Transcript 3 - Gilbert Public Schools

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
8% = .08
136% = 1.36
Fractions,
Decimals, Percents
(5)
⅛
1⁄
5
¼
⅓
½
¾
.125
.2
.25
.33
.50
.75
12.5%
20%
25%
33%
50%
75%
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
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 = 4
4
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
4
=
9 ÷ 4 = 2¼
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 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
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
6
2:6
2 to 6
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
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)
√b3 = Cube Root
(b·b·b = b3)
3
√27 = 3
3
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
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
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 = +9
n
= 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
5
n=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
3
n = 36
D=rxt
(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.
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)
Commutative
Property (57)
Numbers can be added or multiplied in any
order and not change the answer.
45 + 29 + 55 = 29 + 45 + 55
4x3x5=3x5x4
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 = 18
n=1
Property of Zero
(60)
Any number times zero is zero
18n = 0
n=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
To find n: 2.5 + 2.5 + n = 9
5+n=9
n = 4 in
2.5in
Area of Triangle
(68)
½bh
or
b×h
2
b=base h=height
Area of
Parallelogram
(69)
Parallelogram: b × h
b=base h=height
Rectangle: l × w
l=length w=width
Area of a
Trapezoid
(70)
½h × (b1+b2)
h × (b1+b2)
2
or
b1 and b2 are always directly across
from each other
b1
h
b2
Area of Composite
Figure (71)
Area of triangle = ½ × 4 × 2 = 4
Area of rectangle = 2 × 3 = 6
4 + 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 – triangle
4 sides – quadrilateral (square/rectangle)
5 sides – pentagon
6 sides – hexagon
7 sides – septagon
8 sides – octagon
9 sides – nonagon
10 sides - decagon
Parts of a Circle
(83)
radius
arc
chord
diameter
center
Chord does NOT go through the center
Transformations
(84)
Rotation:
Reflection:
Translation: R I R
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
3ft = 1yd
5280ft = 1mi
8oz = 1 cup
2 cups = 1 pint
2 pints = 1 quart
4 quarts = 1 gallon
16oz = 1lb (pound)
2000lb = 1 ton
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
Frequency
Chart (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