8.9Summary

1. $x\% = \dfrac{x}{100}$. Convert freely between percentage, fraction and decimal.
2. Percentages can exceed $100\%$ (quantity exceeds the whole) or be less than $1\%$ (very small fraction).
3. Find $x\%$ of $Q$: compute $\dfrac{x}{100} \times Q$. Express $A$ as a percentage of $B$: $\dfrac{A}{B} \times 100\%$.
4. Percentage change $= \dfrac{\text{New} - \text{Original}}{\text{Original}} \times 100\%$. Always divide by the original.
5. Reverse percentage: the value given is a percentage of the original. Go through $1\%$ to reach $100\%$.
6. Profit $\%$ and Loss $\%$ are based on cost price. Discount $\%$ is based on marked price.
7. Singapore GST is $9\%$. Price with GST $= 1.09 \times$ price before GST. An inclusive price is $109\%$, so work back through $1\%$.
8. Commission $=$ commission rate $\times$ sales value.