ASVAB: Arithmetic Reasoning

convert a fraction ro decimal

8/25= 8 divided by 25= 0.32

consecutive numbers

any series of numbers listed in the order they appear on the number line; Ex: consecutive integers= 3, 4, 5, 6 consecutive even integers= 2, 4, 6, 8 consecutive multiples of -9= -9, -18, -27

percents

ratios of an amount to 100. Increase or decrease a # by a given percent: to increase 25 by 60%, 1st gif 60% of 25. 25 X 0.6= 15 (then add to the original) 25 + 15= 40 to decrease 25 by the same % subtract the 15 25 - 15= 10

rate

ratio that compares 2 things, related quantities. R= distance/time, R=amount/time, R= cost/units

absolute value

the distance a number is from zero on a number line. Ex: |-3|=3, |x-2|+3= 7 -3 -3 |x-2|= 4 x-2= 4 x=6

greatest common factor (GCF)

the largest factor that two or more numbers have in common

least common multiple (LCM)

the least number that is a common multiple of two or more numbers

mode

# that appears most often

associative property

(a+b)+c=a+(b+c)

percent change

100% X new value - original value/ original value percent change increase= positive percent change decrease= negative Ex: investment that decreased 20%, then that increased by 50%, percent change? 100-20= 80 80+40= 120 (40 is 50% of 80) 20% increase

perfect square

1^2= 1 6^2= 36 11^2= 121 2^2= 4 7^2= 49 12^2= 144 3^2= 9 8^2= 64 4^2= 16 9^2= 81 5^2= 25 10^2= 100

divisibility rules

2: all even #'s 3: (+) up all digits of the #. If the total is divisible by 3 4: take the last 2 digits and divide by 2, if divisible 5: all #'s ending in 5 or 0 6: all even #'s that meet the #3 rule 8: divide the # by 2 twice if men then divisible 9: (+) up all the digits, if result = 9 then divisible

coefficient

6x^7 X 2x^5= (6X2) (x^7-5)= 12x^12

Fractions to Decimals

Divide the numerator by the denominator. 1/4 = 1 divided by 4 = 0.25

arithmetic sequence

Ex: 1, 3, 5, 7 (+2, +2, +2) What is the mean of this ________________ -3, 0, 3, 6, 9, 12, 15 ~in a _____________ the median=mean which is 6

the order of operations

PEMDAS (parenthesis, Exponents, Multiplication, Division, Addition, Subtraction)

factor

a number that is multiplied by another number to find a product; factors of 12= 1, 2, 3, 4, 6, 12

square root

a number that when multiplied by itself equals a given number

prime numbers

a number which can only be divided by itself and 1; 2, 3, 5, 7, 11, 59, 83

multiple

a product of a given whole number and any other whole number. Ex: multiples of 12= 0, 12, 24, 60

distributive property

a(b + c) = ab + ac

communitive property

a+b=b+a

ratios

are either part to part or part to whole. Ex: a class contains 12 males and 21 females. Part to part 12/27= 4/7, part to whole 12/ 12 +21= 12/33= 4/11 (:)

mean

average

prime factorization

breaking down a composite number until all of the factors are prime

adding fractions

change the fractions into the lowest common denominator and add the numerators

/

divided by, over, quotient, per, out of, into

proportion

equation of 2 ratios, show comparative relationship

subtracting fractions

find a common denominator then subtract the numerator

dividing fractions

invert (reciprocal) the second fraction and multiply

=

is, was, equals, is equivalent to, is the same as, added up to

median

middle value of a group of #'s Ex: # set= 1, 2 ,7, -3, 0, 5, 2 mean= -3 + 0 + 1 + 2 + 2 + 5 + 7/ 7= 14/7= 2 mode= 2 range= 7+ (-3)= 10 median= -3, 0, 1, 2, 2, 5, 7 =2 ~if 2 #'s are in the middle the average of the 2 #'s

-

minus, less than, difference, between, decreased by

compare fractions

multiple the numerator of the first fraction by the denominator of the second fraction to get a product. Then, multiply the numerator of the second fraction by the denominator of the first fraction to get a second product. If the first product is greater, the first fraction is greater. If the second product is greater, the second fraction is greater

multipling fractions

multiply straight across

combined work

of people or things can be added together to obtain a rate. Ex: Jose can paint a room in 3 hrs. Jill can in 2 hrs. How long if they work together. 1/3 + 1/2= 2/6 + 3/6= 5 rooms/ 6 hours. If it takes 6hrs to paint 5 rooms, it would take 6/5 hours to paint 1 room. 6/5= 5/5+ 1/5= 1 1/5= 1.2 hours Ex: 3 pipes that can fill a tank, 1 in 2 hours. 1 in 3 hours. 1 in 6 hours. If they work together how long? 1/2 + 1/3 + 1/6= 3/6 + 2/6 + 1/6= 6/6 tanks/hours = 1 hour

convert a decimal to a fraction

set the decimal over 1. Then move the decimal over as many places as it takes until it is immediately to the right of the units digit. Reduce

probability

shown as a (a/b), (.), or (%) probability= # of outcomes of interest/# of possible outcomes 9/12= 3/4 or 75% chance Ex: if you toss a coin 3 times and it lands on heads each time, what is the chance it will land on heads the next toss? 1/2= 50% Ex: drawing 2 cards out of a deck (52 cards) whats the chance of grabbing a king? the 1st card chance is 4/52, but the 2nd card: if the first card is not a king then the card has a 3/51 chance. If the 1st card was not a king then the card has a 4/51 chance

range

subtract the smallest # from biggest

averages

sum of all the terms/# of all terms Ex: average of 3, 4, 8? 3 + 4 + 8/ 3= 15/3 Ex: 6 people went fishing, average 7 fit each. How many fish total? 7= total/6 7 X 6= 42 fish Ex: Lola's final grade is based on the average of 4 tests, 90. Her first 3 test scores were 93, 80, and 90. Whats the 4th? 93 + 80 + 90 + t/4= 90, 90 X 4= 263 + t/4 360= 263 + t= 97 90 X 4= 360, 90 + 80 + 93= 263

+

sum, plus, more than, assed to, combined, total

X

times, product, multiplied by, of

integers

whole numbers and their opposites; -900, -3, 0, 1, 54

exponents

x^2 + x^3= can't be combined a^2 + b^2= can't be combined when you multiply just (+) exponents (if same base) Ex: 2^3 X 2^2= 2^5 (x^2)^4= x x^2X4= x^8