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Use Ratio with Map Scales

In this worksheet, students will apply map scales to find the scale values of real life elements or the real values of scaled elements on maps.

'Use Ratio with Map Scales' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change, Mensuration

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Units and Measurement

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

One of the most common applications for ratios is using them in map scales.

Normally ratios are given as two numbers (e.g. 1:5000) where both numbers must have the same units.

 

However, in map scales, because the numbers are usually quite large, they can be given with different units.

Examples of map scales may look like this:

1:50 k > 1 cm on the map would be 50000 cm in real life

1 cm:5 miles > 1 cm represents 5 miles in real life

 

 

Let's look at these ratios in action now in some examples. 

 

 

e.g. A map has a scale of 1:25 k. If a river was 2 cm long on this map, how long would it be in real life?

 

Step 1: Write the ratio out in full:

1:25000

 

Step 2: Write in the information you know under this:

1:25000

2: ?

 

Step 3: Look at the numbers you know and work out the relationship between them to apply to find the missing number:

In this case, we multiply 1 by 2 to reach 2 so our rule is '× 2'.

1:25000 × 2

2:50000

 

This means the river is 50,000 cm long in real life.

 

 

e.g. Two car parks are 15 miles apart. If the scale for a map is 1 cm: 5 miles, how far apart are the car parks on the map?

 

Step 1: Write the ratio out in full:

1 cm:5 miles

 

Step 2: Write in the information you know under this:

1 cm:5 miles

?:15 miles

 

Step 3: Look at the numbers you know and work out the relationship between them to apply to find the missing number:

5 × 15 = 3 so our rule here is '× 3'. 

1 cm:5 miles

3 cm:15 miles

 

This means the car parks are 3 cm apart on the map.

 

 

 

In this activity, we will apply map scales to find the scale values of real life elements or the real values of scaled elements on maps. 

Type a word in the space to complete the sentence below. 

Type two words in the space to complete the sentence below. 

A map has a scale of 1 cm:50 km.

 

What is the ratio we will need to work with in this case, expressed in its simplest form? 

A map has a scale of 4 cm:1 km.

 

What is the ratio we will need to work with in this case, expressed in its simplest form? 

A river measures 3 cm on a map with a scale of 1 cm:50 km.

 

How long is the river in real life?

50 km

150 km

100 km

Two picnic spots are 7.3 cm apart on a map with a scale of 1 cm:2 km.

 

How far apart are the picnic spots in real life?

 

Type your answer as a number below without any units, as these have already been provided for you. 

50 km

150 km

100 km

A map has a scale of 1 cm:5 km.

 

Match each scaled measurement on the left with the correct real life measurement on the right. 

Column A

Column B

1 cm in the map
26 km in real life
2 cm in the map
35 km in real life
7 cm in the map
10 km in real life
5.2 cm in the map
5 km in real life

A map has a scale of 1 cm:7 km.

 

Match each real life measurement on the left with the correct scaled measurement on the right. 

Column A

Column B

7 km in real life
2 cm in the map
14 km in real life
5.4 cm in the map
28 km in real life
4 cm in the map
37.8 km in real life
1 cm in the map

A map has a scale of 1:25 k.

 

How far is 3.1 cm on the map in real life?

 

Type your answer as a number below without any units, as these have already been provided for you. 

Column A

Column B

7 km in real life
2 cm in the map
14 km in real life
5.4 cm in the map
28 km in real life
4 cm in the map
37.8 km in real life
1 cm in the map

Two towns are 41 km apart.

 

The map showing their location uses a scale of 1:50 k.

 

How far apart are the two towns on the map?

 

Type your answer as a number below without any units, as these have already been provided for you. 

Column A

Column B

7 km in real life
2 cm in the map
14 km in real life
5.4 cm in the map
28 km in real life
4 cm in the map
37.8 km in real life
1 cm in the map
  • Question 1

Type a word in the space to complete the sentence below. 

CORRECT ANSWER
EDDIE SAYS
Maps scales are much easier to apply if we first write out the ratio we are applying in full, and then fill in the information which we already know. Following both of these steps leads us to a conversion factor, which we can then apply to find the missing variable.
  • Question 2

Type two words in the space to complete the sentence below. 

CORRECT ANSWER
EDDIE SAYS
Conversion factors tell us what we need to multiply or divide by in order to find a missing variable. If we know the two scaled measurements, then we will need to multiply to make the units we are working with larger. If we know the two real life measurements, then we will need to divide to make the units we are working with smaller. Does that make sense? Let's apply this logic in the remainder of this activity.
  • Question 3

A map has a scale of 1 cm:50 km.

 

What is the ratio we will need to work with in this case, expressed in its simplest form? 

