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Math
Math Foundations
ASVAB Arithmetic Reasoning
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ASVAB Arithmetic Reasoning Flashcards
Terms in this set (41)
Integers
whole numbers, including 0 and negative whole numbers
fractions
a fraction is a number that is written in the form A/B where A is the numerator and B is the denominator
Improper fraction
a number that is greater than 1 or less than 1 that is written in the form of a fraction.
Prime numbers
an integer greater than 1 that has no factors other than 1 and itself
factor
a positive integer that divides evenly into a given number with no remainder
multiple
a number that a given number will divide into with no remainder
prime factorization
keep breaking it down until you are left with only prime numbers
ex] 168=2x2x2x3x7
greatest common factor
(GCF) break down both integers into their prime factorizations and multiply all prime factors they have in common
common multiple
multiply them together
least common multiple
(LCM) multiple all of the prime factors of each integer as many times as they appear
Order of Operations
Please Excuse My Dear Aunt Sally
Parentheses, Excuse, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)
Reduce fractions
cancel all factors that the numerator and denominator have in common
to add fractions:
get a common denominator and then add the numerators
to subtract fractions:
get a common denominator and then subtract the numerators
to multiply fractions:
multiply the numerators and multiply the denominators
to divide fractions:
invert the second fraction and multiple
to 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.
to convert a fraction to a decimal:
divide the denominator into the numerator
to 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
scientific notation
the exponent of a power of 10 indicates how many zeros the number would contain if it were written out
ex] 5x10^4 means 5 with 4 zeros or 50000
to add terms with exponents:
as long as exponent is the same, you can add the coefficients
ex] 2^x+2^x=2x^2
to subtract terms with exponents:
as long as the exponents are the same, you can subtract the coefficients
to multiply terms with exponents:
multiply the coefficients and add the exponents
ex] 2a^5
3a^4 = (2
3)^(5=4) = 6^9
to divide terms with exponents:
divide the coefficients and subtract the exponents
to raise a power to an exponent:
multiply the exponents
ex) (x^2)^4 = x^(2*4) = x^8
to add or subtract radicals:
make sure the numbers under the radicals are the same. If they are, you can add or subtract the coefficients outside the radical signs
to simply radicals:
factor out the perfect square under the radical, unsquare them and put the result in front of the radical
to multiply or divide radicals:
multiple or divide the coefficients outside the radical. Multiply or divide the numbers inside the radicals
to take the square root of a fraction:
break the fraction into two separate roots and take a square root of the numerator and the denominator
factorial
7!= 1x2x3x4x5x6x7
proportion
a type of ratio that shows the comparative relation between parts, things or elements with respect to size, amount or degree
rate
a ratio that compares distance over time, or amount over time, or cost over units
average
average= (sum of the terms)/(number of terms)
probability
the likelihood that a desired outcome will occur
probability = (number of favorable outcomes)/(number of possible outcomes)
to find the probability that two events will occur:
multiply the probability of the first event by the probability of the second event
ex) if the probability of selecting a green marble is 50% and the probability of selecting a red marble is 30% what is the probability of selecting a green and red marble?
50% times 30% is equal to 15%
+
sum, plus, more than, added to, combined, total

minus, less than, difference between, decreased by
=
is, was, equals, is equivalent to, is the same as, adds up to
x
times, product, multiplied by, of, twice, double, triple
/
divide by, over, quotient, per, out of, into
ate
distance over time
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