Addition and Subtraction are the most basic forms of mathematics. Adding is putting two numbers together, to make a larger number. Subtracting is taking one number away from another number, to make a smaller number.

However, there is an exception when adding or subtracting with positives or negatives when the sign are directly beside each other.

• + and + make a positive

• - and - make a positive

• + and - or - and + make a negativeEXAMPLES

12 + (-5) + (-7)

= 12 – 5 – 7

= 7 – 7

= 0

= a negative because there is a positive and a negative beside each other

Multiplication and Division are the two other basic forms of mathematics. Multiplication is a form used to make a number larger by basically making a certain number of groups for a certain number. (8 x 3 = 8 + 8 + 8 = 24) Division is a form used to make a number smaller by basically calculating how many of a certain number can fit into a certain number. (24 / 6 = 4) Another way to figure out the answer is by finding a variable.

(6 x n = 24 so, 6 x 4 = 24)

the positive and negatives don’t have to be directly beside each other

EXAMPLES

(80) / (-8)

= -10

Since one is +’ve and one is –’ve, the outcome is –’ve

When solving large expression with integers, we use a process called BEDMAS. BEDMAS is an acronym used to guide you to complete an expression properly.

The acronym stands for:

ultiplication

xponents

ivision

rackets

ddition

ubtraction

This is the order you solve in.

EXAMPLES

4 (9-7)³ + 2 – 6

= 4 x 2³ + 2 – 6

= 4 x 8 + 2 – 6

= 32 + 2 – 6

= 34 – 6

= 28

Since Brackets is first, we eliminate the brackets

Next, we eliminate the exponent

Now we do the multiplication since it is next in the acronym

Finally we solve

Variables

•a letter or symbol used to represent an unspecified number

•a letter that takes the place of an unknown value

•the variable is most commonly “x”

When given the variable, we plug it into the expression, then solve.

EXAMPLES

X = -2

X + 6

= -2 + 6

=4

x= -1 y= 3

-xy

= -1 x -1 x 3

= 1 x 3

= 3Since there is a “-x”, it simply means that the variable has a coefficient of -1

FRACTION FORM

When adding and subtracting rational numbers in fraction form, we must find a common denominator.

2 and 3

3 4x = 12

Here we can multiply the denominators of both to find the common denominator, then add or subtract together

MULTIPLYING AND DIVIDING

When multiplying numbers in fraction form, we use the rules of multiplying integers.

When multiplying numbers in fraction form, we multiply the numerator and denominator together.

When dividing, we flip the reciprical, then multiply.

EXAMPLES

3 x 6

5 7

= 18

35

5 / 3

10 5

= 5 / 5

10 3

=25

30

We flip the reciprical, then multiply

REAL NUMBER- any number you can think of is a real number

INTEGERS- positive or negative whole numbers

WHOLE NUMBERS- positive whole numbers include 0 (0,1,2….)

NATURALL NUMBERS- positive whole numbers (1,2,3) also known as counting numbers

RATIONAL NUMBERS- -numbers written in the form a/b where b can’t be 0

-includes all fractions, all integers, all terminating decimals and all repeating decimals

IRATIONAL NUMBERS--simply means “not rational”

-Numbers that can’t be expressed as factions and have neither terminating nor repeating decimals

A Ratio is a comparison of two numbers with the same units.

Ratios must be in lowest terms like fractions.

A rate is a comparison of two numbers expressed in different units. They are usually written as a unit rate where the second term is 1.

MULTIPLICATION LAW

-when multiplying powers with the same base, you add the exponents together

3³ x3²

=3^5

DIVISION LAW

-when dividing powers with the same base, you subtract the exponents together

6^14 / 6³

= 6^11

We add the exponents together

We subtract the exponents together

POWER OF A POWER LAW

-when raising a power to a power, you multiply the exponents

5³ x 5²

=5^6We multiply the exponents

Scientific Notation is a way of writing numbers that accommodates for values that are too large or too small to conveniently be written in simple decimal notation.

A x 10^b

In scientific notation, a number has the form a x 10^b, where “a” is greater or equal to one but less than zero.

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