Study.com Math
What is the Mass of a liquid with a density of 2.12 g/ml and a volume of 53.0 ml (to the nearest gram)?
112 g
To covert feet to inches, multiply by?
12
in a Town with 400 commuters 120 ride a car to work the rest use a bike, what is the ratio of drivers to cyclist
120:280
4^2-(2^3/(4*2)) Simply: Order of Operations
15
5 yards = ____ feet?
15 feet
Covert Percent into a Fraction: 15%
15/100 (Still need to simpify) 3/20
given 51 * 28 what is a valid estimate answer
1500
4 gallons = ? quarts
16 quarts
3.25 * 5.15
16.7375
8 m * 2 m
16m 2
convert 178300 ml in to liters
178.3 l
convert 19 l into milliliters
19,000 ml
if one in ten thousand planets in the universe could possibly support life there are an estimated of 3 trillion planets in the universe how many planets might support life
1:10,000. p=3,000,000,000,000 answer:300,000,000
1 m * 1 lb =
1m lb
1x * 1y=
1xy
Simplify: [6*(4-2)+6]/3²
2
2 feet = ? inches
2 * 12 = 24
Prism Surface Area
2(lw+lh+wh)
How many imaginary lines need to be drawn to label points?
2, by drawing imaginary horizontal and vertical lines from the point, we find where the point crosses each axis
9 * .25
2.25
8.3g/3.5cm^3
2.4g/cm^3
Covert 0.2 into a Fraction
2/10 = 1/5
2 feet = ? yards
2/3=0.667
If 3/5 of people have one per and 2/3 of those pets are cats, then what Fraction of the people with a cat?
2/5
Covert Fraction into a Decimal: 2/5
2/5=0.4
What is the place value of 2 in the number 23?
20
Covert Percent into a Fraction: 20%
20/100 (Still need to simplify) 1/5
Simplify: 24/2^2+6*3 (Order of Operations)
24
If a square prism and a square Pyramid have the same base and same height, what would the volume of the Pyraid be if the volume of the square prism was 75 cubic inches?
25 cubic inches
Covert 0.25 into a Fraction
25/100 = 1/4
A recipe calls for 3 3/8 tablespoons of sugar. If you want to make 1/2 the recipe, then how much sugar do you need?
27/8 x 1/2 = 27/16 = 1 11/16
0 degrees Celsius equals
273 Kelvins
Convert 2000 meters into kilometers
2km
P= (rectangle)
2w+2l
Cylinder Surface Area
2πr(h+r)
what is the slope? 3x + 9
3
Susan is making a dress. She buys 3 3/4 yards of fabric. She uses 9/10 of this fabric. How many yards of fabric did she use?
3 3/4 = 15/4 * 9/10 = 135/40 = 3 3/8
How many feet are in a yard?
3 feet
How many ml are in 3.4 L?
3,400 mL
pi
3.14
Circle Area
3.14 x r^2
How many feet is 5ft 3 inches?
3/12= 0.25
Divide (3/4) (1/2) =
3/2
What is 3/4 as a percentage?
3/4 = 0.75 75%
(3/4) * (1/2)
3/8
If you have 300 grams of water, how many milliters?
300ml
Degrees Celsius Poem
30c is hot 20c is nice 10c is cold 0c is ice
Covert Percentage into a Decimal: 34%
34% = 0.34
70 mi / 2 hours - use division
35 mi/hr
Angie's car batteries cells car batteries and gnomes in a ratio of 35 to 2. by the time Angie has sold 280 car batteries how many goals did she sell
35:2 280:g , cross multiply to get g. answer: 280:16
Divide: (9/8) (3/4)
36/24 = 6/4 = 3/2
10 cm - 6 cm
4 cm
16 inches divided into fourths
4 in
Every gallon has ? quarts?
4 quarts
Sphere Volume
4/3πr³
Simplify: 40-6*2^2/4+6 (Order of Operations)
40
Simplify: 7*5-2+11 Order Of Operations
44
ratio for quarts to gallons
4:1 - there are 4 quarts in a gallon
1m * 4 =
4m
Perimeter of a square
4s
Sphere Surface Area
4πr²
convert 5300 km into m
5,300.00 m
1/12 + 3/4
5/6
AT a hot wings restaurant, 5/9 of the patrons ordered the inferno hot wings and 1/8 of those patrons passed out from the intensity of the sauce. What Fraction of the patrons passed out?
