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neurologyYou need to know

• A percentage means “out of 100”, so `p\% = \frac{p}{100}`.
• To find `p\%` of an amount `A`, calculate `\frac{p}{100}\times A`.
• Simple interest is interest calculated only on the original principal (the starting amount), not on previously earned interest.
• Simple interest each time period is constant and is found using `\text{interest per period} = \frac{r}{100}\times P`, where `P` is the principal and `r` is the percentage rate per period.
• Total simple interest after `t` periods is `I = P\times \frac{r}{100}\times t`.
• The final amount after simple interest is `A = P + I = P\left(1 + \frac{rt}{100}\right)`.
• Percentage change compares an amount to its original value using `\text{percentage change} = \frac{\text{new} - \text{original}}{\text{original}}\times 100\%`.
• If the new value is greater than the original, the percentage change is an increase; if it is smaller, the percentage change is a decrease.
• A multiplier converts a percentage change into a single step: increasing by `p\%` uses multiplier `1 + \frac{p}{100}`; decreasing by `p\%` uses multiplier `1 - \frac{p}{100}`.
• After a percentage change, `\text{new} = \text{original} \times \text{multiplier}`.
• Reverse percentages find the original amount when the final amount and the percentage change are known.
• For reverse percentages, `\text{original} = \frac{\text{new}}{\text{multiplier}}`.
• If an amount is “now 120% of the original”, the multiplier is `1.2`; if it is “now 80% of the original”, the multiplier is `0.8`.
• A common error in reverse percentages is subtracting the percentage from the final amount instead of dividing by the multiplier.
• A percentage increase and the same percentage decrease do not cancel out, because the change is applied to different starting values (for example, +20% then −20% does not return to the start).

• Calculate simple interest over time by identifying `P`, `r`, and `t`, then using `I = P\times \frac{r}{100}\times t` and `A = P + I`, with correct units (years/months) matching the rate.
• Find `p\%` of an amount using a non-calculator method (e.g. `10\%`, `5\%`, and `1\%`) and/or a calculator method `\frac{p}{100}\times A`, and state the result clearly with a money symbol where appropriate.
• Calculate percentage change by subtracting to find the difference, dividing by the original, then multiplying by 100, and labelling the result as increase or decrease.
• Use a multiplier to apply a percentage increase or decrease in one step, showing the multiplier used (e.g. `\times 1.15` for `+15\%`, `\times 0.92` for `-8\%`).
• Solve reverse percentage problems by converting the situation into a multiplier, then dividing the final amount by that multiplier to find the original.
• Check reverse percentage answers by applying the percentage change forward to the calculated original and confirming it returns to the given final amount.
• Interpret multi-step percentage contexts by applying and combining multipliers; explain that the order of pure percentage multipliers does not affect the final value unless intermediate rounding or other contextual conditions apply.