1. Greatest Common Factor (1)
Largest Factor that equally divides into both numbers.
Example: GCF of 12 and 18
12: 1,2,3,4,6,12
18: 1,2,3,6,9,18
GCF is 6

2. Least Common Multiple (2)
Lowest multiple that both numbers divide into.
Example: The LCM of 8 and 12
8: 8,16,24,32,40,48,56,64,72,80
12: 12,24,36,48,60,72,84,96,108
LCM = 24

3. Decimal to a Percent (3)
Move the decimal 2 places to the right. Put a % at the end of the number. If no decimal is present, the decimal is after the last number. Fill in empty spaces with zeros
.025 = 2.5% =300% .8 = 80%

4. Percent to a Decimal (4)
Move decimal 2 place to the left and remove the percent sign. Fill in empty spaces with zeros. If there is no decimal, the decimal is after the last number.
25% = % = 1.36
8% = .08

5. Fractions, Decimals, Percents (5)
⅛ %
1⁄ %
¼ %
⅓ %
½ %
¾ %

6. Algebraic Function Terms (6)
+ : sum, increase, more than, greater than, plus
: difference, decrease, less than, minus
x : product, factors, times, multiplied by
÷ : quotient, equal shares, divided by

7. Algebraic Expression (7)
An algebraic sentence (one that contains a variable) that does not contain an equal sign
h + 4

8. Algebraic Equation (8) 5 + a = 8 a=3
An algebraic sentence (one that contains a variable) that contains an equal sign and has only one possible answer.
5 + a = a=3

9. Numerator Denominator
Fractions (9)
Numerator
Denominator

10. Equivalent Fractions (10)
Fractions that equal the same amount but have different numerators and denominators.
1 = 2 = = 4

11. Numerator is bigger than the denominator 8 3
Improper Fraction (11)
Numerator is bigger than the denominator 8 3

12. Contain both a whole number and a fraction 3⅓
Mixed Number (12)
Contain both a whole number and a fraction 3⅓

13. Changing Improper Fractions to Mixed Numbers (13)
Drop and Divide. Divide the numerator by the denominator. The answer is the whole number, the remainder is the numerator, and the divisor is the denominator.
9 = ÷ 4 = 2¼ 4

14. Changing Mixed Numbers to Improper Fractions (14)
-Multiply denominator and whole number
-then add the numerator
-that answer becomes the numerator
-denominator stays the same
2¼ = 4x2+1 = 9 = 9 4

15. Adding or Subtracting Fractions (15)
Find a common denominator and make equivalent fractions using the common denominator, then add or subtract the numerators and the denominator stays the same. 12 2/3 8/12
+ 3 1/4 3/12
______________________________________
/12

16. Subtract Fractions Magic of 1 (16)
Borrow 1 from the top whole number. “Magic of 1” changes it into a fraction with the same denominator as the bottom fraction. Numerator and denominator are the same number for the “magic of 1”
/12
- 3 5/ /12
____________________________________
8 7/12

17. Multiply Fractions (17)
If the fraction is a mixed number, change to improper fraction.
Cross cancel
Multiply across
If answer is an improper fraction, change it to a mixed number.

18. Dividing Fractions (18) -change mixed numbers to improper fractions
-party girl flip the second fraction (reciprocal)
-change ÷ to x
-cross cancel
-multiply across
-if improper, change to mixed number

19. Add or Subtract Decimals (19)
Line up the decimals and add/subtract as usual
3.25
15.40

20. Multiply Decimals (20)
Right justify the two numbers you are multiplying. Count how many numbers are to the right of the decimal. The answer should have the same amount of numbers to the right of the decimal.
numbers
x number
numbers

21. Divide Decimals (21)
There can not be a decimal in the divisor. If there is, move the decimal to the right until the divisor is a whole number. Move the decimal inside the house in the dividend the same number of spaces then kick the decimal to the top of the house. Divide as usual.

