# Change Units in Algebraic Contexts

In this worksheet, students will convert algebraic amounts between units by applying one (e.g. kg to g, m to mm, etc.) or two (e.g. m/s to km/h, g/m to kg/km, etc.) conversion factors.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Difficulty level:

### QUESTION 1 of 10

You may already be familiar with converting between metric units.

Let's review this now so you can be sure of what this means.

e.g. What is 17 cm in mm?

We know that there are 10 mm in 1 cm, so we have to multiply by 10.

17 × 10 = 170 mm

How to Convert Algebraic Units

When we are dealing with quantities as algebra, the same rules will apply.

We still need to use conversion factors, but we just have to calculate them in terms of the original algebraic quantity.

Let's explore an example to see how to do this.

e.g. Convert K cm into mm.

We know that to change cm into mm, we need to multiply by 10.

This means that K cm = 10 K mm.

Makes sense, doesn't it?

Let's try another, more complex, example now.

e.g. Convert P m/s into km/h.

This is a two-step problem as we have two units of measurement present: distance (m/km) and time (s/h).

1) We know that there are 3600 seconds in 1 hour.

So P metres = 1 second

3600P metres  = 1 hour

2) We know there are 1000 metres in a kilometre.

3600 P metres  = 1 hour

3.6P km = 1 hour

Therefore, P m/s = 3.6P km/hr.

In this activity, you will practise converting algebraic amounts between different units by finding and applying one or more conversion factors.

Add a word into the gap to complete the sentence below.

If we convert P metres (m) into cm, how will our new amount be represented?

100P cm

0.01P cm

10P cm

If we convert T cm into km, how will our new amount be represented?

0.001T km

0.00001T km

0.01T km

0.0001T km

Match the algebraic conversions below to their new amounts.

## Column B

T cm into metres
10T
T cm into mm
0.01T
T cm into kilometres
0.000001T

If we convert R cm2 into mm2, how will our new amount be represented?

Just write a number in the space as the unit has already been provided for you.

## Column B

T cm into metres
10T
T cm into mm
0.01T
T cm into kilometres
0.000001T

Which of the following can be used to convert m/s into km/h?

× 3.6

÷ 3.6

× 18/5

× 3600/1000

× 5/18

Which of these options is the correct conversion for T g/cm3 in kg/m3?

1000T kg/m3

0.1T kg/m3

0.001T kg/m3

If we convert 36U km/h into m/s, how will our new amount be represented?

Just write a number in the space as the unit has already been provided for you.

1000T kg/m3

0.1T kg/m3

0.001T kg/m3

If we convert D kg/m3 into g/m3, how will our new amount be represented?

Just write a number in the space as the unit has already been provided for you.

1000T kg/m3

0.1T kg/m3

0.001T kg/m3

If we convert 750N g/cm3 into kg/cm3, how will our new amount be represented?

Just write a number in the space as the unit has already been provided for you.

1000T kg/m3

0.1T kg/m3

0.001T kg/m3

• Question 1

Add a word into the gap to complete the sentence below.

EDDIE SAYS
If you are not sure about this one, why not go back and read over the Introduction again? When we are dealing with quantities as algebra, the same rules apply as with numbers, so we still use conversion factors. However, we need to apply the same process, but in terms of the original algebraic quantity. Let's explore what this means now in the rest of this activity.
• Question 2

If we convert P metres (m) into cm, how will our new amount be represented?

100P cm
EDDIE SAYS
We know that the conversion factor between m and cm is 100. As cm are smaller than metres, there will be more of them used to represent the same length, so we have to multiply P by this conversion factor: P × 100 = 100P cm Does that make sense?
• Question 3

If we convert T cm into km, how will our new amount be represented?

0.00001T km
EDDIE SAYS
We know that the conversion factor between cm and m is 100, then m and km is 1000. If we multiply these together, we find that the conversion factor we need to use here is 100,000. Which means that there are 100,000 cm in 1 km. As km are (much!) larger than cm, there will be much less of them used to represent the same length, so we have to divide T by this conversion factor: T ÷ 100000 = 0.00001T km Hopefully, all these decimals didn't trip you up!
• Question 4

Match the algebraic conversions below to their new amounts.

## Column B

T cm into metres
0.01T
T cm into mm
10T
T cm into kilometres
0.000001T
EDDIE SAYS
This question is all about knowing your conversion factors: Centi > m = 100 Milli > centi = 10 Centi > kilo = 100 x 1000 = 100,000 In each case, we need to decide if our starting unit is larger or smaller than our new unit. If it is larger, then we need to multiply. If it is smaller, then we need to divide. Can you apply these conversion rates and rules to match the pairs accurately?
• Question 5

If we convert R cm2 into mm2, how will our new amount be represented?

Just write a number in the space as the unit has already been provided for you.

EDDIE SAYS
This is a bit more complicated. Changing cm into mm uses a conversion factor of x 10, but this is an area, so we need to multiply by 102: R × 102 = 100R mm2 A little bit of a trickier one, hey?
• Question 6

Which of the following can be used to convert m/s into km/h?

× 3.6
× 18/5
× 3600/1000
EDDIE SAYS
There's a number of ways we can convert m/s into km/h. We need to remember that we have two measurements to convert here - distance (m/km) and time (s/h). Let's start with the distance element - what is the conversion rate between m and km? It's ÷ 1000. And between seconds and hours? There are 60 seconds in a minute and 60 minutes in an hour, so we need to work out: 60 × 60 = 3600 So our conversion factor here is multiply by 3600. 3600 ÷ 1000 = 3.6 This amount can be written in three different ways that are all equivalent - did you find all three in this list?
• Question 7

Which of these options is the correct conversion for T g/cm3 in kg/m3?

1000T kg/m3
EDDIE SAYS
Firstly, we need to know the conversion factors for each. g > kg = ÷ 1000 Changing cm3 into m3 is not as easy as it looks. There are 100 cm in a metre, but we are dealing with cubes too. 1m3 = 100 x 100 x 100 = 10,00,000 cm3 If we tie these two conversions together, we find that: 10000000 ÷ 1000 = 100 So our final answer should be 100T kg/m3
• Question 8

If we convert 36U km/h into m/s, how will our new amount be represented?

Just write a number in the space as the unit has already been provided for you.

EDDIE SAYS
We need to remember that we have two measurements to convert here - distance (km/m) and time (h/s). Let's start with the distance element - what is the conversion rate between km and m? It's × 1000. And between hours and seconds? There are 60 seconds in a minute and 60 minutes in an hour, so we need to work out: 60 × 60 = 3600 So our conversion factor here is divide by 3600. 1000 ÷ 3600 = 3.6 36U ÷ 3.6 = 10U m/s Did you remember to just type the number in, as the units have already been provided for you?
• Question 9

If we convert D kg/m3 into g/m3, how will our new amount be represented?

Just write a number in the space as the unit has already been provided for you.

EDDIE SAYS
We only need to convert the weight (kg/g) element this time, as the distance (m3) stays the same so does not require converting. So what is the conversion rate between kg and g? It's × 1000. D × 1000 = 1000D kg/m3 Did you remember to just type the number in?
• Question 10

If we convert 750N g/cm3 into kg/cm3, how will our new amount be represented?

Just write a number in the space as the unit has already been provided for you.

EDDIE SAYS
We only need to convert the weight (g/kg) element this time, as the distance (cm3) stays the same again. So what is the conversion rate between g and kg? It's ÷ 1000. 750N ÷ 1000 = 0.75D kg/cm3 You can now convert algebraic amounts into different units using one or two conversion factors combined - great job!
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