fractions - ANSWER represent part of a whole written as a/b where a is the numerator (part) and b is the denominator (whole)
fraction to decimal conversion - ANSWER divide numerator (top #) with denominator (bottom #)
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fractions - ANSWER represent part of a whole written as a/b where a is the numerator (part) and b is the denominator (whole)
fraction to decimal conversion - ANSWER divide numerator (top #) with denominator (bottom #)
ex: 5/8=0.6250 (5 divided by 8)
decimals - ANSWER number amount in decimal form
decimal to fraction conversion - ANSWER RULE:
-a decimal value less than one is put over its place value
ex: 0.48 (the eight is in the hundreths place so its 48/100) if it were 0.048 it would be in the thousandths place so its 48/1000
-a decimal greater than one
1. move the decimal place to the right until you have a whole number
2. count how many decimal places you moved to the right and that's how many zeros you add after the one in the denominator
3. that is the final fraction
ex: decimal 3.24
moves two places to the right to make it 324/100
percentages - ANSWER always over 100 (look at page 2 of the math section)
decimal to fraction to percents - ANSWER decimal to percent: multiply by 100
ex: 0.35 x 100=35%
fraction to percent:
1. turn fraction into a decimal
2. turn decimal to percent
ex: 1/4=0.25 x100 =25%
order of operations - ANSWER PEMDAS (parenthesis, Exponents, Multiplication, Division, Addition, Subtraction)
operations within parenthesis - ANSWER when two or more operations are taking place do them from left to right
ex: 225/(3+2 x11) -4
1. 3+22
2.225/25-4
3.9-4=5
computation with fractions - ANSWER divide numerator by denominator but first complete PEMDAS on top and bottom
ex: 47-5/5+9=42/14=3
rational number - ANSWER CAN be written as a fraction ex: 4 can be written as 12/3 or 16/4
irrational numbers - ANSWER CANNOT be written in fraction form
ex: the square root of 2
comparing rational numbers - ANSWER > greater than
< less than
> greater than or equal to (with the line under it)
< less than or equal to (with a line under it)
finding the least common denominator - ANSWER 1. find the least common denominator
2. rewrite each fraction as an equivalent fraction using the lowest common multiple in the denominator
ex: 2/5, 1/6, 4/15
5, 10, 15, 20, 25, 30, 35, 40, 45
6, 12, 18, 24, 30, 36, 42, 48, 54
15, 30, 45, 60, 75, 90
they all have 30 in common so the LCD=30
multiply
2 x 6 = 12
5 x 6 = 30
1 x 5 = 5
6 x 5 =30
4 x 2 = 8
15 x 2 = 30
variable - ANSWER letter
constant - ANSWER a number
term - ANSWER a number or variable or product of the two (separated by an addition or subtraction sign)
coefficient - ANSWER the number part of the variable term
inverse operations - ANSWER opposite of each other and undo each other
percents (revisited) - ANSWER percent = per 100 or /100
ex: at a major airport, 15% of all flights were delayed or cancelled due to weather. If there were 220 flights total, how many flights were cancelled or delayed
1. 15%= 15/100 = 0.15
2. take the flight number which is 220 x 0.15= 33
- 33 flights were cancelled or delayed
percent increase or decrease - ANSWER ex: kathryn purchases $60 worth of groceries and pays 8% sales tax. how much did she pay total including tax?
1. 8%= 8/100 =0.08
2. $60 x 0.08= $4.80
3. $60 + 4.80= $64.80
ex 2: james purchases a new jacket originally priced at $140.00. the store offers a 30% discount. how much does jams pay for the jacket including the discount?
1. 30%= 30/100= 0.30
2. $140 x 0.30 = $42 (discount)
3. $140 -$42 = $98
increase (addition +) - ANSWER -tax
-mark up
-increased by
-gained
decrease (subtraction -) - ANSWER -discount
-mark down
-decreased by
-depreciation
-loss
metric measurements - ANSWER millimeter (mm) ---> thickness of a cellphone
centimeter (cm) ---> width of a wedding ring
meter (m) ---> doorway just over 2m tall
kilometer (km) ---> 1 km= 2/3 of a mile
gram (g) ---> weight of a grape
kilogram (kg) ---> 10 lb bag of dog food
degrees celsius ---> 0=freezing 20=warm
volume - ANSWER - measured in cubic units (cm^3)
- in liters or milliliters
1 liter = 1,000 milliliters 1cc=1mL
general estimation and rounding rule - ANSWER 5 or greater--> round up
4 or smaller--> round down
rounding fractions - ANSWER - if a numerator is greater than or equal to half of the denominator --> round up to the next whole number
-if not round down to the next whole number
proportion - ANSWER fraction set equal to another fraction
1/2=3/4
solving a proportion - ANSWER ex: if a map has a legend and has a scale of 1cm= 20 miles and you measure 6.4 cm between the two destinations. what proportion can be made to calculate how many miles are represented by 6.4 cm?
