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neurologyYou need to know

• A percentage is a proportion out of 100, so `p\%` means `\frac{p}{100}` of a whole.
• `100\%` represents the whole amount, `50\%` is half, `25\%` is a quarter, and `10\%` is one tenth.
• To express one quantity as a percentage of another, the percentage is `\frac{\text{part}}{\text{whole}}\times 100` (the whole must match the part’s unit).
• A fraction or decimal can be converted to a percentage by multiplying by 100; a percentage can be converted to a decimal by dividing by 100.
• Finding `p\%` of an amount is equivalent to multiplying the amount by `\frac{p}{100}` (or by the decimal multiplier).
• For integer percentages, `p\%` can be split into helpful parts (for example `17\%=10\%+5\%+2\%`) and added together.
• Useful percentage facts include `1\%` is `\frac{1}{100}` of an amount and `5\%` is half of `10\%` of the amount.
• Increasing an amount by `p\%` means the new amount is the original plus `p\%` of the original.
• Decreasing an amount by `p\%` means the new amount is the original minus `p\%` of the original.
• The multiplier for an increase of `p\%` is `1+\frac{p}{100}` (for example an increase of `17\%` uses multiplier `1.17`).
• The multiplier for a decrease of `p\%` is `1-\frac{p}{100}` (for example a decrease of `62\%` uses multiplier `0.38`).
• When expressing a percentage of another quantity, the answer can be greater than `100\%` if the part is larger than the whole.
• Percentages are unitless, but the part and whole must be comparable (e.g. both in pounds, both in grams, or both in the same time units).
• For a given amount, increasing by `p\%` and then decreasing by `p\%` does not return to the original amount because the second percentage is calculated from a different base.
• Rounding may be needed when a percentage calculation gives a non-integer result, but the method should still be accurate.

• Calculate `p\%` of an amount by multiplying by `\frac{p}{100}` or its decimal equivalent, showing a clear method.
• Express one quantity as a percentage of another by dividing part by whole, multiplying by 100, and stating the result with the percent symbol.
• Decompose a complex integer percentage (e.g. `62\%`) into benchmark parts (e.g. `50\%+10\%+2\%`) and combine the partial results accurately.
• Increase an amount by `p\%` using either “find `p\%` then add” or the multiplier `1+\frac{p}{100}`, and give the final value.
• Decrease an amount by `p\%` using either “find `p\%` then subtract” or the multiplier `1-\frac{p}{100}`, and give the final value.
• Choose and apply an efficient strategy for the numbers involved (e.g. using `1\%` to build `17\%`, or using `10\%` then scaling), and check the result is reasonable (increase gives a larger answer; decrease gives a smaller answer).