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