22. Divisor Dividend Dividend Divisor Dividend ÷ Divisor
Dividing (22)
Divisor Dividend
Dividend
Divisor
Dividend ÷ Divisor

23. Decimal to
Fraction (23)
Find the place value of the last number after the decimal. That place value is the denominator. The numerator is the entire number after the decimal.
.402 = 402
1000

24. Fraction to
Decimal (24)
If the fraction is a mixed number, change it to an improper fraction. Drop and divide. Numerator drops into division house and is divided by the denominator. Put a decimal after the number in the division house and divide as usual.
1.25
1¼ = 4

25. Percent to
Fraction (25)
Change the percent to a decimal and then follow the rules for changing a decimal to a fraction
25% = = = 1

26. Fraction to
Percent (26)
Change the fraction to a decimal and then follow the rule for changing a decimal to a percent
¼ = 1 ÷ 4 = .25 = 25%

27. Rounding (27)
Underline the number you intend to round. Circle the number directly to the right of that number. Look at the circled number, if it is…
5-9: round underlined number up by 1
0-4: underlined number stays the same
All numbers to the right of the number you are rounding turn to zeros
3, = 3,300.0

28. Factor Tree (28) 24

29. Prime Factorization (29)
Make a factor tree. Write the product by using the prime numbers circled and exponents.
24 = 23 x 3

30. Prime Numbers (30)
Numbers that have only 2 factors, the number 1 and itself.
2,3,5,7,11,13,17,19,23,29,31…

31. Numbers that have more than 2 factors. 4,6,8,9,10,12,14,15,16,18,20….
Composite Numbers (31)
Numbers that have more than 2 factors.
4,6,8,9,10,12,14,15,16,18,20….

32. A comparison of two quantities by division Ex: 2 2:6 2 to 6 6
Ratios(32)
A comparison of two quantities by division
Ex: : to 6 6

33. Proportions (33) Cross multiply and solve for the variable 2in = 12in
1mi n
2 x n = 1 x n = 12
2n = 12
n = 6 mi

34. Rate (34) A ratio comparing two quantities of different kinds of units
Ex: 50 miles
5 seconds

35. A rate with a denominator of 1 unit. Ex: 10 miles 1 second
Unit Rate (35)
A rate with a denominator of 1 unit.
Ex: 10 miles
1 second

36. Any number that can be written as a fraction Ex: 2, 3.5, 2⅓
Rational Number(36)
Any number that can be written as a fraction
Ex: 2, 3.5, 2⅓

37. Integers(37) Positive whole numbers, negative whole numbers, and zero
Ex: 1, 5, 0, -4, -10

38. Any whole number that is greater than zero Ex: 1, 6, 101
Positive Integers(38)
Any whole number that is greater than zero
Ex: 1, 6, 101

39. Any whole number that is less than zero Ex: -1, -5, -101
Negative Integers(39)
Any whole number that is less than zero
Ex: -1, -5, -101

40. Opposite Numbers(40)
Numbers that are the same distance from zero on a number line, but in opposite directions.
Ex: 5 and -5

41. Absolute
Value (41)
The distance a number is from Zero on a number line
I4I = 4 I-2I = 2
*Any number and its negative have the same absolute value.
Ex: 5 and -5 have the same absolute value

42. PEMDAS (42) Parenthesis = ( ) Exponents = 23 (or sq. roots)
Multiplication/Division in order from Left to Right
Addition/Subtraction in order from Left to Right

43. Square Root (43)
√ b2 = b
(b·b = b2)
Example: √ 9 = 3

44. Cube Root (44)
3√b3 = Cube Root
(b·b·b = b3)
3√27 = 3

45. Powers and Exponents (45)
How many times a base number is multiplied by itself.
Ex: 83 = 8 x 8 x 8 = 512
8 is the base number
3 is the exponent

46. Inverse Operation (46) The opposite operation:
Opposite of Addition is Subtraction
Opposite of Subtraction of Addition
Opposite of Multiplication is Division
Opposite of Division is Multiplication

47. Subtraction Property of Equality (47)
In an addition problem, you must subtract the same number on both sides of the equation to get the variable on one side of the equation by itself.
n + 3 = 12
n = 9

48. Addition Property of Equality (48)
In a subtraction problem, you must add the same number on both sides of the equation to get the variable on one side of the equation by itself.
n – 9 = 12
+ 9 = +9
n = 21