5/72
23/24 - 1/3
5/8
Covert Percent into a Fraction: 50%
50/100 (Still need to simplify) 1/2
500 ml of water is closed to?
500 g
(11/12) * (5/6)
55/72
How many sides does a cube have?
6
6 inches = ? feet
6 /12=0.5 feet
Convert 0.6 to a Fraction
6/10= 3/5
What is the area of a rectangle with a width of 10 check and a length of 6cm
60 SQ cm
3 ft + 4 ft
7 ft
21 in/3 oz
7 in/oz
5/6 + 11/12
7/4
If you napped for 1 1/16 hours on Monday and 2 1/2 times as long as Tuesday, then how long was Tuesday´s nap?
7/6 x 5/2 = 35/12 = 2 11/12
7/8 / 12
7/8 / 12/1 = 7/8 / 1/12
10/9 - 1/3
7/9
(17/15) * (5/3)
85/45 = 17/9
What is the place value of 9 in the number 3,544,021.3927
9 hundredths
right angle
90 degree angle or quarter of a circle
What is 0.98 as a percentage?
98%
ratio
A comparison of two quantities by division 5:10
vertical angles
A pair of opposite congruent angles formed by intersecting lines (opposite)
Trapezoid
A quadrilateral with exactly one pair of parallel sides
cylinder
A solid shape with one curved surface and two congruent circular bases.
what saying to use for conversion of the metric system
King Henry died by drinking chocolate milk
Rectangle Area
L x W
Yards is a measurement unit for what?
Length (USA)
How to find the area?
Length * Width = area ft^2 (keep measurements in feet)
In 3 dimensional objects, what measurements are taken?
Length, Width & Height
1-dimensional geometry, set of all points that fall along a straight path in both directions without end
Line
The collection of points that line between two specific endpoints
Line Segment
The basic unit for volume is __________.
Liter.
What is the metric unit for volume?
Liters
How to turn an improper fraction into a mixed number
Long Division Top number on the division is the mixed number, bottom number is the numerator and side left number is the demonator
______________ is how much of something you have, or the amount of matter
Mass
If all other statistical procedures fail, the best predictor of a score will be the
Mean
This is used to find out what score is most likely to happen
Mean
What are the three main measured of Central Tendency
Mean, Median & Mode
Set of descriptive treasures which indicate the typical score
Measures of Central Tendency
Are useful for understanding what the Central part of the data looks like
Median
Median
Middle number
How is length measured?
Miles, feet, inches, centimeters
For distances much shorter than a meter, we would use either centimeter or ?
Millimeter
What is least likely to be reported due to it being the one most likely to change by the introduction of additional scores?
Mode
How to Covert a Percentage into a decimal?
Move the decimal point two places to the left
How to Covert decimal into a Percentage?
Move the decimal two places to the right
62.18 * .06
Multiply 6218 * 6 = 37308 (Then do the trick to count the number of decimal places to the right of the decimals in total) Final Answer = 3.7308
How to covert yards into feet?
Multiply by 3
To covert quarts to gallons
Multiply by 4; multiply quarts by 4
How do you multiply fractions?
Multiply the tops and then multiply the bottoms 2/3 * 17/3 = 34/9 (2 * 17) (3* 3)
What do you do first to multiply decimals? 1.25 * 3.5
Multiply the two numbers while ignoring the decimal So multiply 125 * 35 = 4375 Time for the trick! ... Count the number of decimal places we have in total. We have a total of 3 all together behind the decimal. There should be there numbers to the right of the decimal in the final answer. The final answer is: 4.375
adjacent angles
Neighboring Angles Next to each other (do not need to to add up to a specific angle)
Trapezoid Perimeter
Not a formula, just add up the four sides
Anything that centi- is ____ __________ the size of that base unit.
