Basics Flashcards
Order of Operations
P = Parentheses E = Exponents M = Multiplication in order from left to right D = Division A = Addition in order from left to right S = Subtraction If an expression has parentheses within parentheses, work from the innermost out. This mnemonic will help you remember the order of operations: Please Excuse My Dear Aunt Sally (PEMDAS). Example: 30 – 5 × 4 + (7 – 3)2 ÷ 8 First, perform any operations within parentheses. 30 – 5 × 4 + 42 ÷ 8 Next, raise to any powers indicated by exponents. 30 – 5 × 4 + 16 ÷ 8 Then do all multiplication and division in order from left to right. 30 – 20 + 2 Last, do all addition and subtraction in order from left to right. 10 + 2 Answer: 12
Commutative Law
It doesn’t matter in what order the operation is performed. Addition and multiplication are both commutative, while division and subtraction are not commutative. Example: 5 + 8 = 8 + 5 2 × 6 = 6 × 2 3 – 2 ≠ 2 – 3 6 ÷ 2 ≠ 2 ÷ 6
Associative Law
The terms can be regrouped without changing the result. Addition and multiplication are also associative, while division and subtraction are not.
Distributive Law
Factoring
Numerator
Denominator
Equivalent Fractions
Radicals in the Denominator
Lowest Terms
Reducing a Fraction
Canceling in Fractions
Requirement for Adding or Subtracting
Fractions
Least Common Multiple
Multiplying Fractions
Dividing Fractions Procedure
Complex Fractions
Complex Fractions Simplifation Methods
Comparing Fractions
Common Fraction to Decimal Equivalencies
Benchmark Value
Digits and Places
Comparing Decimals- Technique
1/100
.01 OR 1%
1/50
.02 or 2%
1/40
.025
1/25
.04
1/20
.05
1/10
.1
1/9
.1111111…
1/8
.125
1/5
.2
1/4
.25
1/3
.333…
2/3
.666
2/5
.4
3/5
.6
4/5
.8
5/4
1.25
1/6
.16 and 2/3 or .166666666
5/6
.83 and 1/3 or .83333333333….
1/7
.14 and 2/7 .1428 then it gets more complicated
1/8
.125
2/8
.25
3/8
.375
1/11
.09090909….
2/11
.181818….
3/11
.27272727…
1/12
.08 and a 1/3 or .08333…
Coefficent
Base
Exponment
Square of a number
Cube of a number
Multiplying two terms with the same base
Dividing two terms with the same base
Raising a power to another power
Multiplying two terms with the same exponents but different bases
A number rasied to the first power equals what?
A number raised to the zero power is what?
0 raised to the zero power is what?
Undefined
A negative exponent indicates what
a reciprical
Procedure for raising a fraction to an exponent
Bases of 10
Raising a positive fraction less than 1 to an exponent results in: A smaller or larger number?
Smaller
E.G. 2/4^2 is 4/9
10^6
1 + 6 Zeros or 1,000,000
4x 10^3
Move the decimal 3 places to the right. 4000.
4,000,000/10^6
Move decimal 6 palces to the left. 4
4,000,000x10^-3
Same as dividing by 10^3. Move decimal three places to the left. 4,000
Radicals refer to positive numbers only on the GMAT? True or flase?
True
Adding Radicals
pg 669
Subtracting Radicals
pg669
Multiplying Radicals
pg 669
Dividing Radicals
pg 669
Factoring out radicals
Exponents and radicals
Radical 13^4
Equal to
13^2
Rule for decimal under square root sign