Math Formulas

giga

G - multiplication factor of 1,000,000,000

mega

M - multiplication factor of 1,000,000

Bridget can clean an entire house in 12 hrs while her brother takes 8 hrs. how long would it take for B and T to clean 2 houses together?

b = 1/12 t = 1/8 1/12 + 1/8 = 5/24 h = (5/24)t 2 = (5/24)t t = 48/5 = 9 3/5 hours

a store owner bought a case of 48 backpacks for $476.00. he sold 17 for $18 each, the rest for $15. what was the salesman profits?

backpacks = 48 cost = 476 backpacks sold for $18 = 17 x 18 = backpacks sold for $15 = 48 - 17 = 31 31 x 15 = total profit = income - cost x = 306 + 465 - 476

centi

c - .01

percent change

calculate how much a given quantity changed instead of using the "part" use the "amount of change"

find the quotient when 40 is divided by .25

change .25 to 25 next change the divided to match the divisor by moving the decimal 2 spaces to the right - 4000 4000/25 = 160

find 0.8/0.2

change 0.2 to 2, then 0.8 to 8 and divide

deci

d - 0.1

deca

da - 10

Taylor is going to paint a square wall that is 3.5 m tall. how much paint will he need?

each side of the square wall is 3.5 m a = 3.5 x 3.5 = 12.25 m

there are 90 voters on a room, and each is either a democrat or a republican. the ratio of democrats to republicans is 5:$. how many republicans are there?

we know that there are 5 d for every 4 r in the room which means for every 9 people there are 4 republicans. fraction of demo: 5/9 fraction of rep:4/9 if 4/9 are republicans then, 4/9 x 90 = 40 voters republican

Jim spent 30% of his paycheck at the fair. he spend $15 for a hat, $30 for a shirt, $20 playing games. how much was his check?

whole = part/percent 15 + 30 + 20/.30 = $217.00 $65/.30 = $217.00

45 is 15% of what number

whole = part/percent 45/.15 = 300

a shoe store charges 40% mark up on the shoes it sells. how much did the store pay for a pair for shoes purchased by a customer for $63?

you're solving for the original price, but you don't know the amount of change. you need to create an expression for the amount of change - x = 63 - x /.4 .4x = 63 - x 1.4x = 63 x = 45 the store paid $45 for the shoes

one acre of wheat requires 500 gallons of water. how many acres can be waters with 2600 gallons?

1 acre/500 gallons = x acres/ 2600 gallons x = 26/5 = 5.2 acres

1 cm3

1 mL

is 65% greater than, less than, or equal to 13/20?

1. same format: 65/100 2. 13/20 multiplied each by 5, to get 100 as the denominator 65/100 3. EQUALS

1 mile

1.61 km

a recipe calls for 1/4 cup of sugar. if 8.5 beaches are needed, how many cups of sugar will be used?

1/4 x 8 1/2 8 X 2 /2 =16/2 + 1/2 = 17/2 17/2 x 1/4 = 17/8 cups of sugar

a train traveling 120 miles takes 3 hours to get to its destination. how long will it take for the train to travel 180 miles?

120 miles/ 3 hours = 180 miles/ x 120 miles x x hours = 3 hours x 180 miles x = 4.5

what is the median of 24, 27, 18, and 19

18, 19, 24, 27 take the two middle terms and divide by 2 19 + 24/2 = 21.5

what is the made of 2, 5, 4, 4, 3, 2, 8, 9, 2, 7, 2

2 - because it appears the most

1 oz

2.35 g

1 in

2.54 cm

Find the mean of 24, 27, and 18

24 + 27 + 18 / 3 = 23

what is the product of 0.25 X 1.4

25 X 14 = 350, there are 2 digits after the decimal in .25 and one digit after 1.4 - therefore the product should have 3 digits after the decimal - .350

1 gallon

3.785 L

if 35:5 :: 49:x, find x

35/5 = 49/x 35x = 49 x 5 x = 7

1 hour

3600 s

is 4 3/4 greater than , equal, or less than 18/4?