One-hundredth (0..01)
The following data represents the test scores of 8 students.The student who got a 45% is a 92, 91, 89, 95, 45, 88, 90, 91
Outliner
Triangle Perimeter
P= S₁+S₂+S₃ (just add up all the sides)
What is the rule for order of operatons?
PEMDAS
What does PEMDAS stand for?
Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction - Please excuse my dear Aunt Sally
What would you need to calcuate for the amount of fencing for yards?
Perimeter
A place in space that has no length or dimension.
Point
Are Two-dimentional shapes made up of line segments
Polygons
USA unit for mass
Pound-mass
US Measurement Units
Pounds, inches, gallons
Mass is measured in
Pounds, kilograms
Variable ´r´ in geometry
Radius
All fractions are
Rational numbers - can be proper or improper
Has a starting point and then continues into infinity in one direction
Ray
If there are two modes, you should?
Report both
A section or part of the population and would be anywhere from 1% to 99%
Sample
A special table for listing times and events
Schedules
Variable ´S´ in geometry
Side
____________ have very high densities because their particles are super-close to each other.
Solids
Variable
Symbol for something we don´t know
Surface Area
The areas of each of the shapes comparing the three-dimensional shapes
Radius
The distance from a circles exact center to its edge
36.12/4
The number we are dividing by is already a whole number so we don´t need to covert it or move any decimal points. Go ahead and do the long division Answer 9.03 Don´t forget to line up decimal points
Place Value
The value of a digit based on its position within a number
Minutes is a measurement unit for what?
Time
Examples of 2-dimenational shapes
Triangles, rectangles, polygons, and circles
supplementary angles
Two angles whose sum is 180 degrees (together add up to 180)
complementary angles
Two angles whose sum is 90 degrees (they add up together) - ex- 50 + 40 = 90
How to measure volume?
USA - Gallons The rest of the world - Liters
Smaller measurements for length
USA - Inches, Feet, Yards Rest of the World - Centimeters, millimeters, meters
Length for long distance
USA - Miles Rest of the world - Kilometers
Small units of volume measurements
USA - Ounces The rest of the world - Mililiters
70 miles every 2 hours
Use division to find the speed: 35 mi/hr
Square Pyramid Volume
V= 1/3 s²H
____________ is the measure of how much space it takes up.
Volume
How to covert from a Fraction into a decimal?
We just divide!
How to covert a percentage into a decimal?
We just move the decimal point!
_____________ is the force of gravity on an object
Weight
What situation is best for using an approximation to find out the area of an irregular shape?
When the shape cannot be broken down into basic shapes
A meter is a little longer than a ____________.
Yard
What to do? 3 ft + 36 inches
You can covert feet into inches or inches into feet 36/12 = 3 ft = 3ft + 3 ft = 6ft
Transveral
a line that intersects two or more lines
proportion
a pair of ratios that are equal to each other ex: a/b=c/d or a/b=a:b=c:d
Cartesian Coordinate System
a system in which the location of a point is given by coordinates that represent its distances from perpendicular lines that intersect at a point called the origin
Kelvin scale
a temperature scale that begins at absolute zero
linear your rates are change by determined by what repeatedly
adding
Straight Angle
an angle that measures 180 degrees - flat line
an exponential rate of change is represented by
an equation involving an exponent
a linear rate of change is represented by
an equation that only involves multiplication or addition
Is a place where two lines intersect
angle
Rational Numbers
any number that can be written as a fraction or integers
Mass and weight
are two different quantities
The amount of space inside a space
area
Is the amount of space on the INSIDE of a 2 dimensional shape
area (given in square units)
-meter
at the end of a word, means measurement
Mean
average (add up the numbers, divide by the number of numbers
What happens if there are two Central numbers for a median
average the two
Pythagorean Theorem
a²+b²=c²
Mass is measured using a _______________.
