Ratio, Proportion and Rates of Change

Ratio, proportion and rates of change in GCSE Maths include unit conversions, scale factors, ratios, percentages, direct and inverse proportion, compound measures, growth and decay, and average and instantaneous rates of change.

For metric to ft and inches conversions, use the conversion information given in the question; similarly, square meter vs square feet or sq meter vs sq ft conversions require the correct squared conversion factor because area units are squared.

The metric system vs imperial system uses different units, so GCSE questions may involve converting length, area, volume, capacity and mass, while comparisons such as ounces vs milliliters or ml versus grams require additional information such as density because mass and volume are different quantities.

A ratio compares quantities and is written in forms such as $a:b$; ratio Corbettmaths-style GCSE questions commonly involve simplifying ratios, sharing quantities, unit conversion, mixing, scaling, comparison and best-buy problems.

To divide a quantity in the ratio $a:b$, first calculate $a+b$, divide the total by this number of parts, and then multiply by each ratio part.

A scale factor describes multiplicative enlargement or reduction, and scale drawings and maps use ratios to connect drawing measurements with real measurements; for similar shapes, length uses scale factor $k$, area uses $k^2$ and volume uses $k^3$.

Proportion means two ratios are equal, and a multiplicative relationship between two quantities can be expressed as a ratio, fraction or equation; ratios can also be related to fractions and linear functions.

A percentage means a number of parts per hundred, and percentage calculations can be performed using fractions, decimals or multipliers, which is the key method behind calculate online percentage and percentage calculator UK searches.

For a percentage increase of $r\%$, multiply by $1+\frac{r}{100}$, while a percentage decrease or off percent calculator uses $1-\frac{r}{100}$; these multipliers also support increase calculator and percentage decrease calculator problems.

Reverse percentages work backwards from a changed value by dividing by the relevant multiplier, which is the core method used in reverse percentages Corbettmaths questions and original-value problems.

Percentage change is calculated using $\frac{\text{change}}{\text{original value}}\times100\%$, and percentages greater than 100%, comparison of quantities, simple interest and financial percentage problems are all part of GCSE percentage applications.

Direct proportion can be written as $y=kx$ and inverse proportion as $y=\frac{k}{x}$, with equations, tables and graphs used to recognise, construct and solve direct and inverse proportion problems.

Compound measures combine different units, including speed, density, pressure, rates of pay and unit pricing; speed is $\frac{\text{distance}}{\text{time}}$, so time calculator with distance and speed problems are solved by rearranging the same relationship.

Volume estimator, tank capacity calculator, sq mt calculator and square meter calculator problems rely on choosing the correct length, area, volume or capacity formula and keeping all measurements in compatible units before calculating.

Growth and decay problems use repeated percentage multipliers, compound interest Corbettmaths and savings calculator questions use repeated growth such as $A=P(1+r)^n$, and rates of change are interpreted from graph gradients, with the gradient of a chord giving average rate of change and the gradient of a tangent giving instantaneous rate of change.