4 3/4 = 19/4 19/4 < 18/4

There are 42 people on the varsity football team. this is 8 moe than half the number of people on the swim team. There are 6 fewer boys on the swim team than girls. how many girls are on the swim team?

the quantity we want to solve is the number of girls on the swim team, so it will be x. number of boys on the swim team will be y. y=x-6 total number of boys + girls = x + y 42 is 8 more than half this number 42 = 8 + (x + x - 7)/2 34=(2x-6)/2 68 = 2x - 6 74 = 2x x = 37

1/10

.1

1/9

.11

1/8

.125

1/7

.142857

1/6

.166

1/5

.2

1/4

.25

1/3

.33

convert 0.45 into a fraction

.45 = 45/100 - the last number in the decimal is in the hundredths place so we can place it over 100 reduce 9/20

1 lb

.454 kg

1/2

.5

1 yd

.914 m

1 cal

4.19 J

1 F

5/9 (F-32)

percent change formula

= amount of change/original amount

original amount formula

= amount of change/percent change

amount of change formula

= original amount X percent change

Raw score

A raw score is an unaltered measurement. For example, let's say you took a test in class and scored 85. This is a raw score, an unaltered measurement of how you did. You scored 85. A raw data set is a collection of raw scores from all the tests.

square area & perimeter

A=a2 P=4a

triangle area & perimeter

A=hb/2 P=a+b+c

rectangle area & perimeter

A=wl P=2(l+w)

circle area & perimeter

A=πr2 C=2πr

stanine

Stanine (STAndard NINE) is a method of scaling test scores on a nine-point standard scale with a mean of five and a standard deviation of two. Some web sources attribute stanines to the U.S. Army Air Forces during World War II.

tera

T - multiplication factor of 1,000,000,000,000

grade equivalent

The grade equivalent represents the grade level and month of the typical (median) score for students. For example, a 5th-grade student who earns a 5.9 on a norm-referenced test has earned a score similar to the 50th percentile students in the test's norming group who were in their ninth month of fifth grade.

micro

U - .0000001

Alex takes 2 hours to shine 500 silver spoons, and Julian takes 3 hours to shine 450 silver spoons. how long will they take, working together, to shine 1000 spoons?

alex = 500 s/2 hrs = 250/1 julian=450s/3hrs=150s/1.5hr together=250+150/hr =400 spoons in an hr 1 hr/400 spoons X 1000 spoons = 1000/400 = 2.5 hours

a computer software retailer marks up its games by 40% above the wholesale price when it sells them to the customer. find the price of a game for a customer if the game cost the retailer $25.

amount of change = original amount X percent change 25 X .4 = 10 if the amount of change is 10, that means the store adds a mark up of $10, so the game costs $35.

Will drove from his home to the airport at an average speed of 30 mph. He then boarded a helicopter and flew to the hospital with an average speed of 60 mph. The entire distance was 150 miles, and the trip took 3 hours. Find the distance from the airport to the hospital?

create a table d r t d: d 30 t f: 150-d 60 3 - t first row: d = 30t second row: 150-d=60(3-t) 150 - 30t = 180 - 60t - 30 = - 30t 1 = t driving: 30t = 30 miles flying: 150 - d = 120 miles

David, Jess, Mark shoveled snow and made a total of $100. They agreed to split in based on how much each worked, David will take $10 more than Jesse, who will take $15 more than Mark. how much money is David getting.

d + j + m = 100 j = d - 10 m = j - 15 m = (d-10) - 15 = d -25 d + (d - 10) + ( d - 25) = 100 3d - 35 = 100 3d = 135 d = 45 $45

two cyclists start at the same time from opposite ends of a course that is 45 miles long. one cyclists is riding at 14 mph, and the second is 16 mph. how long after they begin will they meet?

d r t C #1 d 14 t C #2 45-d 16 t C #1: d =14t C #2: 45 - d = 16t 45 - 14t = 16t 45 =30t t = 1.5 hours

A bag contains 75 balls, if the probability that a ball selected from the bag will be red is 0.6, how many red balls are in the bags?

desired outcomes = probability x total possible outcomes desired outcome = 0.6 x 75 = 45, there are 45 red balls in the bag

a golf shop pays its wholesaler $40 for a club, and then sells it to a golfer for $75. what is the markup rate?

first calculate the amount of change 1. 75 - 40 = 35 now you can set up the equation to solve percent change = amount of change / original amount 35/40 = .875 or 87.5%

hecto

h - multiplication factor of 100

kilo

k - multiplication factor of 1,000

milli

m - .001

standard deviation of 62, 63, 61, and 66?