balance
Variable ´b´ in geometry
base
Two-dimentional areas come into use as surface area or the area of the
base of the solid
Triangle Area
bh/2 -----bottom x height/2
what is regrouping another name for addition and subtraction
carrying and borrowing
another word for regrouping
carrying or borrowing
Covert
change
Squares and Triangles are considered polygons, while ____________ is not
circles
Variable ´C´ in geometry
circumference
what is a concise phrase that sums up the definition of estimate
close enough
estimation is about getting
close enough answer
Parallel Lines have
congruent slopes
Parallel Lines
coplanar lines that do not intersect
When dividing measurments,
covert numbers to the same unit
One millimeter is the exact same size as a
cubic centimeter
Volume is measured in
cubic units
When converting decimals into fractions, take out the --------
decimal point and count the decimal places
the right of the decimal...
decreases in powers of 10
What is the metric unit for temperature?
degrees Celsius
Distance across a circle
diameter
when multiplying fraction equations
divide from each side which is the inverse operation
what to do when your variable is negative. ex -x=34
divide negative x by each side negative divided by negative cancels out and becomes positive are for the variable is positive
One dimentional distance can be measured along the
edges
estimating prior to working out an exact calculation helps to
ensure that the mistakes are caught
process by which an answer that is close to but not exactly the correct answer
estimation
regrouping
the process of making groups of tens when adding or subtracting two digit numbers or more and is another name for carrying and borrowing
common difference is also known as
the rate of change
Remember that to simplify, you need to be able to divide both numbers by?
the same number (ex: 11/12 * 4/3) 12 and 4 both can be divided by four, simplify and then multiply)
The second place to the left of the decimal is?
the tens place AKA 10 to the power of 1
A circles diameter is equal to
twice it's radius or 2r
estimation sign
two curved lines
Being reciprocals means that one slope will be the
upside down or flipped version of the other
what is the first step in solving word problems
visualize the problem
The amount of space inside of a solid
volume
The measure of 3-dimensional space is called
volume
Ounces can be measured for
weight and volume
when do you need to regroup
when the bottom number is bigger than the top number
horizontal axis
x-axis
vertical axis
y-axis
How many yards are in 15 ft?
yards =
What is the formula to convert feet (ft) to yards (yd)?
yd= ft * 3
How many diminsions does a point have
zero
Cone Surface Area
πr(r+Square Root of r^2 + h^2
Circles Area
πr²
Cylinder Volume
πr²h
Anything that has the prefix milli- is ______________ the size of it's base unit.
1,000th (.001 meters)
How to divide mixed numbers?
1. ) Convert to improper fractions 2.) Flip the second Fraction 3.) Multiply the fractions 4.) Simpfily as needed
Covert Fraction into a Percentage process
1. Perform the division 2.) Multiply by 100
steps of a word problem
1. visualize the problem - highlight the important parts find out what the problem is asking. 2. write the equation - what is x what is the whole what is the part are you looking for the part or the whole. 3. solve the equations
How to Covert from a Decimal into a Fraction?
1.) Count the decimal places 2.) Multiply accordingly
Steps of Multiplying Mixed Numbers
1.) Covert to improper fractions 2.) mUltiple top 3.) multiple bottom 4.) Simplify
How to divide fractions?
1.) Flip the second Fraction 2.) Multiply the fractions 3.) Simplfiy as needed
Operation of Operation Steps
1.) Simplify all the parenthses including grouping symbols, such as brackets and braces, in addition to parenthses 2.) Simplify all multiple and division from left to right 3.) Simplify all addition and subtraction from left to right.
Cone Volume
1/3πr²h
Covert Fraction into a Percentage: 1/4
1/4= 0.25 * 100 = 25%
Convert Fraction into a Percentage: 1/5
1/5 = 0.25 * 100 = 20%
Decka
10
What is 5 divided into 0.5
10
the easiest way to estimate is to round to the nearest multiple of
10
Subtracting - 10 ft - 120 inches
10 * 12 = 120 inches
convert 10 kg into grams
10,000g
what is 10.5 km converted into meters
10,500 m
Hecto
100
There are _________centimeters in a meter
100 (easy to remember as there are 100 cents in a dollar)
What is the boiling point of water in degrees celsius?
100 degrees Celsius
Kilo
1000
A kilometer is equivalent to exactly ______________- meters
1000 meters
Another that has the word kilo in it is equal to?
1000 units
There are ___________ millimeters in a meter.
