Ratio and Proportion

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infoWhy this? Ratio and proportion provide efficient ways to share quantities, scale situations, and describe how variables change together. Connecting ratios with fractions and percentages strengthens flexible multiplicative reasoning in practical and abstract contexts.

scheduleWhy now? This unit extends Year 7 simplification and direct proportion to sharing, recipes, missing quantities, and introductory inverse proportion. Prior fraction and percentage work allows us to move confidently among different representations of the same relationship.

A ratio compares two or more quantities, showing how many times one value contains or is contained within the other or others.
Each share in a ratio can be written as a fraction of the whole; for example, in the ratio `2:5`, the two shares are `\frac{2}{7}` and `\frac{5}{7}` of the whole.
Each share in a ratio can be expressed as a percentage by converting its fraction of the whole to a percentage; for example, in the ratio `2:3`, the two shares are 40% and 60%.
Sharing a quantity in a given ratio means dividing the total into parts according to the ratio.
In a ratio `a:b`, the total number of parts is `a + b`.
Proportion describes the relationship between quantities that change in relation to each other.
In direct proportion, when one quantity is multiplied by a scale factor, the other quantity is multiplied by the same scale factor.
In inverse proportion, as one quantity increases, the other decreases so that their product remains constant.
Recipe problems involve scaling quantities up or down in direct proportion.
Inverse proportion problems can be identified by the phrase 'the more... the less...' or similar wording.

rocket_launchYou must be able to

Write each share in a ratio as a fraction of the whole or as a percentage.
Share a quantity into a given ratio, showing all steps.
Use a given ratio to find a missing quantity when one part or the total is known.
Use proportion to solve recipe problems, including scaling recipes up or down.
Solve simple worded problems involving inverse proportion, including setting up and solving the appropriate equation.

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