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JSS2: MATHEMATICS - 3RD TERM

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Scale on a map is defined as the ratio of actual distance to distance on map. 

Map scale = \( \frac {actual \; distance}{distance \; on \; map} \)

Map scales are normally written in the ratio form 1 : 7 e.g. 1 : 50 000 means 1cm represents 50 000cm. 

Example 4

Rewrite the scales in ratio form 

a. 1cm represents 10m 
b. 1cm represents 20cm 
c. 1cm represents 20km   

Solution 

a. 1cm represents 10m 

both have different units: change 10m to cm. 

1m =  100cm 

10m = 10 x 100cm = 1000cm 

Scale = 1 : 1000

b. 1cm represents 20cm 

both are in the same units 

scale = 1 : 20 

c. 1cm represents 20km 

convert 20km to cm 

1km  = 1000m 

= 1000 x 100cm 

1km = 100 000cm 

20km = 20 x 100 000cm

= 2 000 000cm 

Scale = 1 : 2000 000  

Example 5

Two cities are 70km apart. The distance between them is 20cm on the map. What is the scale of the map?

Solution 

Let the scale be 1 : n

1 cm → n cm 

20 cm → 70 km 

20 x n cm = 70km x 1 

Convert 70km to cm 

1km = 100 000cm 

70km = 7 000 000cm 

:- 20 x n cm = 7 000 000 cm

20n = 7 000 000

n =   \( \frac {7\;000\; 000}{20} \)

n = 350 000

The scale = 1 : 350 000

OR 

Using the formula 

Map scale = \( \frac {actual \; distance}{distance \; on \; map} \\ = \frac {7\;000\;000}{20} \\ = \scriptsize 350\;000 \)

The scale on map = 1 : 350 000

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