 11.67 m/s Hopefully, you noticed that the answer here was a recurring decimal. Our answer should be 11.67 not 11.66, as we need to round it up. You can now convert speed values between different units of measurement with ease - amazing!
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