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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=50\%`.
• To convert a fraction to a decimal, divide the numerator by the denominator.
• To convert a decimal to a percentage, multiply by 100; to convert a percentage to a decimal, divide by 100.
• To compare and order fractions, decimals and percentages, it is usually easiest to convert them to the same form.
• Equivalent fractions have the same value because the numerator and denominator have been multiplied or divided by the same non-zero number.
• Fractions can only be added or subtracted directly when they have a common denominator.
• The lowest common multiple of the denominators can be used as a common denominator when adding or subtracting fractions with different denominators.
• To multiply fractions, multiply the numerators and multiply the denominators, then simplify if possible.
• 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, for example the reciprocal of `\frac{3}{4}` is `\frac{4}{3}`.
• An integer can be written as a fraction with denominator 1, for example `5=\frac{5}{1}`.
• A mixed number is made from an integer part and a proper fraction part, for example `2\frac{1}{3}`.
• Mixed numbers are often converted to improper fractions before multiplication or division.
• A fraction of an amount is found by dividing the amount by the denominator and multiplying by the numerator.
• If a fraction of an original amount is known, the original amount can be found by dividing by the numerator and multiplying by the denominator.
• When multiplying decimals, the number of decimal places in the answer is the total number of decimal places in the factors before simplification or adjustment.
• When dividing by a decimal, multiplying both numbers by the same power of 10 creates an equivalent division with a whole-number divisor.
• Algebraic fractions with integer denominators follow the same fraction rules as numerical fractions, but like algebraic terms must be collected when simplifying.
• A recurring decimal has a digit or group of digits that repeats forever, for example `0.333\ldots=0.\dot{3}`.
• A recurring decimal can be converted to a fraction by using place value and subtraction to remove the repeating part.

• Convert between fractions, decimals and percentages accurately, including using division for fractions and multiplying or dividing by 100 for percentages.
• Order a mixed list of fractions, decimals and percentages by converting them to a common form and comparing their values.
• Add and subtract fractions with different denominators by finding a common denominator, creating equivalent fractions, calculating, and simplifying the answer.
• Multiply and divide fractions, integers and mixed numbers by converting to improper fractions where needed and using reciprocals for division.
• Perform all four operations with decimals, aligning place value for addition and subtraction and using scaling for multiplication and division.
• Find a fraction of an amount by dividing by the denominator and multiplying by the numerator, choosing an efficient order of calculation.
• Find the original quantity when given a fraction of it by using inverse operations or a unit fraction method.
• Find the reciprocal of a fraction, integer, mixed number or terminating decimal by first writing it as a single fraction and then inverting it.
• Perform all four operations on algebraic fractions with integer denominators by applying fraction rules and simplifying algebraic terms correctly.
• Convert a recurring decimal to a fraction by forming equations with powers of 10, subtracting to remove the recurring part, and simplifying the fraction.