1000th (0.001)
convert 10000 m into kilometers
10km
common difference
never changes in a linear function
The slopes of perpendicular Lines are
opposite reciprocals of each other
The order that we use to simplify expressions in Math is called
order of operations
Can be given a position such as x, y
ordered pair
When you plug an ____________ into the mean, it will skew your results
outlier
A point of data that is distant from the others, either extremely high or extremely low (way off to the side)
outlier (will skew your results)
Percentage
per 100
The distance AROUND a shape
perimeter
With 2 dimentional, you can measure ...
perimeter
Coplanar
points that lie on the same plane
The complete collection to be studied
population
Weight is the
pound force
What is an example of a 3-dimensional solid
pyramid
Distance halfway across a circle
radius
if there is more on the floor go next door
regrouping
Slope =
rise/run
an easy and efficient method to use when estimating is what
rounding to the nearest multiple of 10
Square Pyramid Surface Area
s(s+2l)
The whole world tells the time.... the same
seconds, minutes and hours
guitar players outnumber drummers 13 to 3. which is your typical garage Rock loving town there are 12 drummers. how many guitar players are there.
set this up as 13:3 equals g:12, cross multiply 3g equals 12 * 13. answer: 52
intercepts method
set x to 0 to get a point. Then setting y to 0. Get a total of two points. Plot the two points and draw a line through it.
use estimation to find an estimate of the correct answer to 515 + 100 + 13 + 280 + 425
since the rounding went down more than up it is assumed that the accurate result will be slightly higher than this. The closest answer in the right direction is 1333. when added up accurately the sum is 1333.
little Timmy is up late watching the weather he knows that have 12 in of snow falls overnight School be canceled if the snow is falling at a rate of 2 inches per hour how many hours will it take for 12 in the fall
so the rate of snow 2 hours is 2:1. 2:1=12:h. cross multiply and you will find at 6 hours for school to get canceled
Area is always measured in
square units
a linear rate of change has a graph that is
straight
180
straight line
Linear
straight line
Data organised in rows and columns
tables
how to set up the conversion
the basic ingredients what you're starting with * the smoothie what you want to end up with equals the blender what you need to get there
The third place to the left of the decimal is?
the hundreds place AKA 10 to the power of 2
The second place to the right of the decimal is
the hundredths place or 10 to the power of - 2
The first place to the left of the decimal is?
the ones place AKA 10 to the power of zero
$12.50/2
$6.25
How much money is the 7 worth $57,689.10
$7,000
If four of your friends each give you $20.75, how much will you have total?
$83.00
0 Kelvin is equal to?
-273 Celsius
What is the freezing point of water for degrees celsius?
0
Using the intercepts method, what are the two points to plot when graphing the line x + 3y = 6
0, 2 6, 0
milli
0.001
centi
0.01
Deci
0.1
What is 54% as a decimal?
0.54
3 quarts = ? gallons
0.75
What is the density of a solid that has a Mass of 9.2 grams and a volume of 12.3cm^3? Would this object float or sink?
0.75 g/cm^3
Covert Decimal into a Percentage: 0.87
0.87 = 87% (Multiply by 100)
What is 7/8 as a decimal?
0.875
1/2 + 1/2
1
a student makes a table for an equation and determines that the common difference is 1/3 what is the rate of change
1 / 3
Density of Water =
1 g/mL
Base Unit of Length
1 meter
Area of a triangle
A= 1/2 bh
Area for a square
A= s^2
Trapezoid Area
A=h(b1+b2)/2
Area of a circle
A=πr²
For the answer of area>>>
Always in square feet ft^2
obtuse angle
An angle that measures more than 90 degrees but less than 180 degrees
Can can attach the prefix kilo - to ?
Anything. kilosecond, kilotree. (1000 units)
What would you need to find out in order to paint or carpet your bedroom?
Area
What do you do when you need to add or subtract fractions?
Find the common demonator and then add or subtract
Perimeter of a Circle
C=dπ
AKA Circle Perimeter
Circumfrance
Find the area: 7ft 6 in (width) * 10 ft (length)
Convert width into a decimal. 6/12 =0.5 7.5ft * 10ft = 75 ft2
Perpendicular Lines
Coplanar Lines that interset and form a 90-degree angle
What do you do first when dividing decimals?
