Scale factors
A scale factor is a number which scales or multiples a quantity. Scale factors are used to create maps and other scale diagrams.
When things are too big to draw on paper, scale factors are used to calculate smaller, Proportion is used to show how quantities and amounts are related to each other. The amount that one quantity changes in relation to another quantity is governed by proportion rules. measurements.
Floor plans for house designs are drawn on a smaller scale. This will help a designer to see if things will fit together well in each room of the house.
The scale used on this plan means that every 1 cm on the page is 100 cm (or 1 m) in real life.
Converting using a scale factor
To convert from a scale drawing to real life, measure a line in the drawing and multiply it by the scale factor to find the real length.
Example
If a floor plan shows a scale of \(1 \:\text{cm} = 100 \:\text{cm}\) and the kitchen measures 4 cm long on the drawing, then the real kitchen size would be \(4 \times 100 = 400 \:\text{cm}\) (or 4 m) long.
To convert from real life to a scale drawing, divide the real life measurement by the scale factor.
Example
A map is drawn using a scale of \(2 \:\text{cm} = 3.5 \:\text{km}\). The actual distance between M and O is 8.5 km. Work out the distance between M and O on the map.
The length on the drawing would be \(2 \div 3.5 \times 8.5 = 4.9 \:\text{cm}\) (to 1 dp).
More guides on this topic
- NEW: Equivalent ratios and simplifying ratios
- NEW: Ratio and fractions, and sharing in a ratio
- NEW: Scale drawings and maps
- NEW: Percentages of an amount
- NEW: Percentage change
- NEW: Repeated percentage change, interest and exponential change
- NEW: Working with proportion
- NEW: Equations of direct and inverse proportion
- Percentages - AQA
- Direct and inverse proportion - AQA
