(a + b)²

a² + 2ab + b²

a² - b²

(a - b)(a + b)

fraction

a measure of how something is to be divided up or shared out

numerator

the top number in a fraction

denominator

the bottom number in a fraction

proper fraction

a fraction in which the numerator is smaller than the denominator

equivalent fractions

are two or more fractions that have the same value but are different in form eg

3/4, 6/8, 63/84, 75%, 0.75

all look different but they all have the same value

product

the product is the result given by the operation of **multiplication**

quotient

the quotient is the result given by the operation of **division**

32 divided by 8 is 4

the quotient is 4

divisor

the number in a division sum that does the dividing

18 divided by 9 is 2

the divisor is 9

test for dividing by 3

if the digits in the number add up to a multiple of 3

3597 is divisible by 3 since

3+5+9+7 = 24

square -- (as a verb)

to square a number means to multiply it by itself

isosceles triangle

a triangle which has two sides with the same length

there will be two angles of the same size as well

equilateral triangle

a triangle in which all three sides have the same length

therefore the angles in an equilateral triangle are the same

each is 60º

negative times negative

positive

4

###
- even
- square

3, 4, ?

5 -- 3, 4, 5 is a pythagorean triple ie when these 3 numbers are considered as lengths of the sides of a triangle the angle opposite the longest side will necessarily be a right angle

5, 12, ?

13 -- 5, 12, 13 is a pythagorean triple

9

###
- odd
- square

{1, 8, 27, 64, 125}

the set of the first 5 cube numbers

16

###
- even
- square
- 2 to the power of 4

25

###
- odd
- square

{2, 3, 5, 7, 11, 13, 17, 19, 23}

the set of the first 9 prime numbers

how to divide by a fraction?

###
- "kiss and flip"
- eg 8 divided by ½ is the same as 8 times 2

mixed number

an improper fraction written as a whole number followed by a proper fraction

eg 2¾ = 11/4

cancel -- as a verb

to express a fraction in its simplest or lowest terms

eg 6/8 = 3/4 -- we have cancelled the factor of 2 on the left hand side of the '=' sign by dividing top and bottom of the fraction by 2 to get the fraction in its lowest terms (3 and 4 do not have any common factors)

surd

a number that cannot be expressed as fraction, or ratio of whole numbers, hence it is sometimes called an irrational number

the square root of 2

the cube root of 5

3 + sqrt(2)

negative divided by a negative

positive