Arithmetic Flashcards
Rational numbers
All numbers that can be expressed as tge ratio of two integers (all integers and fractions)
Real Numbers
All numbers on the number line
Irrational numbers
All real numbers that are not rational, both positive and negative
Integers
All numbers with no fractional or decimal parts, multiples of 1
Commutative law
Addition and multiplication are both commutative; it doesn’t matter in what order the operation is performed.
Associative law
Addition and multiplication are associative; the terms can be regrouped without changing the result
(a+b)+c = a+(b+c)
Distributive law
The distributive law of multiplication/division allows us to distribute a factor among the terms being added or subtracted.
a(b+c) = ab+ac
What percent of 60 is 45?
Percent = Part / Whole 45/60 = 3/4 = 75%
What is 20% of 80
Part = Percent * Whole
0.20 * 80 = 16
1/8
0.125 = 12.5%
1/6
0.1667 = 16.67%
1/5
0.2 = 20%
1/4
0.25 = 25%
1/3
0.3333 = 33.33%
3/8
0.375 = 37.5%
2/5
0.4 = 40%
1/2
0.5 = 50%
3/5
0.6 = 60%
5/8
0.625 = 62.5%
2/3
0.6667 = 66.67%
3/4
0.75 = 75%
4/5
0.8 = 80%
5/6
0.8333 = 83.33%
7/8
0.875 = 87.5%
sqrt(a^2)
sqrt(a^2) = | a |,
for all values of a
How to work with absolute values
x + 3 | = 4x
Tree of possible outcomes
x + 3 = 4x
x + 3 = -4x
5^18 + 100(5^16) vs 5^19
Divide both sides with the largest common factor, 5^16, to see that the quantities are equal
a^2 - sqrt(a) vs 0, a > 0, a != 1
Classic trap! When picking numbers, remember to try fractions between 0 and 1, to find that the relationship cannot be determined.
sqrt(a)/sqrt(b)
sqrt(a/b)
Triangle inequality
a + b | <= | a | + | b |
a | * | b |
a * b |
Are all prime numbers odd?
All except 2!
The average of a set of n evenly spaced numbers
Is the same as the median for the set.
