Percentage of an amount $p\%\text{ of }N=\dfrac{p}{100}\times N$or find $10\%$ (÷10) and $1\%$ (÷100) and build up
Increase / decrease $\times\left(1\pm\dfrac{p}{100}\right)$increase by $20\%$: $\times1.2$; decrease by $20\%$: $\times0.8$
Percentage change $\dfrac{\text{change}}{\text{original}}\times100$always divide by the ORIGINAL amount
Reverse percentage $\text{original}=\dfrac{\text{new value}}{\text{multiplier}}$£48 after $20\%$ off is $80\%$ of the original: $48\div0.8$
Of an amount · $15\%$ of $80$
$10\%=8$, $5\%=4$
$15\%=8+4=12$
Increase · increase $40$ by $20\%$
multiplier $=1.2$
$40\times1.2=48$
Change · $25\to30$
change $=5$
$\dfrac{5}{25}\times100=20\%$ increase
Percentage: a number out of $100$; $30\%=\dfrac{30}{100}=0.3$.
Multiplier: the decimal you multiply by, e.g. $\times1.15$ for a $15\%$ increase.
Percentage change: $\dfrac{\text{change}}{\text{original}}\times100$ – profit, loss, increase or decrease.
Reverse percentage: finding the ORIGINAL amount before a percentage change.
Depreciation: a decrease in value over time (a percentage decrease).
✗ Percentage change $\div$ the NEW value
✓ divide the change by the ORIGINAL value.
✗ Reverse %: taking $20\%$ off the sale price
✓ the sale price is $80\%$ of the original, so $\div0.8$ (do NOT add $20\%$ back).
✗ Decrease by $20\%$ $=\times0.2$
✓ it is $\times0.8$ (you keep $80\%$).
✗ Adding two percentages of different amounts
✓ each percentage is OF a different total – work them out separately.
• $10\%$ is $\div10$; $1\%$ is $\div100$; $5\%$ is half of $10\%$.
• To increase by $p\%$, multiply by $1+\dfrac{p}{100}$; to decrease, by $1-\dfrac{p}{100}$.
• Percentage change always divides by the ORIGINAL value.
• Non-calculator: build up from $10\%$, $5\%$ and $1\%$.
• Calculator: use a single multiplier ($\times1.2$, $\times0.85$, …).
• Reverse %: decide what percentage the amount you are given represents, then divide.
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