Math Concepts Flashcards
Prime Number
Number that has exactly 2 factors.
Only positive integers.
2 is the only prime number. Every even prime number greater than 2 has at least 3 factors.
First 8 prime numbers: 2,3,5,7,11,13,17,19
Factor Foundation Rule
If c is divisible by primes a and b, then c is divisible by (a*b)
“Greatest number than x must be divisible by”
LCM
Double Cross Method
Use when adding fractions and when finding when a fraction is greater than or equal to other fractions
What percent
x/100
What percent of
turn what percent into x/100, then multiply.
ex: What percent of 200 is 60 = (x/100)200=60
x% of
1) Convert x% into decimal/fraction
2) Multiply, or
1) find a power of 10 of x%
2) multiple/divide to get to x%
ex: 30% of 200 = 0.30x200 = 60
30% = 20x3 = 60
percent change formula
Percent change (as percent of original)
=
Change in value/Original Value
Unknown Multiplier
The number by which you multiply the ratio to get to the actual number.
*Always the same for all parts of a ratio
Least common multiple (LCM)
The LCM of 2 numbers is the smallest number that is a multiple of both numbers
i.e: 3 & 10 = 30
6 & 9 = 18
*If x is divisibke by A & by B, then x is divisible by the LCM of A & B no matter what
The double cross Method
1) Draw arrows and multiple
2) Add the numerators
3) Simplify
ex: 5/6 + 3/8 = ((58) + (36))/(6*8) = (40 + 18)/48 = 58/48=29/24
Double Cross Fraction Comparison
1) set the fractions up near each other
2) Multiple “up” the arrows. Be sure to put the resulting number at the top of each respective error
3) Compare the numbers. The side with the bigger number is the bigger fraction
ex: 3/5 and 4/7
(37) and (45) = 21 and 20.
Since 21 is greater than 20, 3/5 is greater than 4/7
Improper fraction to mixed number
1) rewrite the number as a sum
2) Split the fraction
ex:
1) 13/4 = 12/4 + 1/4 = 3 + 1/4 =3 1/4
2) 11/6 = 6/6 + 5/6 = 1 5/6
3) 100/11 = 99/11 + 1/11 = 99 1/11
Mixed Number to Improper fraction
Shortcut:
((denom) (integer) + num)/denom
ex:
7 3/8 => ((8) (7) +3)/8= 59/8
Note: I already do it this way
% decrease of 50%
= New percent of 50%
= Multiple original value by 0.5 or 1/2
Divide a number by (+) 10^-x
When dividing any number by a negative power of 10, move the decimal to the right
ex:
53.0447/10^-2 = 5304.47
Multiple a number by (+)10^x
When multiplying any number by a positive power of 10, move the decimal to the right of the specified number of places
ex:
3.9742 x 10^3 = 3,974.2
Multiple a Decimal & a Big Number
When one number is very big and the other is very small, you can trade powers of 10 from the big one to the small one.
Similar to: Move one decimal point to the left and the other to the right.
ex:
4,000,000 x 0.0003 = 400 x 3 = 120
50,000 x 0.007 = 50 x 7 = 350
Numerator and Denominator Rules
1) (up arrow) numerator, -denom => (up arrow) fraction
2) (up arrow) denom, =numer => (down arrow) fraction
3) adding same value to both numer & denom => fraction goes toward 1
a) if fraction <1, then fraction increases as it approaches 1
b) if fraction >1, then fraction decreases as it approaches 1
Interest Formula
Total Amount = P(1 + r/n)^nt
P = Principal, r = rate (in decimal form), n = number of times/year, t= number of years
Multiply a number by (+) 10^-x
When multiplying any number by a negative power of 10, move the decimal to the left
e.x: 6782.01 x 10^-3 =6.78201
Exponent base
Fractional Base: When base id (+) proper decimal/fraction, the exponent (up arrow) the value of the expression (down arrow)
Compound base: an exponent can be distributed a product (10^3 = (2x5)^3 = 2^3 x 5^3)
Base of -1: (-1)^odd = -1
(-1)^even = 1
Negative base: the exponent does not distribute unless the (-)ve sign is inside the parenthesis
Combining exponential terms
When multiplying 2 exponential terms, w/the same base, add the exponents
When dividing 2 exponential terms w/the same base, subtract the exponent
Any base to the 0 power = 1
0^0 is undefined
X^-3 = 1/x^3
When you raise an exponential term, multiply the exponents
Divide 2 decimals
Write the division as a fraction
Move the decimals in the same direction on the top and the bottom
Ex.: 300/0.05 = 30,000/5 = 6000
12.39/0.003 = 12,390/3=4130
Expression
Represents a value
Does not contain an equal sign
To simplify: 1) Combine like terms 2) Find a common denominator 3) Pull out a common factor Cancel common factors
High school algebra rule
1) N variables require N equations to solve
2) Good to use when P.S.
Does not always work w/D.S
Odd exponents
Less than -1=> result is smaller
Between -1 and 0 =>result is bigger
Between 0 and 1 =>result is smaller
Greater than 1 => result is bigger
Odd exponents preserve the sign of the original expression
Even exponents
Less than -1=> result is bigger
Between -1 and 0 => result I bigger
Between 0 and 1 => result is smaller
Greater than 1 => result is bigger
Even exponents hide the sign of the original number
An integer raised to a positive even power, is always a perfect square
Equation I xI = a
When you have an equation in the form I x I =a with a>0, then x=+/- a
Divide a number by (+) 10^x
When dividing any number by a positive power of 10, move the decimal to the left the specified number of places.
e.x: 4,162.9 /10^2 = 41.629
Sector Area/Circle Area=
Arc Length/Circumference
The Triangle Inequality Theorem
The sum of any 2 sides of a triangle must be greater than the measure of the third side
Relationship between triangle side lengths and angles
Sides correspond to their opposite angles. The longest side is opposite the largest angle, and the smallest side is opposite the smallest angle.
Parallelogram
Any 4-sided figure in which the opposite sides and a parallel and equal. Opposite angles are also equal, and adjacent angles add up to 180 degrees.
Perimeter=Sum of all sides
Area=base x height
For any even number of consecutive integers,
the sum of all the integers is never a multiple of the number of integers
Triple Venn diagrams can be solved with the following formula:
Sum of totals in three individual categories – (sum of items in exactly two categories) - (2 * number of items in all three categories) + Neither = Total
