even + even = - ANSWER even
even - even = - ANSWER even
even + odd = - ANSWER odd
even - odd = - ANSWER odd
odd + odd = - ANSWER even
odd - odd = - ANSWER even
odd × odd = - ANSWER odd
even × odd = - ANSWER even
even × even = - ANSWER even
least common multiple - ANSWER the least positive integer that is a multiple of both a
and b. For example, the least common multiple of 30 and 75 is 150. This is because the
positive multiples of 30 are 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, etc., and the
positive multiples of 75 are 75, 150, 225, 300, 375, 450, etc. Thus, the common positive
multiples of 30 and 75 are 150, 300, 450, etc., and the least of these is 150.
1
,greatest common divisor (or greatest common factor) - ANSWER the greatest positive
integer that is a divisor of both a and b. For example, the greatest common divisor of 30 and
75 is 15. This is because the positive divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, and the
positive divisors of 75 are 1, 3, 5, 15, 25, and 75. Thus, the common positive divisors of 30
and 75 are 1, 3, 5, and 15, and the greatest of these is 15.
prime number - ANSWER an integer greater than 1 that has only two positive divisors: 1
and itself
first ten prime numbers - ANSWER 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29
prime factorization - ANSWER Every integer greater than 1 either is a prime number or
can be uniquely expressed as a product of factors that are prime numbers, or prime divisors
composite number - ANSWER An integer greater than 1 that is not a prime number
The first ten composite numbers - ANSWER 4, 6, 8, 9, 10, 12, 14, 15, 16, and 18
add two fractions with the same denominator - ANSWER add the numerators and keep
the same denominator. For example, - + = -8 + = -
add two fractions with different denominators - ANSWER To add two fractions with
different denominators, first find a common denominator, which is a common multiple of
the two denominators. Then convert both fractions to equivalent fractions with the same
denominator. Finally, add the numerators and keep the common denominator. So: 1/3 + -2/5
= 5/15 + -6/15 = -1/15
To multiply two fractions - ANSWER multiply the two numerators and multiply the two
denominators. So: (10/7) (-1/3) = (10)(-1) / (7)(3) = -10/21
2
, To divide one fraction by another - ANSWER first invert the second fraction—that is, find
its reciprocal—then multiply the first fraction by the inverted fraction. So (3/10)/(7/13) =
(3/10)(13/7) = 39/70
negative number raised to even power = - ANSWER positive
negative number raised to odd power = - ANSWER negative
√a√b - ANSWER √ab
(√a)^2 - ANSWER a
√a^2 - ANSWER a
√a/√b - ANSWER √ab
interval - ANSWER The set of all real numbers that are between, say, 5 and 8 is called an
interval, and the double inequality is often used to represent that interval: 5 < x < 8
ratio - ANSWER The ratio of one quantity to another is a way to express their relative
sizes, often in the form of a fraction, where the first quantity is the numerator and the
second quantity is the denominator. Thus, if s and t are positive quantities, then the ratio of
s to t can be written as the fraction .st The notation "s to t" or "s : t" is also used to express
this ratio. For example, if there are 2 apples and 3 oranges in a basket, we can say that the
ratio of the number of apples to the number of oranges is 2/3 or that it is 2 to 3 or that it is
2:3.
Ratio Box - ANSWER X item Y item Total
Ratio
Multiply by
3
even - even = - ANSWER even
even + odd = - ANSWER odd
even - odd = - ANSWER odd
odd + odd = - ANSWER even
odd - odd = - ANSWER even
odd × odd = - ANSWER odd
even × odd = - ANSWER even
even × even = - ANSWER even
least common multiple - ANSWER the least positive integer that is a multiple of both a
and b. For example, the least common multiple of 30 and 75 is 150. This is because the
positive multiples of 30 are 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, etc., and the
positive multiples of 75 are 75, 150, 225, 300, 375, 450, etc. Thus, the common positive
multiples of 30 and 75 are 150, 300, 450, etc., and the least of these is 150.
1
,greatest common divisor (or greatest common factor) - ANSWER the greatest positive
integer that is a divisor of both a and b. For example, the greatest common divisor of 30 and
75 is 15. This is because the positive divisors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30, and the
positive divisors of 75 are 1, 3, 5, 15, 25, and 75. Thus, the common positive divisors of 30
and 75 are 1, 3, 5, and 15, and the greatest of these is 15.
prime number - ANSWER an integer greater than 1 that has only two positive divisors: 1
and itself
first ten prime numbers - ANSWER 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29
prime factorization - ANSWER Every integer greater than 1 either is a prime number or
can be uniquely expressed as a product of factors that are prime numbers, or prime divisors
composite number - ANSWER An integer greater than 1 that is not a prime number
The first ten composite numbers - ANSWER 4, 6, 8, 9, 10, 12, 14, 15, 16, and 18
add two fractions with the same denominator - ANSWER add the numerators and keep
the same denominator. For example, - + = -8 + = -
add two fractions with different denominators - ANSWER To add two fractions with
different denominators, first find a common denominator, which is a common multiple of
the two denominators. Then convert both fractions to equivalent fractions with the same
denominator. Finally, add the numerators and keep the common denominator. So: 1/3 + -2/5
= 5/15 + -6/15 = -1/15
To multiply two fractions - ANSWER multiply the two numerators and multiply the two
denominators. So: (10/7) (-1/3) = (10)(-1) / (7)(3) = -10/21
2
, To divide one fraction by another - ANSWER first invert the second fraction—that is, find
its reciprocal—then multiply the first fraction by the inverted fraction. So (3/10)/(7/13) =
(3/10)(13/7) = 39/70
negative number raised to even power = - ANSWER positive
negative number raised to odd power = - ANSWER negative
√a√b - ANSWER √ab
(√a)^2 - ANSWER a
√a^2 - ANSWER a
√a/√b - ANSWER √ab
interval - ANSWER The set of all real numbers that are between, say, 5 and 8 is called an
interval, and the double inequality is often used to represent that interval: 5 < x < 8
ratio - ANSWER The ratio of one quantity to another is a way to express their relative
sizes, often in the form of a fraction, where the first quantity is the numerator and the
second quantity is the denominator. Thus, if s and t are positive quantities, then the ratio of
s to t can be written as the fraction .st The notation "s to t" or "s : t" is also used to express
this ratio. For example, if there are 2 apples and 3 oranges in a basket, we can say that the
ratio of the number of apples to the number of oranges is 2/3 or that it is 2 to 3 or that it is
2:3.
Ratio Box - ANSWER X item Y item Total
Ratio
Multiply by
3
