 # Map Scales

In this worksheet, students practise applying ratios to map scales. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation, Units and Measurement

Difficulty level:   ### QUESTION 1 of 10

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

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

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

Examples of map scales may look like this 1:25k, 1:50k (These are the two that are used for ordanance survey maps) or something along the lines of 1cm:5miles

1 : 25k would mean that every 1 cm on the map would be 25000 cm in real life. 1 cm : 5 miles would mean 1cm represents 5 miles in real life.

Example 1:

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

Step 1: Write the ratio out in full

1 : 25 000

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

1 : 25 000

2: x

Step 3: Look at the numbers you know (the 1 and 2) and work out the realtionship (In this case, it is multiply by 2) and so the same to the other side of the ratio.

1 : 25 000

2: 50 000

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

Example 2:

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

x       : 15 miles

Step 3: Look at the numbers you know (the 5 and 15) and work out the relationship (In this case, it is multiply by 3) and so the same to the other side of the ratio.

1 cm : 5 miles

3 cm : 15 miles

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

Complete the following sentence.

Scales on a map are a conversion factor...

A map has a scale of 1cm : 50 km. Write this out as a ratio in it's simplest form.

(Hint, make it into the same units first)

A map has a scale of 4cm : 1 km. Write this out as a ratio in it's simplest form.

(Hint, make it into the same units first)

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

How long is the river in real life?

150 km

50 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 rivers in real life?

7.3 km

14.6 km

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

Match the scale length with the lengths in real life

## Column B

1 cm in the map
10 km in real life
2 cm in the map
35 km in real life
7 cm in the map
26 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 the scale length with the lengths in real life

## Column B

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

Give you answer in km (don't worry about putting in the units.)

Two towns are 41 km apart.

A map has a scale of 1: 50 k. How far apart are the two towns on the map

Give you answer in cm (don't worry about putting in the units.)

• Question 1

Complete the following sentence.

EDDIE SAYS
Maps scales are made a lot easier if we write the ratio out and then fill in what we know. This lets us find the conversion factor.
• Question 2

Scales on a map are a conversion factor...

EDDIE SAYS
Conversion factors mean we multiply if we are making it bigger (scale diagram to real life) or divide if we are making it smaller (real life to map scale)
• Question 3

A map has a scale of 1cm : 50 km. Write this out as a ratio in it's simplest form.

(Hint, make it into the same units first)

1:5000000
1 : 5000000
1 :5000000
1: 5000000
EDDIE SAYS
We know that there are 1000m in a km and 100 cm in a m. This means we have to multiply the 50 by 1000 and then by 100 This gives 5000000
• Question 4

A map has a scale of 4cm : 1 km. Write this out as a ratio in it's simplest form.

(Hint, make it into the same units first)

1:25000
1 : 25000
1 :25000
1: 25000
EDDIE SAYS
We know that there are 1000m in a km and 100 cm in a m. This means we have to multiply the 1km by 1000 and then by 100 This gives 100000 Writing the ratio out now gives 4 : 1000000 We can then just cancel down
• 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?

150 km
EDDIE SAYS
Remember the rules? 1) Write out the ratio and what you know. 1 cm : 50 km 3 cm: X 2) Work out your multiplier. You know 1 cm and 3cm, so your multiplier is x3 3) Use this to work out the real-life length of the river.
• 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 rivers in real life?

14.6 km
EDDIE SAYS
Remember the rules? 1) Write out the ratio and what you know. 1 cm : 2 km 7.3 cm: X 2) Work out your multiplier. You know 1 cm and 7.3cm, so your multiplier is x7.3 3) Use this to work out the real-life distance between the picnic spots
• Question 7

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

Match the scale length with the lengths in real life

## 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
If the scale is 1 cm: 5 km, this means that the real-life measurements will be 5 times bigger than the ones on the map.
• Question 8

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

Match the scale length with the lengths in real life

## 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
If the scale is 1 cm: 7 km, this means that the real-life measurements will be 7 times bigger than the ones on the map.
• Question 9

A map has a scale of 1: 25 k. How far is 3.1 cm on the map in real life?

Give you answer in km (don't worry about putting in the units.)

0.775
EDDIE SAYS
If we use our scale, we can work out that 3.1 cm gives 77 500cm in real life. We need to convert this into km thought. We know that 100cm = 1m and 100 m - 1 km We need to divide by 100 (to change it into metres) and then by 1000 (to change it into km.)
• Question 10

Two towns are 41 km apart.

A map has a scale of 1: 50 k. How far apart are the two towns on the map

Give you answer in cm (don't worry about putting in the units.)

82
EDDIE SAYS
As we are using a ratio that doesn\'t have units. We have to change the 41 km into cm (that\'s what we are asked for on the map.) 41 km = 41 000 m 41 000 m = 4 100 000 cm A scale of 1: 50k gives a conversion factor of 50000 If we divide 4 100 000 by 50 000 we will get...
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