Arithmetic Review Flashcards
Neg x neg
Pos
Pos. x pos.
Pos.
Pos x neg
Neg
When using quotient/remainder result, 6/24=
0 remainder 6
Even + even
Even
Odd + odd
Even
Even + odd
Odd
Even x even
Even
Odd x odd
Odd
Even x odd
Even
T/F: 1 is the first prime number
FALSE. 1 is not counted as a prime number. 2 is the first prime number.
How many even prime numbers?
Only one. 2 is the only even prime.
Not a prime number?
“Composite number”
0 can never be the ________ in a fraction.
Denominator
Can NEVER be 0
To divide fractions
invert second fraction –> multiply
Neg number to an even power is always _________, and a neg number with an odd exponent is always __________.
Neg number to an even power is always positive, and a neg number with an odd exponent is always negative.
All positive numbers have two square roots:
one pos and one neg (except 0; square root of 0 is 0)
PENMDAS
Parentheses, Exponents, NEGATION… M/D, A/S
- √100
-10
Square root of neg. number
undefined by the real number system
(√a)(√b)
√(ab)
(√a)/(√b)
√(a/b)
For odd-order roots, there is/are __________ for every number “n”, even when “n” is negative.
exactly ONE
For even-order roots, there is/are ___________ for every positive number “n”, and ________ roots for any negative number “n”.
exactly two for every positive number “n”
and NO roots for any neg. number “n”
Irrational numbers
decimals that do not repeat or terminate
Real numbers
include rational and irrational (do not terminate or repeat) numbers
absolute value
distance between x and 0
x = | x |
-x = | x |
Division by 0 is
undefined.
Triangle inequality
a+b | ≤ | a | + | b |
a | | b | =
ab |
If 0 < b < 1, then b^2
< b
For ex. (1/5)^2 = (1/25) which is less than (1/5)
Rations, like fractions, can be
reduced. Ex. The ratio 9:12 apples to oranges can be reduced to 3:4, or 3/4, or “3 to 4”
To solve a proportion (equation relating two ratios)…
Cross multiply to solve. Ex. x/49=3/21 –> 21x=(3)(49)
When asked “x is y% of what number?”…
set up equation: y%(z) = x
Example: 15 is 60% of what? 0.6z = 15 so z = 15/0.6
OR… set up proportion 15/z=60/100, then 60z=(15)(100)
300% equals… (fraction)
300/100
To calculate percent change…
larger number - smaller number divided by the base (or first/original) number
End up calculating change/base (multiply by 100 for percent)
