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

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

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% 3=300% .8 = 80%

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

Fractions, Decimals, Percents

(5)

⅛ .125 12.5%1⁄5 .2 20%

¼ .25 25%

⅓ .33 33%

½ .50 50%

¾ .75 75%

Algebraic Function Terms (6)

+ : sum, increase, more than, greater than, plus- : difference, decrease, less than, minusx : product, factors, times, multiplied by÷ : quotient, equal shares, divided by

Algebraic Expression (7)

An algebraic sentence (one that contains a variable) that does not contain an equal sign

h + 4

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 a=3

Fractions (9)

Numerator

Denominator

Equivalent Fractions (10)

Fractions that equal the same amount but have different numerators and denominators.

1 = 2 = 3 = 44 8 12 16

Improper Fraction (11)

Numerator is bigger than the denominator

8

3

Mixed Number (12)

Contain both a whole number and a fraction

3⅓

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

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

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

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

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.

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

Add or Subtract Decimals (19)

Line up the decimals and add/subtract as usual

3.25+ 12.15 15.40

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

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.

Dividing (22)

Divisor Dividend

Dividend

Divisor

Dividend ÷ Divisor

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

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

Percent toFraction (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

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%

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

Factor Tree (28)

24

2 12

2 6

2 3

Prime Factorization (29)

Make a factor tree. Write the product by using the prime numbers circled and exponents.

24 = 23 x 3

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…

Composite Numbers (31)

Numbers that have more than 2 factors.

4,6,8,9,10,12,14,15,16,18,20….

Ratios(32)

A comparison of two quantities by division

Ex: 2 2:6 2 to 6

6

Proportions (33)

Cross multiply and solve for the variable 2in = 12in 1mi n2 x n = 1 x 12 2n = 122n = 12 2 2 n = 6 mi

Rate (34)

A ratio comparing two quantities of different kinds of units

Ex: 50 miles 5 seconds

Unit Rate (35)

A rate with a denominator of 1 unit.

Ex: 10 miles 1 second

Rational Number(36)

Any number that can be written as a fraction

Ex: 2, 3.5, 2⅓

Integers(37)

Positive whole numbers, negative whole numbers, and zero

Ex: 1, 5, 0, -4, -10

Positive Integers(38)

Any whole number that is greater than zero

Ex: 1, 6, 101

Negative Integers(39)

Any whole number that is less than zero

Ex: -1, -5, -101

Opposite Numbers(40)

Numbers that are the same distance from zero on a number line, but in opposite directions.

Ex: 5 and -5

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

PEMDAS (42)

Parenthesis = ( )

Exponents = 23 (or sq. roots)

Multiplication/Division in order from Left to Right

Addition/Subtraction in order from Left to Right

Square Root (43)

√ b2 = b(b·b = b2)

Example: √ 9 = 3

Cube Root (44)

3√b3 = Cube Root (b·b·b = b3)

3√27 = 3

Powers and Exponents (45)

How many times a base number is multiplied by itself.

Ex: 83 = 8 x 8 x 8 = 5128 is the base number3 is the exponent

Inverse Operation (46)

The opposite operation:

Opposite of Addition is SubtractionOpposite of Subtraction of AdditionOpposite of Multiplication is DivisionOpposite of Division is Multiplication

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

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 = +9n = 21

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 5n = 6

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 3n = 36

D = r x t (51)

D = distance

r = rate (or s=speed)

t = time

r = D ÷ t

t = D ÷ r

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

Independent Variable (53)

The input value on a function table

Dependent Variable (54)

The output value on a function table because the value depends on the input

Linear Function (55)

A function whose graph is a line.

AssociativeProperty (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)

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

Distributive Property (58)

12 x 32 = (12 x 30) + (12 x 2)

2(3 + 4) = 2x3 + 2x4

Identity Property of One (59)

1 times any number is that number itself

18n = 18n = 1

Property of Zero (60)

Any number times zero is zero

18n = 0n = 0

Coefficient (61)

A numerical factor of a term that contains a variable

Ex: 4a

Constant (62)

A term without a variable, so just a number by itself

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

Inequalities (64)

> = greater than

< = less than

> = greater than or equal to (minimum, at least)

< = less than or equal to (maximum, no more than)

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)

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)

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

Area of Triangle (68)

½bh or b × h 2

b=base h=height

Area of Parallelogram

(69)

Parallelogram: b × hb=base h=height

Rectangle: l × w l=length w=width

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

Area of Composite Figure (71)

Area of triangle = ½ × 4 × 2 = 4Area of rectangle = 2 × 3 = 64 + 6 = 10 square units

Perimeter (72)

The distance around the outside of a shape.

Triangle: add all 3 sides

Rectangle: add all 4 sides

Polygon: add all sides

Changing Dimensions Effect on Perimeter

(73)

P(figure A) • x = P (figure B)

P = perimeter

x = change in perimeter

Changing Dimensions Effect on Area (74)

A(figure A) • x2 = A (figure B)

A = area

x = change in area

Volume of Rectangular Prism (75)

V = length × width × height

Volume measured in units3

Volume of Triangular Prism (76)

V = area triangle × height prism

Find area of triangle and multiply by height of prism

Volume measured in units3

Surface Area of Rectangular Prism (77)

Surface Area = 2ℓw + 2ℓh + 2wh

ℓ = length

w = width

h = height

Surface Area measured in Units2

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

Surface Area of Pyramid (79)

Surface Area = (Area of Base) + (Area of each Side Triangle)

Surface Area measured in Units2

3-d Shapes (80)

Pyramid: triangular sides

Prism: rectangular sides

Cone: Circular base with one base

Cylinder: Circular base and top

Triangles (81)

Scalene: No congruent sides

Isosceles: 2 congruent sides

Equilateral: 3 congruent sides

Congruent: same size, same shape

Geometric Shapes(82)

3 sides – triangle4 sides – quadrilateral (square/rectangle)

5 sides – pentagon6 sides – hexagon7 sides – septagon8 sides – octagon9 sides – nonagon10 sides - decagon

Parts of a Circle (83)

radiusarc

chord diameter

center

Chord does NOT go through the center

Transformations (84)

Coordinates (85)

(x,y)

( , )

Run over then jump up

(2,3)

Metric System (86)

King Henry Drinks Delicious Chocolate Milk

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

Range (88)

The range of data

Highest value – lowest value = range

12,15,15,17,21,35,46

46 - 12 = 34 is the range

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 2+3+4+6+7+2 = 24

24 ÷ 6 addins = 4

Mean is 4

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

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

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

First Quartile(93)

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

Third Quartile (94)

The median (middle data number) of the upper half of the data

Interquartile Range (95)

The difference between the first quartile and the third quartile

Lower Extreme (96)

The lowest number in the data set

Upper Extreme (97)

The highest number in the data set

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

FrequencyChart (99)

Shows data displayed in frequencies (intervals)

Tally Chart(100)

Chart that shows a tally mark for every piece of data.

Circle Graph (101)

Shows data as parts of a whole

Line Graph(102)

Shows a change in data over time

Histogram(103)

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

Bar Graph(104)

Graph that shows data by categories. Bars of categories do not touch.

Line Plots(105)

Graph that shows how many times each number occurs by marking an “x” on a

number line.

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.

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