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neurologyYou need to know

• A fraction of an amount is found by dividing the amount by the denominator and then multiplying by the numerator.
• A mixed number is made of a whole number and a proper fraction, such as `2\frac{1}{3}`.
• An improper fraction has a numerator greater than or equal to its denominator, such as `\frac{7}{3}`.
• A mixed number can be converted to an improper fraction by multiplying the whole number by the denominator, adding the numerator, and keeping the same denominator.
• An improper fraction can be converted to a mixed number by dividing the numerator by the denominator and writing the remainder as the new numerator.
• To multiply fractions, multiply the numerators together and multiply the denominators together.
• To divide by a fraction, multiply by its reciprocal.
• The reciprocal of a non-zero number is the number that multiplies with it to make 1.
• The reciprocal of `\frac{a}{b}` is `\frac{b}{a}`, as long as `a` and `b` are not zero.
• The reciprocal of an integer `n` is `\frac{1}{n}`, as long as `n` is not zero.
• The reciprocal of a mixed number is found by first converting it to an improper fraction and then swapping the numerator and denominator.
• Zero has no reciprocal because division by zero is undefined.
• When multiplying decimal numbers, the number of decimal places in the answer is the total number of decimal places in the factors before simplifying or writing the final decimal.
• When dividing by a decimal, an equivalent calculation can be made by multiplying both numbers by the same power of 10 so that the divisor becomes an integer.
• The original quantity can be found from a known fraction of it by dividing by the numerator and multiplying by the denominator.
• An algebraic fraction is a fraction that contains an algebraic expression in the numerator, denominator, or both.
• Algebraic fractions with integer denominators can be added or subtracted by using a common denominator and then simplifying the numerator.
• Algebraic fractions with integer denominators can be multiplied or divided using the same fraction rules as numerical fractions.
• A recurring decimal has one or more digits that repeat forever, such as `0.333...` or `0.\dot{1}\dot{6}`.
• A recurring decimal can be converted to a fraction by using place value and subtraction to remove the recurring part.

• Find a fraction of an amount by dividing by the denominator, multiplying by the numerator, and giving the answer with appropriate units.
• Convert between mixed numbers and improper fractions accurately before carrying out operations on mixed numbers.
• Add, subtract, multiply and divide mixed numbers by converting them to improper fractions, applying the correct operation, and simplifying the result.
• Multiply fractions by integers by writing the integer as a fraction over 1, multiplying numerators and denominators, and simplifying where possible.
• Divide fractions by integers and divide integers by fractions by multiplying by the reciprocal of the divisor.
• Multiply and divide decimal numbers by decimal numbers by using powers of 10 or place-value reasoning and placing the decimal point correctly.
• Find the original quantity from a given fraction of it by scaling up to one whole or by using the inverse operation.
• Find the reciprocal of a fraction, integer, mixed number or decimal by first writing it as a fraction and then inverting it.
• Perform all four operations on algebraic fractions with integer denominators by using common denominators, reciprocals, expansion and simplification correctly.
• Convert recurring decimals to fractions by forming equations such as `x=0.\dot{3}`, multiplying by a power of 10, subtracting, and solving for `x`.