Ratio and Proportion

Select a course.

arrow_back

infoWhy this? Ratio, rates, and compound measures allow us to compare value, combine relationships, and quantify how one variable changes relative to another. Speed, density, unit cost, and direct proportion connect multiplicative reasoning with practical decision-making.

scheduleWhy now? Earlier ratio work established sharing, scaling, and direct and inverse relationships, while straight-line graphs introduced gradient. This unit combines those ideas in multi-step contexts and prepares us to interpret a wider range of rates and measures.

A ratio expresses the relative sizes of two or more values, using the format `a : b`.
The difference between two values in a ratio can be used to determine the actual values when the total or another value is known.
Ratios can be combined by finding equivalent ratios with a common term.
Direct proportion means that one quantity is a constant multiple of the other, given by the equation `y = kx`.
In 'best buy' problems, the best value is found by comparing the cost per unit.
The gradient of a straight-line graph representing direct proportion gives the rate of change between the variables.
Average speed is calculated as total distance divided by total time, using the formula `\text{speed} = \text{distance} \div \text{time}`.
The relationship between density, mass, and volume is given by `\text{density} = \text{mass} \div \text{volume}`.
Units must be consistent when calculating speed, such as km/h or m/s, density, such as g/cm³ or kg/m³, and other rates.

rocket_launchYou must be able to

Use the given difference between two values in a ratio to calculate the actual values, given either the total or one part.
Combine two or more ratios by finding equivalent ratios with a common term and solve related problems.
Solve 'best buy' problems by calculating and comparing the unit cost for different products.
Interpret and deduce rates of change from the gradient of direct proportion graphs.
Calculate average speed, distance, or time given any two of these quantities.
Calculate density, mass, or volume given any two of these quantities, using the formula triangle method if appropriate.

Curriculum Portal