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Scale drawings and maps: real length and length on the paper
Mathematics Prep 1 Term 1, Unit 1, Lesson 2
GoalUse a scale to find a real length from a drawing and a drawing length from a real length.
New words
scale · length in the drawing : real lengthenlargement · a drawing bigger than the real thing (scale above 1)reduction · a drawing smaller than the real thing (scale below 1)real length · the length of the actual object or distance
Explanation
A scale drawing keeps the shape of the real thing and changes only its size. The scale is the length in the drawing : the real length, and both lengths must be in the same unit. A scale of 1 : 600,000 means 1 cm on the map stands for 600,000 cm in the real world. To find a real length, multiply the drawing length by the second number of the scale. To find a drawing length, divide the real length by it. Remember 1 m = 100 cm and 1 km = 100,000 cm. If the scale is bigger than 1 the drawing is an enlargement; if it is smaller than 1 it is a reduction.
ƒFormula
scale = length in drawing : real length
Use the same unit for both lengths.
Worked examples
A toy car is 12 cm long and the real car is 4.8 m long. Change 4.8 m to 480 cm. The scale is 12 : 480. Divide both terms by 12 to get 1 : 40. The toy is a reduction.
A map has the scale 1 : 600,000. Two towns are 4.5 cm apart on the map. Real distance = 4.5 × 600,000 = 2,700,000 cm. Divide by 100,000 to change to km: 27 km.
A room is 5 m long and 4 m wide. Draw it with the scale 1 : 100. Drawing length = 500 cm ÷ 100 = 5 cm and drawing width = 400 cm ÷ 100 = 4 cm. The real area is 5 × 4 = 20 m². The drawing area is 5 × 4 = 20 cm². The area scale is not 1 : 100.
Class activity
Draw your room. With a grown-up, measure the length and width of your room or kitchen in metres. Choose the scale 1 : 100 and draw it on paper. How long are the sides in your drawing?
Practice
1
A map has the scale 1 : 50,000. A road is 6 cm long on the map. What is the real length in km?
6 × 50,000 = 300,000 cm = 3 km.
2
Two cities are 18 km apart. How far apart are they on a map with the scale 1 : 600,000?
18 km = 1,800,000 cm and 1,800,000 ÷ 600,000 = 3 cm.
3
A drawing of a ant is 6 cm long. The real ant is 3 mm long. Find the scale. Is it an enlargement?
6 cm = 60 mm, so the scale is 60 : 3 = 20 : 1. It is an enlargement.
4
A football pitch is 100 m long and is drawn 10 cm long. What is the scale?
100 m = 10,000 cm. The scale is 10 : 10,000 = 1 : 1,000.
5
Nour says the scale “1 cm represents 5 m” is 1 : 5. What is wrong?
The units differ. 5 m = 500 cm, so the scale is 1 : 500.