Integers (6.3)
An ____________________ is any whole number (no fractions or decimals), positive or negative
and zero.
example:
…-5, -4, -3, -2, -1, 0, 1, 2, 3…
The distance a number is from zero is called _______________________________. It is always a
positive value.
example:
|-3| = 3
|5| = 5
4
1
2
5
3
1
Sequences (6.17)
In an _________________________ sequence the same value is ___________________ each time to get
the next term in the sequence. The number that is added each time is called the
_________________________________________.
example:
5, 3, 1, -1, -3 is an arithmetic sequence with a common difference of -3
In a ___________________________ sequence each term is ________________________ by the same value
to get the next term in the sequence. The number that you multiply by each time is called
the ________________________________________.
example:
4, 2, 1, ½ ¼ is a geometric sequence with a common ratio of 1/2
2
1
Perfect Squares and Exponents (6.5)
A _______________________________ is a number that is multiplied by itself.
example:
32 = 9
The perfect squares under 100 are: _____, _____, _____, _____, _____, _____, _____, _____, _____, _____,
In this number 53 the 5 is __________________ by itself _________ times.
example:
53 = 5 x 5 x 5 = 125
Any real number raised to the first power is ___________. Any real number raised to the zero
power is ___________.
example:
21 = 2
20 = 1
2
1
3
2
4
Order of Operations (6.8)
1. P__________________________
2. E _________________________
3. M/D _____________________________________ (left to right)
4. A/S _____________________________________ (left to right)
example:
20 ÷ 5 + 42 × 2
20 ÷ 5 + 16 × 2
4 + 16 × 2
4 + 32
36
1
2
3
3
Ratios (6.1)
A _______________ is a comparison of two quantities by division. It can be written three ways:
______:______
______ to ______
________
In a ratio ______________________ matters!
example: The pet store had 5 kittens and 15 puppies. The ratio of puppies to kittens
is 15:5 or 3:1.
1
2
Fractions, Decimals, and Percents (6.2)
A ______________________ is a part of a group, number or whole.
𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟
𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟
A number written after the ______________________ is part of a whole. Each number has a
place value. A decimal point is a symbol that separates the whole number part from the
fractional part of a number.
example:
ones
5
.
.
tenths
8
hundredths
2
thousandths
4
A ______________________ is a number out of 100. A number with a percent symbol (%) is
equivalent to that number with a denominator of 100.
Fractions to Decimals
Long division!
3
example:
= 3 ÷ 4 = 0.75
Fractions to Percents
Find an equivalent fraction with the
denominator of 100. Write the numerator
with a percent sign.
3
75
example:
=
= 75%
4
0.75
4 3.0 0
-28
20
-2 0
00
4
4
100
Decimals to Percents
Move the decimal 2 places to the right and
add a % sign.
example:
Decimals to Fractions
Write the number as the numerator and a
power of 10 (depending on the place
value) as the denominator.
example: 0.75 = 75 hundredths =
75
3
=
100 4
Percents to Decimals
Move the decimal 2 places to the left and
take off the % sign.
If there is no decimal, it is at the end of the
number.
example: 75% = 0.75
0.75 = 75%
Percents to Fractions
Write the percent as a fraction with the
denominator of 100. Then simplify the
fraction to lowest terms.
75
3
example: 75% =
=
100
4
1
3
2
4
Multiplication of Fractions (6.4)
Count the number of rows _____________, out of the total number of __________, and multiply
by the number of columns _____________ out of the total number of _______________.
example:
3
4
1
3
1
× 6 = 24 = 8
5
1
Mixed Numbers/Improper Fractions (6.6)
Improper Fraction to a Mixed Number
Divide the numerator by the denominator
The answer is your whole number
The remainder gets put over the original denominator
example:
14
5
= 14÷5 = 2
2
5 14
- 10
4
4
5
Mixed Number to an Improper Fraction
Backwards “C”
Multiply the whole number by the denominator
Add that to the numerator
Keep the denominator
example:
1
1
3
×
+
=
4
3
1
2
6
Fraction Operations (6.6)
Adding/Subtracting Fractions
1
3
Find the __________________________________ (LCD)
example:
+ =
3 5
______________________ the fractions
5
9
14
Add or subtract the numerators
+ =
15 15 15
Keep the new denominator
Simplify
Multiplying Fractions
Dividing Fractions
Multiply the ____________________
Multiply the ____________________
Simplify
example:
3
4
1
3
3
12
× =
=
_________ the first fraction
_________ the second fraction
_________ the sign to multiplication
Then multiply fractions
1
4
example:
3
4
3
4
1
3
2
4
7
1
÷ =
3
3
9
1
1
4
4
× = =2
5
7
8
6
Decimal Operations (6.7)
Adding/Subtracting Decimals
________________________ the numbers at the decimal point
Fill in any spaces at the end with __________________
example:
2.395 – 1.48= 0.915
1 13
2.395
- 1.480
0.915
Multiplying Decimals
Multiply regularly (ignore the decimal)
_______________ the number of digits past the decimal in the problem (both numbers)
_______________ your decimal over that many places in your answer
example: 3.75 × 2.1= 7.875
1 1
3.75
× 2.1
375
+7 5 0 0
7.8 7 5
8
Dividing Decimals
Move the decimal for the number outside the house so that you have a _______________
Move the decimal for the number inside the house the _____________ number of spaces
Divide normally
Place the decimal ______________ the decimal inside the house
example:
66 ÷ 0.5 = 132
0.5 6 6.
1 3 2.
0 5. 6 6 0.
