Ratio and proportion

At the end of this chapter, you should be able to:

• define ratio • perform calculations with ratios • define direct proportion • perform calculations with direct proportion, including Hooke’s law, Charles’s law and Ohm’s law • define inverse proportion • perform calculations with inverse proportion, including Boyle’s law

Ratio is a way of comparing amounts of something; it shows how much bigger one thing is than the other. Some practical examples include mixing paint, sand and cement, or screen wash. Gears, map scales, food recipes, scale drawings and metal alloy constituents all use ratios. Two quantities are in direct proportion when they increase or decrease in the same ratio. There are

several practical engineering laws which rely on direct proportion. Also, calculating currency exchange rates and converting imperial to metric units rely on direct proportion. Sometimes, as one quantity increases at a particular rate, another quantity decreases at the same rate; this is called inverse proportion. For example, the time taken to do a job is inversely proportional to the number of people in a team: double the people, half the time.