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neurologyYou need to know

• In a fraction, the numerator shows how many equal parts are selected and the denominator shows how many equal parts make one whole.
• A proper fraction has a numerator smaller than its denominator, so its value is less than 1.
• An improper fraction has a numerator greater than or equal to its denominator, so its value is 1 or more.
• A mixed number is made of a whole number and a proper fraction, such as `2 \frac{3}{5}`.
• Equivalent fractions have the same value even though they are written with different numerators and denominators.
• To express an improper fraction as a mixed number, divide the numerator by the denominator; the quotient is the whole number and the remainder becomes the numerator of the fractional part.
• To express a mixed number as an improper fraction, multiply the whole number by the denominator and add the numerator, keeping the same denominator.
• When finding a fraction of an amount, the denominator tells you how many equal groups to split the amount into and the numerator tells you how many of those groups to take.
• To find `\frac{a}{b}` of an amount, divide the amount by `b` and then multiply by `a`.
• If a fraction is equivalent to a simpler fraction, the answer should usually be written in its simplest form.
• To add or subtract mixed numbers, the fractional parts must represent equal-sized parts, so the fractions need a common denominator.
• A common denominator is a shared multiple of the denominators, and using the lowest common denominator often makes the calculation simpler.
• When adding mixed numbers, extra fractional parts that make one whole can be regrouped into the whole-number part.
• When subtracting mixed numbers, one whole can be exchanged for a fraction equal to the denominator over the denominator if the fractional part is too small to subtract.
• To multiply mixed numbers, it is usually most efficient to convert them to improper fractions first, then multiply the numerators and multiply the denominators.
• To divide by a fraction, multiply by its reciprocal, where the numerator and denominator are swapped.
• After multiplying or dividing fractions, an improper fraction answer can be converted back to a mixed number if needed.
• A reciprocal pair multiplies to make 1, for example `\frac{3}{4}` and `\frac{4}{3}`.

• Find a fraction of an amount by dividing the amount by the denominator and then multiplying by the numerator.
• Convert an improper fraction to a mixed number by dividing the numerator by the denominator and writing the remainder over the original denominator.
• Convert a mixed number to an improper fraction by multiplying the whole number by the denominator, adding the numerator, and keeping the denominator unchanged.
• Add mixed numbers by converting to improper fractions or by using a common denominator, then simplifying and regrouping any fraction greater than 1.
• Subtract mixed numbers by using a common denominator and, when needed, exchanging one whole for an equivalent fraction before simplifying the result.
• Multiply mixed numbers by converting each one to an improper fraction, multiplying numerators and denominators, and cancelling common factors where possible.
• Divide mixed numbers by converting to improper fractions, changing division to multiplication by the reciprocal, and simplifying the answer.
• Simplify fractional answers by dividing the numerator and denominator by their highest common factor and converting improper fractions to mixed numbers when appropriate.