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neurologyYou need to know

• A percentage means ‘per hundred’, so `p\% = \frac{p}{100}` of a quantity.
• To find a percentage of an amount, you can divide by 100 then multiply by the percentage, e.g. `p\% of A = \frac{p}{100} \times A`.
• A decimal percentage can be used directly as a fraction of 1, e.g. `12.5\% = 0.125` and `0.4\% = 0.004`.
• Converting between forms uses `p\% = \frac{p}{100} = 0.p` (after dividing by 100), and multiplying by 100 converts a decimal to a percentage.
• A multiplier is the single number you multiply by to carry out a percentage change in one step.
• The multiplier for an increase of `p\%` is `1 + \frac{p}{100}`, and the multiplier for a decrease of `p\%` is `1 - \frac{p}{100}`.
• A percentage increase makes the new value greater than the original, and a percentage decrease makes it smaller (unless the percentage is 0).
• Expressing one quantity as a percentage of another uses `\frac{\text{part}}{\text{whole}} \times 100\%` (the ‘whole’ is the reference amount).
• Percentage change compares a new value to an original value using `\frac{\text{new} - \text{original}}{\text{original}} \times 100\%`.
• A positive percentage change is an increase and a negative percentage change is a decrease (often reported as ‘x\% decrease’).
• Reverse percentages find the original amount from a final amount by dividing by the relevant multiplier, e.g. original `= \frac{\text{final}}{1.2}` for a 20% increase.
• Simple interest adds the same amount each time period because it is calculated on the original principal only.
• Simple interest can be calculated using `I = P \times r \times t`, where `P` is principal, `r` is the interest rate as a decimal, and `t` is time in years (or matching time units).
• Compound interest (and depreciation) repeatedly multiplies by the same multiplier each time period, so the amount changes by a constant percentage each period.
• Compound growth uses `A = P(1+r)^t` and compound depreciation uses `A = P(1-r)^t`, where `r` is the rate as a decimal and `t` is the number of periods.

• Calculate `p\%` of an amount by converting `p\%` to a fraction/decimal and multiplying by the amount, showing correct working and units.
• Express one quantity as a percentage of another by forming `\frac{\text{part}}{\text{whole}}`, multiplying by 100, and stating the answer with the `%` symbol.
• Increase or decrease an amount by `p\%` by finding `p\%` of the original and adding/subtracting it, or by using a multiplier, and checking the result is sensible (larger for increases, smaller for decreases).
• Use multipliers to find a percentage of an amount by multiplying by `\frac{p}{100}` (or the decimal equivalent) and rounding appropriately for the context.
• Use multipliers to complete percentage increases/decreases in one step by multiplying by `1 + \frac{p}{100}` or `1 - \frac{p}{100}`.
• Calculate percentage change by finding the difference, dividing by the original value, multiplying by 100, and labelling the result as an increase or decrease.
• Solve reverse percentage problems by identifying the correct multiplier from the percentage change and dividing the final amount by this multiplier to find the original.
• Calculate simple interest and final amount by substituting into `I = P \times r \times t` and using `A = P + I`, keeping time units consistent.
• Calculate compound interest or depreciation over multiple periods by using repeated multiplication by the multiplier or by applying `A = P(1\pm r)^t`, rounding money to the nearest penny where appropriate.