GCSE Foundation Tier Number and Ratio Reference Cheat Sheet

Key Facts

• To convert a fraction to a percentage, calculate $\frac{a}{b} \times 100\%$.
• To find $p\%$ of an amount $A$, calculate $\frac{p}{100} \times A$.
• To increase an amount by $p\%$, multiply by $1 + \frac{p}{100}$.
• To decrease an amount by $p\%$, multiply by $1 - \frac{p}{100}$.
• In standard form, a number is written as $a \times 10^n$, where $1 \leq a < 10$ and $n$ is an integer.
• To share an amount $T$ in the ratio $a:b$, one part is $\frac{T}{a+b}$, so the shares are $a \times \frac{T}{a+b}$ and $b \times \frac{T}{a+b}$.
• For direct proportion, if $y$ is directly proportional to $x$, then $y = kx$ for a constant $k$.
• Speed, distance, and time are linked by $\text{speed} = \frac{\text{distance}}{\text{time}}$.

Vocabulary

Place value

Place value is the value of a digit based on its position in a number, such as ones, tenths, or thousands.

Standard form

Standard form writes a number as $a \times 10^n$, where $1 \leq a < 10$ and $n$ is an integer.

Percentage multiplier

A percentage multiplier is the decimal factor used to increase or decrease an amount by a percentage.

Ratio

A ratio compares quantities by showing how many parts of one quantity match parts of another quantity.

Direct proportion

Direct proportion means two quantities increase or decrease at the same rate, so their ratio stays constant.

Unit rate

A unit rate compares a quantity to one unit of another quantity, such as miles per hour or cost per kilogram.