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25 Cards in this Set

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which are even:
a. odd +/- odd
b. even +/- even
c. odd +/- even
d. odd x odd
e. even x even
f. even x odd
a, b, e, and f are even
c and d are odd
how do you find the least common multiple?
to find the least common multiple, check out the multiples of the larger number until you find one that's also a multiple of the smaller.

LCM of 12 and 15 is 60
how do you find the greatest common factor
the find the greatest common factor, break down both numbers into their prime factorization and take all the prime factors they have in common.

the GCM of 36 and 48 is 12
how do you find the prime factorization of an integer?
to find the prime factorization of an integer, just keep breaking it up into factors until all factors are prime.

72 - 3 x 3 x 2 x 2 x 2
how can you determine if an integer is divisible by 3?
an integer is divisible by 3 if the sum of its digits is divisible by 3. An integer is divisible by 9 if the sum of its digits is divisible by 9.
how do you determine if an integer is divisible by 2?
an integer is divisible by 2 if the last digit is even, An integer is divisible by 4 if the last 2 digits makes a multiple of 4.
how do you determine if an integer is divisible by 5?
An integer is divisible by 4 if the last digit is a 5 or 0. An integer is divisible by 10 if the last digit is 0.
cross multiply: x/y = a/b
bx = ya
how do you add or subtract fractions?
to add or subtract fractions, first find a common denominator, then add or subtract the numerators
how do you multiply fractions?
to multiply fractions, multiply the numerators and multiply the denominators
how do you divide fractions?
to divide fractions, invert the second one and multiply
how do you compare fractions?
one way to compare fractions is to re-express them with a common denominator. Another way to compare fractions is to convert them both to decimals
how do you compare decimal fractions?
the simplest way to compare decimal fractions is to add zeros after the last digit to the right of the decimal point in each decimal fraction until all the decimal fractions you're comparing have the same number of digits
how do you convert decimals into fractions?
to convert a decimal to a fraction, set the decimal over 1 and multiply the numerator and denominator by 10 raised to the number of digits to the right of the decimal point. Then simplify the fraction.
how do you express a % as a fraction in lowest terms?
a percent is a fraction with an implied denominator of 100. set % over 100 and simplify
express 1/10, 1/5, 1/4, 1/3, 2/3, and 1/8 as percentages
1/10 = .10 = 10%
1/5 = .2 = 20%
1/4 = .25 = 25%
1/3 = .333 = 33 1/3%
2/3 = .666 = 66 2/3%
1/8 = .125 = 12 1/2%
how do you find an average?
to find the average of a set of numbers, add them up and divide by the number of numbers
how do you use the average to find the sum?

example: the average of 10 numbers is 50. What is the sum of the 10 numbers?
sum = average x number of terms

if the average of 10 numbers is 50, then they add up to 10 x 50, or 500
how do you use the average to find the missing number?

example: the average of 4 numbers is 7. If 3 of the numbers are 3, 5, and 8, what is the fourth number?
to find a missing number when you're given the average, use the sum.

if the average of 4 numbers is 7, then the sum of those 4 numbers is 4 x 7 or 28. Three of the numbers (3, 5, & 8) add up to 16 of that 28, which leaves 12 for the fourth number
how do you determine the average of consecutive numbers?

example: what is the average of all the integers from 13 through 77 inclusive
to find the average of evenly spaced numbers, just average the smallest and largest.

the average of all the intefers from 13 through 77 is 13 + 77 / 2 = 90/2 = 45
how do you find the median of a group of numbers?
the median is the middle value in a group of numbers. If there's an even number of values, the median is halfway between the two middle values.
median of 12, 15, 23, 40, and 40 is 23 b/c its the middle value.
median of 12, 15, 23, and 40 is 19 b/c its halfway b/w the two middle values of 15 and 23
how do you determine the mode of a group of numbers?
the mode is the number that appears the most often. If two numbers appear equally often, they are both the modes.

the mode of 12, 15, 23, 40, and 40 is 40 b/c it appears more often.
how do you use a ratio to find a number?

example: in a group of 18 people, the ratio of men to women is 1:2. How many women are there?
if the parts add up to the whole, a part-to-part ratio can be turned into 2 part-to-whole ratios by putting each number in the original ratio over the sum of the numbers.
if the ratio of men to women is 1 to 2, then the men-to-people ratio is 1/ 1+ 2 = 1/3. And the women-to-peeps ratio is 2/1+2 = 2/3. 2/3 of the 18 are women, or 12.
what is the distance, rate, time equation in terms of distance?
distance = rate x time.
what is the average rate equation?
Average A per B = total A / total B
Average speed = total distance/total time