1. 1cm/20 miles = 6.4cm/x miles
2. 1cm/20 miles = 6.4 cm/ 6.4 m = 128 miles/ 6.4 cm (cross multiply)
3. x= 128 miles
directly proportional equations - ANSWER y= 4x
y= 8x
y= x/5
y= 2/3x
not directly proportional equations - ANSWER y= 2x+9
y= x-3
y= 4/x
y=6
ratio - ANSWER a comparison of two numbers by a division sign (basically a fraction)
rates - ANSWER ratios (fractions) with units
ex: 2 cats/ 3 dogs (animals in this case are the units)
unit rate - ANSWER a rate (ratio with labels)
expressed per 1 unit
ex: 7 miles/2 hours = 3.5 miles/1 hour
( 7/2 divide the two to get 3.5) and that's the unit rate
slope - ANSWER y=mx+b
ex: melinda keeps a chart on the money she saves each week from her weekly paycheck. by the end of the third week, she has saved $75 and by the end of the 8th week she saved a total of $200 a graph is made.
slope= 200 (y2)-75/8-5 weeks
=$125/5 weeks
=$25/ 1 week
expression - ANSWER has numbers, variables (letters), and addition, subtraction, multiplication or division in it
ex: -3(x-12) or 9-2y
equation - ANSWER relates expressions equal to one another
ex: x=8, 9-2y=27, -3(x-12)=2(3x+15)
inequalities - ANSWER use comparison symbols (like greater than or less than, greater than or equal to less than or equal to
ex: x<8 9-2y<27
translating word problems into equations and inequalities - ANSWER ex: xavier attends a local fair. He spends a total of $25 which includes the $5 admission to the fair and 8 rides. when he returns home his dad wants to know how much it costs for a single ride
r= cost of one ride
8r+5=25
subtract 5 from both sides
8r=20/8
r=20/8 or $2.50
(look at translation to equation and inequalities page in the math section for 2nd example)
ex: vivian is at the supermarket and wants to spend no more than $70 on groceries. She knows that she will spend $45 on necessities but wants to buy pepperoni which costs $7.49/pound. How much pepperoni can she buy with her spending limit
mean - ANSWER average (add all numbers provided together then divide by the amount of numbers there) 2+3+7+9+5=26/5=5.2
median - ANSWER middle number
ex: 3, 3, 3, 7, 8, 9, 9, 13
2. 7+8/2 (bc theres two left)= 7.5
mode - ANSWER (#) there's the most of
ex: 3, 3, 3, 7, 8, 9, 9, 13
answer: 3
range - ANSWER biggest number subtracted by smallest number
ex: 79-28= 51
unimodal peak - ANSWER
Bimodal - ANSWER
skewed right - ANSWER
skewed left - ANSWER
Outlier - ANSWER an unexpected value that does not fit any trend or pattern in the data
correlation - ANSWER how variables relate to each other
Covariance - ANSWER the relationship between variables
variables increase - ANSWER positive covariance exists (directly related)
one variable increases the other decreases - ANSWER negative covariance exists (variables inversely related)
independent variable - ANSWER manipulated variable graphed on the x axis
dependent variable - ANSWER changes in response to the other variables change graphed on the y-axis
circumference - ANSWER the length around a circle
-can be found with formula c=2*3.14*radius
length of an arc (part of a circle) formula - ANSWER C=central angle measure/360*2*3.14*r
perimeter - ANSWER length around the entire shape
look at perimeter page in math section (towards the end)
area - ANSWER how much surface space something takes up (units squared ^2)
area of a square - ANSWER length x length
area of a rectangle - ANSWER length x width
Area of a triangle - ANSWER 1/2 x base x height
Area of a parallelogram - ANSWER height x base
Area of a trapezoid - ANSWER 1/2h(b1+b2)
area of a circle - ANSWER A=πr²
Area of a rhombus - ANSWER A=1/2 x diagonal1 x diagonal 2
metric system - ANSWER
1 foot - ANSWER 12 inches
1 yard - ANSWER 3 feet
36 inches
1 mile - ANSWER 5280 feet (440 inches) 1.6 km 1.09 yards
1 pound - ANSWER 16 ounces
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