Covert it to a whole number
What do you do to add two measurement units that are different?
Covert them into the same units
Angle
Curved measurement on degrees
A common unit which is a combination of two units, Mass and volume
Density
______________ is how tightly packed the particles of an object are.
Density
How to calcuate density?
Density=mass/volume
To covert inches includes to feet?
Divide by 12
How to covert feet to yards?
Divide by 3
To covert gallons to quarts
Divide by 4; divide gallons by 4
How would you convert gallons into quarts?
Divide the number of gallons by 4
How to find the area of Irregular shapes?
Divide the shape into smaller shapes
Things weigh more on Earth than the moon because?
Earth has more weight than things on the moon, even though both have the same mass.
7.24/0.2
First change to 2/72.4 Move over decimal to make the outside number a whole number (the second number) Then move over the decimal in the box (first number) to the right as many times as the decimal was moved in the outside number. Decimal needs to line up in the physical problem Final Answer: 36.2
12 inches to every?
Foot
on a Cartesian graph, when trying to calcuate the intercepts, what should you do first?
For graphing a line, use a table method, and the intercepts method. Calcuate three points, and set x valves to find the you value. Use --negative one, 0, and one.
What is the US Measurement for Volume?
Gallons
_______________ have very low densities because their particles are very spread apart.
Gases
Perpendicular Lines
Have opposite reciprocal slopes
congruent
Having the same size and shape
To remember quarts, remember?
How many quarters are in a dollar, 4. Just like the number of quarts in a gallon
When would you use the Pythagorean Theorem?
If you know two of the lenghts of a right triangle, you can find the distance of the third using this theorem.
the conversion of metric system
KHDBDCM
How do you divide fractions?
Keep, Change, Flip! Then multiply fractions! (flip the second Rational number) then multiply across (make sure the number is simplified!)
What is the metric unit for Mass
Kilogram
Metric Measurement Units
Kilograms, centimeters, liters
two-dimensional
flat, like a piece of paper (no height)
Weight is a
force
regarding conversion of metrics, always remember the units of the ingredients must always be on the opposite side of the what in order to cancel out
fraction bar
How many feet is 10 inches?
ft = 12 /10
The study of shapes, the space that they inhabitant, and the rules that they govern the relationships between them
geometry
The basic unit for Mass is the ________________.
gram
an exponential rate of change has a
has a graph that is curved
Variable ´h´ in geometry
height
Covert 4 feet to inches
inches = 4 * 12 =
How to find increase/decrease percentage?
increase/decrease/first total (beginning or starting number) x 100
The left of the decimal...
increases in powers of three
exponential rate of change
increases or decreases more and more quickly
linear rate of change
increases or decreases very steadily
The first place to the right of the decimal
is the tenths place or 10 to the power of --negative one
The third place to the right of the decimal
is the thousandths place or 10 to the power of - 3
how is estimating helpful when solving math problems in an academic setting
it helps with checking your work by confirming your answer is in the right area
A ________________- is the metric version of our mile
kilometer
Area= (rectangle)
l * w
Does the millions place fall to the right or the left of the decimal? How many places does it fall?
left seven
Acute Angle
less than 90 degrees
Things that are __________ dense float on thing that are ___________ dense.
less/more
Prism Volume
lwh
____________ is the basic unit of length
meter
What is the arrangement from smallest unit to largest unit? cm, m, mm, km
mm, cm, m, km
______________ likely has the weakest link to population due to its sampling bias
mode
Mode
most frequently occurring score
Remember: In order of operations, ________________ does not always come before division. They are worked in the order they appear. Same with _____________- and addition
multiplication/subtraction
You can ______________ measurements of different units
multiply
You can _________________ measurements of different units
multipy (1 m * 1 lb = 1 m lb)
why estimation is a good idea
needing an approximate answer in a hurry and wanting to have an idea of the accurate answer before the calculation is completed
Being opposite means that one slope will be positive and the other will be
negative