49. Division Property of Equality (49)
In an multiplication problem, you must divide the same number on both sides of the equation to get the variable on one side of the equation by itself.
n · 5 = 30
5 5
n = 6

50. Multiplication Property of Equality (50)
In a division problem, you must multiply the same number on both sides of the equation to get the variable on one side of the equation by itself.
3 · n = 12 · 3 3
n = 36

51. D = distance r = rate (or s=speed) t = time r = D ÷ t t = D ÷ r
D = r x t (51)
D = distance
r = rate (or s=speed)
t = time
r = D ÷ t
t = D ÷ r

52. Input / Output Tables (52)
-What was done to the “In” numbers to get the “Out” numbers. Find the pattern/equation.
-Must check at least 3 rows to make sure the equation works.
-Take the 4 answers and see which one fits.
x · 5 = y

53. Independent Variable (53)
The input value on a function table

54. Dependent Variable (54)
The output value on a function table because the value depends on the input

55. Linear Function (55)
A function whose graph is a line.

56. Numbers can be grouped differently and the answer will be the same.
Associative
Property (56)
Numbers can be grouped differently and the answer will be the same.
14 + (7 + 3) = (14 + 7) + 3
(4 x 3) x 2 = 4 x (3 x 2)

57. Commutative Property (57)
Numbers can be added or multiplied in any order and not change the answer. =
4 x 3 x 5 = 3 x 5 x 4

58. Distributive Property (58)
12 x 32 = (12 x 30) + (12 x 2)
2(3 + 4) = 2x3 + 2x4

59. Identity Property of One (59)
1 times any number is that number itself
18n = 18
n = 1

60. Any number times zero is zero
Property of Zero (60)
Any number times zero is zero
18n = 0
n = 0

61. Coefficient (61) A numerical factor of a term that contains a variable
Ex: 4a

62. Constant (62)
A term without a variable, so just a number by itself

63. Combining Like Terms (63)
When you have “like terms”, combine coefficients with the same variable together and combine constants together.
Ex: a + 2b + 3a + 5b = 4a + 7b

64. Inequalities (64) > = greater than < = less than
> = greater than or equal to
(minimum, at least)
< = less than or equal to
(maximum, no more than)

65. Geometric Sequencing (65)
The pattern in a sequence that can be found by multiplying the previous term by the same number.
Ex: 3, 6, 12, 24
(# multiplied by 2 each time)

66. Arithmetic Sequencing (66)
The pattern in a sequence that can be found by adding the same number to the previous term.
Ex: 4, 8, 12, 16
(add 4 each time)

67. Find the missing line segment (67)
2.5in n 2.5in
To find n: n = 9
5 + n = 9
n = 4 in

68. ½bh or b × h 2 b=base h=height
Area of Triangle (68)
½bh or b × h 2
b=base h=height

69. Area of Parallelogram (69)
Parallelogram: b × h
b=base h=height
Rectangle: l × w
l=length w=width

70. Area of a Trapezoid (70) ½h × (b1+b2) or h × (b1+b2) 2
b1 and b2 are always directly across from each other b1 h b2

71. Area of Composite Figure (71)
Area of triangle = ½ × 4 × 2 = 4
Area of rectangle = 2 × 3 = 6
4 + 6 = 10 square units

72. Perimeter (72) The distance around the outside of a shape.
Triangle: add all 3 sides
Rectangle: add all 4 sides
Polygon: add all sides

73. Changing Dimensions Effect on Perimeter (73)
P(figure A) • x = P (figure B)
P = perimeter
x = change in perimeter

74. Changing Dimensions Effect on Area (74)
A(figure A) • x2 = A (figure B)
A = area
x = change in area

75. Volume of Rectangular Prism (75)
V = length × width × height
Volume measured in units3

76. Volume of Triangular Prism (76)
V = area triangle × height prism
Find area of triangle and multiply by height of prism
Volume measured in units3

77. Surface Area of Rectangular Prism (77)
Surface Area = 2ℓw + 2ℓh + 2wh
ℓ = length
w = width
h = height
Surface Area measured in Units2

78. Surface Area of Triangular Prism (78)
Surface Area = (2 × Area of Triangle) + (Area of Rectangle Side 1) + (Area of Rectangle Side 2) + (Area of Rectangle Side 3)
Surface Area measured in Units2

