Ratios are used to compare quantities of 2 or more things. Although you are most likely to see them written using the ‘colon’ format, such as 1:3, you should also be able to work with them as fractions. Proportion is used to compare two ratios. Percentages pop up everywhere, and you should be comfortable working with them – don’t forget, they are just a special fraction where everything is out of 100! See how well you know these three topics in this GCSE Maths quiz.

Ratios can be used in everyday life to scale things up, such as recipes and mixing liquids. Another important area they appear is in map scales, and any budding geographer should know how to correctly apply them! One reason map scales cause problems is down to the lack of units, and problems working through different measurement scales.

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A common OS map scale is 1:50,000, so 1cm on the map represents 50,000 cm in real life. Working in stages, change this to metres (divide by 100), and then to km (divide by 1,000). This gives us something much easier to work with – 1cm is 0.5km, or 2cm to every km.

Make sure you can excel at the *Percentages (F)* quiz before trying this one – you should know how to apply percentage change, and work out the percentage of an amount. Speed up your calculator work when doing percentage problems by using the decimal multiplier – so an increase of 15% will give a multiplier of 1.15, a decrease of 15% gives 0.85 and so on. This becomes very useful when dealing with compound interest problems.

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