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neurologyYou need to know

• A percentage means ‘per hundred’, so `p\% = \frac{p}{100}` of an amount.
• To find `p\%` of an amount, you can multiply the amount by the decimal `\frac{p}{100}`.
• A multiplier is the single number you multiply by to scale an amount (for example, multiply by 3 to triple, or multiply by 0.5 to halve).
• Converting a percentage to a decimal gives the multiplier for ‘`p\%` of’, because `p\% = \frac{p}{100}`.
• To convert a percentage to a decimal, divide by 100 (move the decimal point two places left), for example `12.5\% = 0.125`.
• Decimal percentages can be greater than `100\%` (more than the whole) or less than `1\%` (a very small part), for example `150\% = 1.5` and `0.4\% = 0.004`.
• A multiplier for an increase of `p\%` is `1 + \frac{p}{100}` (because you keep `100\%` and add `p\%`).
• A multiplier for a decrease of `p\%` is `1 - \frac{p}{100}` (because you keep `100\%` and subtract `p\%`).
• Increasing by `p\%` is not the same as adding `p` to the amount; the percentage is taken of the original amount.
• Decreasing by `p\%` is not the same as subtracting `p` from the amount; the percentage is taken of the original amount.
• If you increase by `10\%`, the multiplier is 1.1; if you decrease by `10\%`, the multiplier is 0.9.
• If you increase by `25\%`, the multiplier is 1.25; if you decrease by `25\%`, the multiplier is 0.75.
• If you increase by `50\%`, the multiplier is 1.5; if you decrease by `50\%`, the multiplier is 0.5.
• A `100\%` increase doubles an amount (multiplier 2), and a `100\%` decrease reduces it to zero (multiplier 0).
• When the context is money, the final answer should be in pounds and pence (two decimal places), but the working multiplier may have more decimal places.
• The unit stays the same when you take a percentage or apply a multiplier (for example, £ stays £, and grams stay grams).

• Convert a percentage (including decimal percentages) to a decimal multiplier by calculating `\frac{p}{100}` accurately.
• Calculate `p\%` of any amount by multiplying the amount by `\frac{p}{100}` and giving the answer with the correct unit.
• Choose and apply an ‘increase’ multiplier `1 + \frac{p}{100}` to increase an amount by `p\%`, showing the multiplication clearly.
• Choose and apply a ‘decrease’ multiplier `1 - \frac{p}{100}` to decrease an amount by `p\%`, showing the multiplication clearly.
• Check whether an answer is sensible by estimating (for example, `20\%` should be about one fifth) and by comparing sizes (an increase should make the result larger; a decrease should make it smaller).
• Use a calculator efficiently for multipliers with decimal percentages (enter the multiplier directly, then multiply), while keeping brackets clear if needed.
• Round appropriately at the end of a calculation to match the context (especially money to 2 decimal places), without over-rounding mid-calculation.
• Solve multi-step percentage problems by using the multiplier method in sequence (apply each multiplier to the latest amount in the correct order).