5.5 Scale factors, scale diagrams and maps — Learn

Prerequisites

You should be able to multiply and divide whole numbers and fractions. Check units before comparing quantities.

Key terms

A scale compares a drawing length with a real length. The scale factor is the multiplier between corresponding lengths.

Objectives

• Convert units and use scales to find map, drawing and real lengths.
• Check that the result matches the units and direction of change.

Learn the method

A scale compares drawing and real lengths in the same units. Scale $1:50$ means one drawing unit represents 50 real units. Convert units before applying the scale.

Worked example. A 6 cm drawing represents a 9 m wall. Find drawing:real scale.

• Convert: $9\times100=900$ cm.
• Form the ratio: $6:900$.
• Divide both parts by 6: $1:150$.
• Check: 1 cm represents 150 cm, or 1.5 m.

Progress check: at 1 cm for 1 m, an 18 m path needs 18 cm.

Watch out. Do not compare 9 m with 6 cm before converting units. Write both lengths in centimetres, then simplify the ratio.

You should now be able to

• I can convert lengths into matching units before using a scale.
• I can find drawing lengths and real distances from a scale.
• I can check units and the size of the result.