You will want to refer to Year 7 Maths Chapter 4 for basic knowledge of fractions, decimals and percentages. This section is more advanced and omits finance and other basic concepts.
Some brief definition on simple, but essential terminology:
- Numerator: the number on top of the fraction bar, being divided by the denominator
- Equivalent Fraction: fractions that are equal to each other, more often than not with different numbers in representation
- Improper Fraction: a fraction in which the numerator is larger than the denominator
- Multiples: a number that may be divided by a certain number without remainder
- Reciprocal: the reverse of a fraction, often labelled as “flipping” the number on a fraction, essentially meaning that the numerator and denominator switch places. If number is a mixed numeral, convert to an improper fraction to find the reciprocal
- Lowest Common Multiple: the lowest number that can be divided between two specific numbers, often labelled as LCM and used in simplifying fractions
- Ascending: an increasing set of numbers
- Composite Number: a positive integer which has a divisor that is not 1 or itself
- Denominator: the number on the bottom of the fraction bar in a fraction that is dividing the numerator
- Proper Fraction: a fraction that is less than 1 with the numerator being less than the denominator
- Mixed Numeral: a number that contains a whole number and a fraction
- Factors: can be multiplied together to result in a specific number
- Highest Common Factor: the largest common factor between 2 numbers
- Descending: numbers in a decreasing order
- Rational Numbers: a number that can be expressed as a ratio
- Irrational Numbers: a number that has no end, such as pi
Any number being divided by itself, or if a fraction’s numerator and denominator are equal, the number is equal to 1.
To add and subtract fractions, one needs to make the denominators the same. Do this by finding the lowest common multiple of both denominators, and make that the new denominator. Remember that whatever you do to the denominator, you must do to the numerator.
To multiply fractions, simply multiply the numerators to achieve your numerator, and multiply the denominators to find the denominator. A method to make this easier is the “bow tie” method. To do this, look at the numbers that are opposite each other (for the denominator of the first number, the opposite would be the numerator of the next number) and see if you can “cancel” out anything (multiples and variables). Cross these out and/or replace with new numbers respectively, which, in theory, should make the equation easier.
Brendan’s Note: I don’t usually use the bow tie method unless there are variables/pronumerals, but if it’s easier for you, by all means use it.
To divide fractions, simply find the reciprocal and then multiply the fractions. It is very handy to note though, that for smaller fractions like a half, third and quarter, you should be able to easily just double, triple and quadruple your fractions respectively.
Decimals are simply another way to express parts of a whole, and utilise the base 10 metric system. They are less efficient than fractions, but easier to use.
When adding or subtracting decimals, always be wary of where the decimal point is, especially if using an algorithm.