Ratio and Proportion

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infoWhy this? Ratio and proportion develop multiplicative comparison, allowing us to describe relative size, scale quantities, and solve problems involving equivalent relationships. These ideas are fundamental to rates, percentages, measures, and many practical decisions.

scheduleWhy now? This unit draws directly on factors and HCF when simplifying ratios and marks an important shift from additive to multiplicative reasoning. Establishing equivalent-ratio methods now prepares us for sharing, recipes, percentages, and direct and inverse proportion.

A ratio is a way of comparing two or more quantities by division.
A ratio is in its simplest form when the numbers in the ratio have no common factors other than 1.
To simplify a ratio, each part must be divided by their highest common factor (HCF).
Quantities of the same type must be expressed in the same unit before their ratio is formed or compared; rates compare quantities of different types and retain or combine units.
Quantities of the same type must be converted to the same unit before forming and simplifying their ratio; rates may compare quantities measured in different units.
A ratio in the form `1:n` means the first quantity is 1 part and the second quantity is `n` parts.
A ratio in the form `n:1` means the first quantity is `n` parts and the second quantity is 1 part.
Two quantities are directly proportional when one is a constant multiple of the other; multiplying one quantity by a factor multiplies the other by the same factor, so the ratio of corresponding values is constant.
In problems involving direct proportion, the ratio between corresponding quantities remains constant.

rocket_launchYou must be able to

Write the ratio of one quantity to another using correct mathematical vocabulary and notation.
Simplify a given ratio to its simplest form by dividing each part by their highest common factor.
Convert quantities to the same units before writing or simplifying a ratio.
Express a given ratio in the form `1:n` or `n:1` by dividing both sides of the ratio by the appropriate number.
Solve simple worded problems involving direct proportion by setting up and using equivalent ratios.

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