CORRECT ANSWER
EDDIE SAYS
Here we have two different units of measurement (cm and km), so we need to convert them to the same format to find the ratio. We need to ask ourselves: How many cms are in a km? There are 1000 m in a km, and 100 cm in a m, so we need to calculate: 5 × 1000 × 100 = 500,000 So 1 cm on the map is equivalent to 500,000 cm in real life. Therefore, our ratio is 1:50000.
  • Question 4

A map has a scale of 4 cm:1 km.

 

What is the ratio we will need to work with in this case, expressed in its simplest form? 

CORRECT ANSWER
EDDIE SAYS
Again, we are comparing cm and km here, so we need to convert them into the same format to find the ratio. There are 1000 m in a km, and 100 cm in a m, so we need to calculate: 1 × 1000 × 100 = 100,000 So our ratio at this point is 4:100000. But we can simplify this further by dividing by 4: 4:100000 ÷ 4 1:25000 So 1 cm on the map is equivalent to 25,000 cm in real life. Therefore, our simplest ratio is 1:25000.
  • Question 5

A river measures 3 cm on a map with a scale of 1 cm:50 km.

 

How long is the river in real life?

CORRECT ANSWER
150 km
EDDIE SAYS
Do you remember the rules we learnt in the Introduction? 1) Write out the ratio and what we know so far: 1 cm:50 km 3 cm:? 2) Work out our conversion factor: 1 × 3 = 3 so our rule here is '× 3' 3) Use this to work out the real length of the river: 50 × 3 = 150 km
  • Question 6

Two picnic spots are 7.3 cm apart on a map with a scale of 1 cm:2 km.

 

How far apart are the picnic spots in real life?

 

Type your answer as a number below without any units, as these have already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
Let's apply our process again. 1) Write out the ratio and what we know so far: 1 cm:2 km 7.3 cm:? 2) Work out our conversion factor: 1 × 7.3 = 7.3 so our rule here is '× 7.3' 3) Use this to work out the real length of the river: 2 × 7.3 = 14.6 km
  • Question 7

A map has a scale of 1 cm:5 km.

 

Match each scaled measurement on the left with the correct real life measurement on the right. 

CORRECT ANSWER

Column A

Column B

1 cm in the map
5 km in real life
2 cm in the map
10 km in real life
7 cm in the map
35 km in real life
5.2 cm in the map
26 km in real life
EDDIE SAYS
The scale of 1 cm:5 km means that each centimetre on the map will represent 5 km in real life, so we simply need to multiply each scaled value by 5 to find our matches. Let's work through them one at a time. 1 × 5 = 5 km 2 × 5 = 10 km 7 × 5 = 35 km 5.2 × 5 = 26 km Were you able to match those successfully?
  • Question 8

A map has a scale of 1 cm:7 km.

 

Match each real life measurement on the left with the correct scaled measurement on the right. 

CORRECT ANSWER

Column A

Column B

7 km in real life
1 cm in the map
14 km in real life
2 cm in the map
28 km in real life
4 cm in the map
37.8 km in real life
5.4 cm in the map
EDDIE SAYS
This is the same process as the previous question, but we need to apply the reverse as we are working from real life to scaled in this scenario. The scale of 1 cm:7 km means that each centimetre on the map will represent 7 km in real life, so we simply need to divide each real value by 7 to find our matches. Let's work through them one at a time. 7 ÷ 7 = 1 cm 14 ÷ 7 = 2 cm 28 ÷ 7 = 4 cm 37.8 ÷ 7 = 5.4 cm
  • Question 9

A map has a scale of 1:25 k.

 

How far is 3.1 cm on the map in real life?

 

Type your answer as a number below without any units, as these have already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
Let's apply our process again. 1) Write out the ratio and what we know so far: 1:25000 3.1 cm:? 2) Work out our conversion factor: 1 × 3.1 = 3.1 so our rule here is '× 3.1' 3) Use this to work out the real distance: 25000 × 3.1 = 77,500 cm Let's convert this into a more sensible measurement now: 77500 cm ÷ 100 = 775 m 775 ÷ 1000 = 0.775 km
  • Question 10

Two towns are 41 km apart.

 

The map showing their location uses a scale of 1:50 k.

 

How far apart are the two towns on the map?

 

Type your answer as a number below without any units, as these have already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
Let's apply our process one final time. 1) Write out the ratio and what we know so far: 41 km = 41000 m = 4100000 1:50000 ?:4100000 2) Work out our conversion factor: 4100000 ÷ 50000 = 82 so our rule here is '× 82' 3) Use this to work out the real distance: 1 × 82 = 82 cm You can now apply map scales to find the scale values of real life elements or the real values of scaled elements on maps - a great skill for next time you are using a map!
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