79. Surface Area of Pyramid (79)
Surface Area = (Area of Base) + (Area of each Side Triangle)
Surface Area measured in Units2

80. 3-d Shapes (80) Pyramid: triangular sides Prism: rectangular sides
Cone: Circular base with one base
Cylinder: Circular base and top

81. Triangles (81) Scalene: No congruent sides
Isosceles: 2 congruent sides
Equilateral: 3 congruent sides
Congruent: same size, same shape

82. Geometric Shapes (82) 3 sides – triangle
4 sides – quadrilateral (square/rectangle)
5 sides – pentagon
6 sides – hexagon
7 sides – septagon
8 sides – octagon
9 sides – nonagon
10 sides - decagon

83. radius arc chord diameter center Chord does NOT go through the center
Parts of a Circle (83)
radius
arc
chord
diameter
center
Chord does NOT go through the center

84. Rotation: Reflection: R I Translation: R I R
Transformations (84)
R I R
Rotation:
Reflection: R I
Translation: R I R R

85. (x,y) ( , ) Run over then jump up (2,3)
Coordinates (85)
(x,y)
( , )
Run over then jump up
(2,3)

86. King Henry Drinks Delicious Chocolate Milk
Metric System (86)
King Henry Drinks Delicious Chocolate Milk

87. Standard Conversion (87)
12in = 1ft oz = 1lb (pound)
3ft = 1yd lb = 1 ton
5280ft = 1mi
8oz = 1 cup
2 cups = 1 pint
2 pints = 1 quart
4 quarts = 1 gallon

88. Range (88) The range of data Highest value – lowest value = range
12,15,15,17,21,35,46
= 34 is the range

89. Mean (89)
The average
Add all of the addins together and divide that by the total number of addins.
2,3,4,6,7, = 24
24 ÷ 6 addins = 4
Mean is 4

90. Median (90) -List data in numerical order from least to greatest.
Median is the middle number.
If 2 number are in the middle add them together and divide by 2
12,15,15,17,21,35,46
Median is 17

91. Mode (91) The number that appears most often in a data set.
2,3,4,4,5,9,10,11,11,11,14
Mode is 11

92. Outlier (92)
A data value that is either much greater or much less than the median. Data value must be 1.5 times less than the 1st Quartile and 1.5 times greater than the 3rd Quartile

93. The median (middle data number) of the lower half of the data
First Quartile(93)
The median (middle data number) of the lower half of the data

94. The median (middle data number) of the upper half of the data
Third Quartile (94)
The median (middle data number) of the upper half of the data

95. Interquartile Range (95)
The difference between the first quartile and the third quartile

96. The lowest number in the data set
Lower Extreme (96)
The lowest number in the data set

97. The highest number in the data set
Upper Extreme (97)
The highest number in the data set

98. Mean Absolute Deviation (98)
1. Find mean of data set
2. Find the absolute value of the difference between each data value and the mean
3. Find the average (mean) of the absolute values found in step 2

99. Shows data displayed in frequencies (intervals)
Frequency
Chart (99)
Shows data displayed in frequencies (intervals)

100. Chart that shows a tally mark for every piece of data.
Tally Chart
(100)
Chart that shows a tally mark for every piece of data.

101. Shows data as parts of a whole
Circle Graph
(101)
Shows data as parts of a whole

102. Shows a change in data over time
Line Graph
(102)
Shows a change in data over time

103. Histogram
(103)
Bar Graph where the bars are touching and shows data on the x-axis in intervals.

104. Graph that shows data by categories. Bars of categories do not touch.
Bar Graph
(104)
Graph that shows data by categories. Bars of categories do not touch.

105. Line Plots
(105)
Graph that shows how many times each number occurs by marking an “x” on a number line.

106. (Box-and-whiskers plot)
Box Plots
(Box-and-whiskers plot)
(106)
Graph uses a number line to show the distribution of a set of data using median, quartiles, and extreme values. Useful for large sets of data.

107. Shape of Data Distributions
(107)
Cluster = Data grouped close together
Gap = Numbers that have no data value
Peak = Mode
Symmetry = Left side of the distribution looks exactly like the right side