The document summarizes key mathematical concepts including: 1) Properties of addition and multiplication like the commutative, associative, and distributive properties. 2) How to solve equations by isolating the variable using inverse operations. 3) Scientific notation, coordinate planes, absolute value, adding and subtracting integers, and measures of central tendency like mean, median, and mode. 4) Inequalities and examples of perfect squares.

1. 1. Associative Property of Addition or Multiplication
(6 + 3) + 5 = 6 + (3 + 5) or (2 x 5) x 7 = 2 x (5 x 7)
2. Commutative Property of Addition or
Multiplication
8+9+6=6+8+9 or 6x7=7x6
3. Distributive Property
2(a + b) = 2a + 2b
4. Inverse Property
4 + (-4) = 0 5 x 1/5 = 1
5. Identity of 1
3x1=3 or 7+0=7
6. Multiplication of zero
2x0=0 7x0=0

2. 7. Solving equations
A. Isolate the variable
B. By inverse operation
C. Variable is a letter that stands for an
unknown number
D. Inverse means opposite operation
EX: 4 + n = 18 You want n to be by itself on its
side of the equal sign so you subtract 4 from both
sides of equal sign and you will have n = 12 left.
8. Scientific Notation
Place the decimal after the first non-zero digit.
EX: 21,000 = 2.1 x 104
The decimal was after the last zero and you
Moved it 4 places to after the 2 making so that
Makes it to the 4th power.
9. Coordinate Plane
y
Quadrant II Quadrant I
x
Quadrant III Quadrant IV

3. 10. Absolute Value
The distance a number is from zero.
Ex: |-5| = 5 |5| = 5
11. Adding Integers:
With like signs:
Add and use the sign they have in common.
With unlike signs:
Subtract the smallest absolute value from the
Largest absolute value and use the sign of the
Largest absolute value.
12. Subtracting Integers
Change sign to addition
Change 2nd number to it’s opposite
Follow rules of addition
13. Multiply and Divide Integers

4. Signs alike – positive
Signs different – negative
14. Mean
Sum of data divided by number of data (average)
15.Median
Middle number of an odd number of data items
arranged in order. For an even number of data
items, the median is the average of the two middle
values.
16. Mode
The value or values that occur most often. When
all data occur the same amount, there is no mode.
17. Range
The difference between the greatest and least
values.
18. Outlier
A number that is much greater or less than the other
numbers in a set of data.

5. 19. Square numbers
1 = 12
4 = 22
9 = 32
16 = 42
25 = 52
36 = 62
49 = 72
64 = 82
81 = 92
100 = 102
121 = 112
144 = 122
Therefore if I asked for square root of 144 the answer
would be 12.
If I asked for square root of 69 you would say it is
between 8 and 9 because 69 falls between 64 and 81.

6. Ex. of 32 is: ...
...
...
Inequalities: A mathematical sentence that contains <,
>, = , <, or >.