Arithmetic Flashcards
integer
{…,-3,-2,-1,0,1,2,3,…}
A negative * a negative
a positive
A negative * a positive
a negative
Factorization
listing all of the possible combinations of integers that are multiplied to make a number
Factor or divisor
numbers in a factorization
multiple
25: 25, 50, 75, 100, 125, 150,…
_____ is a factor of every integer
1
_____ is a multiple of every integer
zero
Least common multiple
the least positive number that is a multiple of two numbers, a and b
Multiples of 30
30, 60, 90, 120, 150,…
Greatest common factor
the greatest positive number that is a divisor of two numbers, a and b
Factors of 30
1, 30, 2, 15, 3, 10, 5, 6
Quotient with remainder
when two integers are divided that are not factors of one another;
example: 19/7= 2 remainder 5
The sum (+) of two even integers is….
an even number
The sum (+) of two odd integers is…
an even number
The sum (+) of an even integer and an odd integer is…
an odd number
The product (x) of two even integers is…
an even number
The product (x) of two odd integers is…
an odd number
The product (x) of an even integer and an odd integer is…
an even number
Prime number
integer greater than 1 that only can be divided by 1 and itself;
ex: (3, 5, 7, etc)
____ is not a prime number
One
Prime factorization
list of only the prime-number factors for an integer;
examples: 12= (2)(2)(3)= (2^2)(3)
14= (2)(7)
81= (3)(3)(3)(3)= 3^4
Composite number
an integer greater than 1 that is not a prime number
In a\b, a is the…
numerator
In a/b, b is the….
denominator
Fractions are also called _______ numbers
rational
When adding or subtracting fractions, the _______ must be the same
denominators
example: (7/5) + (1/5) = 8/5
To add or subtract fractions with different denominators, find a ________
common denominator
When multiplying fractions, the _______ do not have to be the same
denominators
example: (1/5) * (2/3) = (2/15)
To divide fractions, ____ the second fraction, and then multiply
invert
example: (17/8) / (3/4) = (17/8)*(4/3)
An expression like 4 3/8 is called
mixed number
Convert to a fraction 4 3/8
(8*4)+3=35/8
If zero is the denominator of a fraction, it’s
undefined
Used to denote the repeated multiplication of a number by itself
exponent
a^0
1
a^(-1)
(1/a)
0^0
undefined
Cube root of 8
2 because 2^3=8
Decimals that do not terminate or repeat are considered…
irrational numbers
All rational numbers and irrational numbers are
real numbers
The distance between an integer and zero on the real number line is
absolute value
denoted: |3| = 3
|-2| = 2
|10.2| = 10.2
a(b + c) =
ab + ac
|a| * |b| =
|ab|
S/t or s:t represents
ratio
An equation relating two ratios
proportion
Examples: 9/12 = 3/4
Solve these problems by cross multiplication
x/49 = 3/21
cross multiply
21x= (3)(49)
x= 7
Meaning per hundred
percent
To compute a percent, divide the PART/WHOLE
example:
What percent of 150 is 12.9?
whole- 150, part- 12.9
12.9/150=0.086, 8.6%
What is 30% of 350?
Multiply the decimal form of 30% (.30) by 350= 105
15 is 60% of what number?
Divide 15 by the decimal form of 60% (.60)
15/.60= 25
To find percent increase…
amount of increase/the whole
example: if quantity increases from 600 to 750, what is the percent increase?
150/600= .25–> 25%
If a quantity size DOUBLES, then the percent increase is…
100%
To find percent decrease…
decrease/the whole
