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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
EXAMPLES
12 + (-5) + (-7)
= 12 – 5 – 7
=7–7
=0
• - and - make a positive
= a negative
because
there is a
positive and a
negative
beside each
other
• + and - or - and + make a negative
EXAMPLES
(80) / (-8)
the positive and
negatives don’t
have to be
directly beside
each other
= -10
Since one
is +’ve and
one is
–’ve, the
outcome
is –’ve
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)
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:
rackets
xponents
ivision
This is the order you solve in.
EXAMPLES
Since Brackets
is first, we
eliminate the
brackets
4 (9-7)³ + 2 – 6
= 4 x 2³ + 2 – 6
Next, we
eliminate
the
exponent
=4x8+2–6
= 32 + 2 – 6
= 34 – 6
ultiplication
ddition
ubtraction
= 28
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
EXAMPLES
x= -1 y= 3
X = -2
-xy
X+6
= -1 x -1 x 3
= -2 + 6
=1x3
=4
=3
•the variable is most
commonly “x”
When given the variable, we
plug it into the expression,
then solve.
Since 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 x
Here we can
multiply the
denominators of
both to find the
common
denominator,
then add or
subtract
together
4
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.
= 12
When dividing, we flip the reciprical,
then multiply.
EXAMPLES
3x6
5 /3
5
10 5
7
= 18
=5 /5
35
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
We add the
exponents
together
DIVISION LAW
POWER OF A POWER LAW
-when raising a power to a power, you
multiply the exponents
5³ x 5²
-when dividing powers with the same base, you subtract
=5^6
the exponents together
6^14 / 6³
= 6^11
We
subtract
the
exponents
together
We 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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