mean = (61+62+63+66)/4 = 63 next find the difference btw each number and square that number 63-62 = 1, 1 sq = 1 63-63= 0 63-61= 2, 2 sq = 4 63 -66 = 3, 3 sq = 9 find the mean of 4 + 1 + 9 + 0/4 = 3.5 then find the sq root of 3.5 = 1.87 SD = 1.87

nano

n - .0000000001

James wants to put in an 18 foot by 51 foot garden in his backyard. if he does, it will reduce the size of this yard by 24%. what will be the area of the remaining yard

need to find out what each number stands for .24% is the percent change multiply 18 by 51 to find the area of the garden = 918 ft= how much smaller the lawn is original amount= amount of change/percent change 918/24 = 3825 original lawn size 3825 - 918 = 2907 the remaining lawn is 2907

pico

p - .0000000000001

a farmer has purchased 100 m of fencing to put around his rectangular garden. if one side of the garden is 20 m long and the other is 28 m, how much fencing will the farmer have left over?

p = 2(20) = 2(28) + 96 m 100-96 = 4 m

A theater has 230 seats: 75 seats are in the orchestra, 100 in the mezzanine, 55 are in the balcony. if a ticket is selected at random, what is the probability that it will be for either mezzanine or balcony

p = do./tpo 100 + 55 / 230 = .67

Grant need to score a 75% on an exam. If the exam has 45 questions, at least how many does he need to answer correctly?

part = whole X percent 45 X.75 = 33.75, so at least 34 questions

Greta and Max sell cable subscriptions.. in a given month, Greta sells 45 and Max sells 51. if 240 are sold in 1 month, what percentages were not sold by Greta & Max.

percent = part/whole 1. 55 + 45/240 = 40% however the question asks how many subscriptions weren't sold but max and greta. 2. 100% - 40% = 60%

what percent of 65 is 39?

percent = part/whole 39/65 = .6 or 60%

percentile

percentile is a number where a certain percentage of scores fall below that percentile. You might know that you scored 67 out of 90 on a test. But that figure has no real meaning unless you know what percentile you fall into. If you know that your score is in the 90th percentile, that means you scored better than 90% of people who took the test.

A bag holds 3 blue marbles, 5 green, and 7 red. if you pick one marble from the bag, what is the probability it will be blue

probability = do/tpo 3/15 = 1/5 probability is 1/5 it'll be blue

percentages

ratio of a part to the whole equations: percent = part/whole part = whole x percent whole = part/percent

The mean of three numbers is 45. If two of the numbers are 38 and 43, what is the third number?

set up the equation for mean with x being the third variable 38 + 43 + x/3 = 45 38 + 43 + x = 135 x = 54

write 8/18 as a decimal

simplify the fraction: 4/9 the fraction is a multiple of 1/9 1/9 x 4 = .11 X 4 = .44

an item priced at $55 is marked up 25% off. what is the sale price?

solve for the amount of change first amount of change = original amount x percent change 1. 55 x .25 = 13.75 2. 55 - 13.75 = $41.25

what is the median of 24, 27 and 18

space the term in order, then pick the middle term 18, 24, 27 24

The sum of three consecutive numbers its 54. What is the middle number?

stat by building an equation one number will be x, so if x is the smallest number then the other two numbers must be (x+1) and (x-1) x + (x + 1) + ( x - 1) = 54 3x + 3 = 54 3x = 51 x=17 the middle equation is 17 + 1, so 18.

proportion

states that two ratios are equal, written in two fractions owned by an equal sign. units must be the same on the numerator and denominator - you will be given 3 variables in an equation and asked to find the fourth - you can solve by cross multiplying

Farmer Dan needs to water his cornfield. one hose can water a field 1.25 faster than a second hose. when both hoses are opened, they water the field in 5 hours. how long would it take to water the field if only the second hose is used.

the second hose completes the job in f hours, so it waters 1/f field per hour. the faster hose waters the filed in 1.25f so 1/1.25f hours. together they take 5 hrs so 1/5. 1/f + 1/1.25f = 1/5 1.25f (1/f + 1/1.25f) = 1.25f(1/5) 1.25 + 1 = .25f 2.25 = .25f f = 9 (1.25)(9) = 11.25 hours

thirty students are working on projects over 2 days. the first day, he gave them 3/5 hour to work. on the second day he gave them 1/2 as much time. how much time did each student have to work on each project?

time on first day = 3/5 hr = 36 minutes time on second day = 18 min 36 + 18 = 54

The probability of selecting a student whose name begins with the letter S from a school attendance log is 7%. if there are 42 students whose names begin with S enrolled at the school, how many students attend the school?

tpo = do/pro 42/.07 = 600 students

write 3/16 as a fraction

use long division .1875