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neurologyYou need to know

• A fraction, a decimal, and a percentage can represent the same proportion, for example, `\frac{1}{2}`, `0.5`, and `50\%` are equivalent.
• A percentage means 'per hundred', so `37\%` is the same as `\frac{37}{100}` and `0.37`.
• Equivalent fractions name the same value, for example, `\frac{3}{4} = \frac{6}{8} = 75\% = 0.75`.
• Multiplying a fraction by an integer means taking several equal parts of the fraction, so `3 \times \frac{2}{5} = \frac{6}{5}`.
• When a fraction is multiplied by an integer, the numerator is multiplied by that integer while the denominator stays the same, for example, `4 \times \frac{3}{7} = \frac{12}{7}`.
• Dividing a fraction by an integer is the same as multiplying by the reciprocal of that integer, for example, `\frac{3}{4} \div 2 = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}`.
• Dividing an integer by a fraction is the same as multiplying the integer by the reciprocal of the fraction, for example, `6 \div \frac{2}{3} = 6 \times \frac{3}{2} = 9`.
• A reciprocal is found by inverting a fraction, so the reciprocal of `\frac{5}{8}` is `\frac{8}{5}`, and the reciprocal of `3` is `\frac{1}{3}`.

• Convert between fractions, decimals, and percentages accurately by using division, scaling to `100`, and multiplying or dividing by `100` as appropriate.
• Order a set of fractions, decimals, and percentages by rewriting them in a common form, such as all decimals, all percentages, or fractions with a common denominator, and comparing their values correctly.
• Compare numbers on the same scale using place value carefully, for example, `0.6` is greater than `0.58`.
• Multiply a fraction by an integer by multiplying the numerator, then simplify the result and convert it to a mixed number if needed.
• Divide a fraction by an integer by multiplying the fraction by the reciprocal of the integer, then simplify fully.
• Divide an integer by a fraction by rewriting the calculation as multiplication by the reciprocal and completing the calculation accurately.
• Find the original quantity when a non-unit fraction of it is given by dividing by the fraction or multiplying by its reciprocal.
• Find the whole from a unit fraction by scaling up from the known part, showing clearly how many equal parts make the whole; for example, if `\frac{1}{7}` of a length is `4 \text{ cm}`, the whole length is `28 \text{ cm}`.
• Write a final answer in a sensible form by simplifying fractions where possible and converting improper fractions to mixed numbers if the context requires it.
• Check whether an answer is reasonable by estimating with benchmark values such as `\frac{1}{2}`, `0.5`, and `50\%` before or after calculating.