by Liz Allen

Created on: April 21, 2007   Last Updated: April 26, 2007

It's difficult to get to grips with math problems if you don't understand the expressions that are used, so let's take a look at some of these.

FACTORS
Factors are numbers that divide exactly into other numbers without leaving a remainder. For example:
the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24
the factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.

MULTIPLES
Multiples are numbers arrived at when one number is multiplied by another. For example:

the first ten multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
the first ten multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70.

Many students confuse factors and multiples. Remember that factors are smaller than or equal to the number, whereas multiples are bigger than or equal to the number.

PRIME NUMBERS
Prime numbers have only two factors: the number itself, and one. Since the number one has only one factor (which is of course one), it is not a prime number. Two is a prime number, as its factors are two and one. Two is, however, the only even number that is prime.

FRACTIONS
When dealing with fractions, every fraction has a numerator, which is the top number. The number at the bottom is called the denominator.

An improper fraction is one that has the numerator larger than the denominator; in other words, it is 'top heavy'. This would usually be changed to a mixed number, which is a whole number followed by a fraction. Thus, fifteen quarters would be changed to three and three quarters.

A reciprocal of a fraction is its inverse in other words, it is turned upside-down. When dividing fractions, we actually multiply the first fraction by the reciprocal of the second.

PRODUCT
The product of two numbers is the answer arrived at when they are multiplied together.

QUOTIENT
The quotient is the answer arrived at when dividing one number by another. The number being divided is called the dividend, whilst the number it is being divided by is the divisor.

BIDMAS
BIDMAS is an acronym that helps you remember in what order operations must be carried out. This is what each letter stands for:
Brackets
Indices
Division
Multiplication
Addition
Sub traction

Thus, if you are solving a problem that contains brackets, whatever is inside the brackets must be worked out first. Division must be carried out before addition, and so on.

AVERAGES
When handling sets of data, you may be asked to find different types of average.

The mean average is calculated by adding up all the values in the set, and then dividing the total by the number of values. Thus the

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