Greatest Common Factor (1)

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 3300 .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 .25 136 1.36
• 8 .08

5
Fractions, Decimals, Percents (5)

• ? .125 12.5
• 1/5 .2 20
• ¼ .25 25
• ? .33 33
• ½ .50 50
• ¾ .75 75

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)

• An algebraic sentence (one that contains a
  variable) that contains an equal sign and has
  only one possible answer.
• 5 a 8 a3

9
Fractions (9)

• Numerator
• Denominator

10
Equivalent Fractions (10)

• Fractions that equal the same amount but have
  different numerators and denominators.
• 1 2 3 4
• 4 8 12 16

11
Improper Fraction (11)

• Numerator is bigger than the denominator
• 8
• 3

12
Mixed Number (12)

• Contain both a whole number and a fraction
• 3?

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 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 4x21 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
• 
  ______________________________________
• 15 11/12

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 11 12/12
• - 3 5/12 - 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
• 12.15
• 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.
• 12.34 2 numbers
• x 1.2 1 number
• 14.808 3 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
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 5 4 5.00 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 .25 25 1
100 4
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
• 3,256.3 3,300.0

28
Factor Tree (28)

• 24
• 2 12
• 2 6
• 2 3

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
Composite Numbers (31)

• Numbers that have more than 2 factors.
• 4,6,8,9,10,12,14,15,16,18,20.

32
Ratios(32)

• A comparison of two quantities by division
• Ex 2 26 2 to 6
• 6

33
Proportions (33)

• Cross multiply and solve for the variable
• 2in 12in
• 1mi n
• 2 x n 1 x 12 2n 12
• 2n 12
• 2 2 n 6 mi

34
Rate (34)

• A ratio comparing two quantities of different
  kinds of units
• Ex 50 miles
• 5 seconds

35
Unit Rate (35)

• A rate with a denominator of 1 unit.
• Ex 10 miles
• 1 second

36
Rational Number(36)

• Any number that can be written as a fraction
• Ex 2, 3.5, 2?

37
Integers(37)

• Positive whole numbers, negative whole numbers,
  and zero
• Ex 1, 5, 0, -4, -10

38
Positive Integers(38)

• Any whole number that is greater than zero
• Ex 1, 6, 101

39
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/Di
vision in order from Left to Right Addition/Subtr
action in order from Left to Right
43
Square Root (43)
v b2 b (bb b2) Example v 9 3
44
Cube Root (44)
3vb3 Cube Root (bbb b3) 3v27 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
• -3 -3
• 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 r x t (51)

• D distance
• r rate (or sspeed)
• 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
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. 45 29 55 29
45 55 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
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)
gt greater than lt less than gt
greater than or equal to
(minimum, at least) lt 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)

• 9in
• 2.5in n 2.5in
• To find n 2.5 2.5 n 9
• 5 n 9
• n 4 in

68
Area of Triangle (68)

• ½bh or b h
• 2
• bbase hheight

69
Area of Parallelogram (69)

• Parallelogram b h
• bbase hheight
• Rectangle l w
• llength wwidth

70
Area of a Trapezoid(70)

• ½h (b1b2) or h (b1b2)
• 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
Parts of a Circle (83)

• radius
• arc
• chord
• diameter
• center
• Chord does NOT go through the center

84
Transformations (84)
R I
R

• Rotation
• Reflection R I
• Translation R I R

R
85
Coordinates (85)

• (x,y)
• ( , )
• Run over then jump up
• (2,3)

86
Metric System (86)

• King Henry Drinks Delicious Chocolate Milk

87
Standard Conversion (87)

• 12in 1ft 16oz 1lb
  (pound)
• 3ft 1yd 2000lb 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
• 46 - 12 34 is the range

89
Mean (89)

• The average
• Add all of the addins together and divide that by
  the total number of addins.
• 2,3,4,6,7,2 234672 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
First Quartile(93)

• The median (middle data number) of the lower half
  of the data

94
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
Lower Extreme (96)

• The lowest number in the data set

97
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
Frequency Chart (99)
Shows data displayed in frequencies (intervals)
100
Tally Chart (100)
Chart that shows a tally mark for every piece of
data.
101
Circle Graph (101)
Shows data as parts of a whole
102
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
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 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