-5
16
-15
10
-10
0
3
1
4
2
Properties (6.19)
Identity Property of Addition
The sum of a number and _____________ is that number.
example:
4+0=4
Identity Property of Multiplication
The product of a number and ______________ is that number.
example:
5×1=5
9
Multiplicative Property of Zero
The product of a number and zero is _______________.
example: 6 × 0 = 0
Inverse Property of Multiplication
The product of a number and its inverse is 1.
Remember: When you have a whole number the denominator is _________.
example:
1
2× =1
2
2
1
Algebra (6.18)
Word
Definition
Example
A quantity that stays the same. It is a number
2x + 5
that stands alone.
A letter used to represent an unknown
2x + 5
quantity.
A number that is multiplied by a variable. It is
2x + 5
written in the front of the variable.
The parts that are added or subtracted in an
2x + 5
expression or equation. They are constants,
variables or coefficients with variables.
A number phrase. It does not have an equal
2x + 5
sign.
A statement that says two expressions are
2x + 5 = 15
equal to each other. It does have an equal sign.
The opposite operation.
For addition it is
_______________________.
For multiplication it is
_______________________.
When solving an equation we need to isolate the ________________ on one side and the
_________________ on the other side. We do this by performing inverse (opposite) operations.
example: 15 = 3m
4 + b = 10
3
3
5=m
-4
10
-4
b=6
1
3
2
Graphing Inequalities (6.20)
Make sure you read the inequality starting with the ____________________ because order
matters! x<5 is not the same as 5<x (read it!).
<
>
≤
≥
x<8
“x is less than 8”
Use an open circle
x cannot be 8, but it can be anything less than 8
x>2
“x is greater than 2”
Use an open circle
x cannot be 2, but it can be anything greater than 2
x≤4
“x is less than or equal to 4”
Use a closed circle
x can be 4, and anything less than 4
X≥7
“x is greater than or equal to 7”
Use a closed circle
x can be 7, and anything greater than 7
1
2
11
Coordinate Plane (6.11)
The coordinate plane is broken into four regions called _______________________.
These number lines that divide the quadrants are called ______________. Typically x is used
for the __________________ axis and y is used for the __________________ axis.
Quadrant I ( , )
Quadrant II ( , )
Quadrant III ( , )
Quadrant IV ( , )
In a coordinate plane, the coordinates of a point are
typically represented by the _________________ (x, y).
An ordered pair tells you an exact location of the
point.
The origin is the point at the intersection of the x-axis and y-axis. The coordinates of this
point are ( , ).
2
3
1
Congruence (6.12)
These figures have exactly the same ______________ and the same ________________.
example:
=
12
2
1
Quadrilaterals (6.13)
Name of Quadrilateral
Description
Drawing
Quadrilateral
Parallelogram
Rectangle
Square
Rhombus
Kite
Trapezoid
1
2
3
13
Circles (6.10ab)
example:
d = 6cm
C = πd or C = 2πr
A = πr2
π = 3.14
C = πd
C = 3.14 x 6
C = 18.84cm
A = πr2
A = 3.14 x 32
A = 3.14 x 9
A = 28.26cm2
3
1
2
4
Surface Area and Volume (6.10cd)
_________________________ is the amount of area on the outside of the box.
__________________ is the amount of space to fill up the box.
S.A. = 2× l × w + 2× l × h + 2× w × h
V=l×w×h
example:
SA = 2× 6 × 2 + 2× 6 × 3 + 2× 2 × 3
SA = 24 + 36 + 12
SA = 72 inches2
V=l×w×h
V=6×2×3
V = 36 inches3
3 inches
6 inches
2 inches
14
3
1
2
4
Measurement (6.9)
1 kilometer is a little farther than half a mile
1 quart is a little less than 1 liter
1 inch is about 2.5 centimeters
example:
2km ≈ 1.2 miles
4 liters ≈ 4 quarts
1
2
3
4
15
10cm ≈ 4 inches
Mean, Median, Mode (6.15)
Measure of
Center
Mean
or
“___________”
Median
Mode
Definition
The point on a
number line where
the data is
_____________________.
The _____________ value
in an ordered set of
data.
The piece of data that
occurs ________________.
Example
When it’s best to use
example 1:
When the data has no
x
x
x
very high or very low
x x x
x x numbers.
1 2 3 4 5 6 7 8
Mean: ___________
example 2:
3, 24, 7, 15, 51, 30, 11
Mean: ___________
example 1:
41, 7, 66, 18, 98, 22
Median: ___________
example 1:
6, 52 ,17, 31, 52, 71, 17
Mode: ___________
1
3
2
16
When there are a few
values much higher or
lower than most of the
others.
When there are some
identical values or in
surveys with yes or no
questions.
Circle Graphs (6.14)
Circle graphs show a relationship of a part to a ________________.
example:
What fraction of people picked cake?
20
100
=
2
10
=
1
5
What
3
1
2
4
17
Probability (6.16)
O means it is _____________________ and 1 means it is ________________________ to happen. The
closer to _______ the less likely the event is to occur. The closer to 1 the ____________ likely
the event is to occur.
___________________________events mean that the outcome of one event has no effect on the
outcome of the other event.
example:
When rolling two number cubes, what is the probability of rolling a 3 on
one, and a 4 on the other?
1 1
1
P(3 and 4) = P(3) • P(4) = • =
6
6
36
________________________ events mean that the outcome of one event is influenced by the
outcome of the other event.
example:
You have a bag with a blue, red, and yellow marble. When pulling two
out of the bag without replacing the first, what is the probability of
getting a blue on the first pick, and red on the second pick?
1 1 1
P(blue and red) = P(blue) • P(red after blue) = • =
3
1
3
4
2
18
2
6