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31 Cards in this Set
- Front
- Back
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Basic Order of Operations
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1st: powers and roots
2nd: multiplication and division 3rd: addition and subtraction |
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Negative Exponent
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...is the denominator of a fraction
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Absolute Value
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...is how far a number is from 0
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√x2 =
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|x| when you don't know if x is positive or negative
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Commutative Property of Addition and Multiplication
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...says that the order doesn't matter
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Associative Property of Addition and Multiplication
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...assures you that you can group or associate terms differently and get the same result.
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Distributive Property of Multiplication over Additions or Subtraction
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...allows you to multiply a factor times several terms within a grouping symbol
a(b+c) = ab +ac a(b-c) = ab-ac |
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Additive Identity
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0
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Multiplicative Identity
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1
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Additive Inverse
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-x
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Multiplicative Inverse
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1/x
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Multiplicative Property of 0
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Xx0=0 and 0xX=0
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When multiplying two exponents with the same base...
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...add their exponents
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When dividing two exponents with the same base
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...subtract their exponents
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When raising value that has exponent to another power...
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...multiply the exponents
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The product of two numbers raised to a power is...
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...equal to raising each of the numbers to that power and then multiplying them together
(a*b)ⁿ = aⁿ*bⁿ |
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The quotient of two numbers raised to a power is...
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...equal to the power of each of the numbers in the quotient
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A value raised to a negative power can be rewritten...
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...as a fraction with the positive power of that number in the denominator
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Any number (except 0) raised to the 0 power...
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...= 1
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Irrational Numbers
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The square roots of numbers that aren't perfect squares
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Rationalization
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...is performed to write a fraction that is equivalent to the first but no longer has a radical in the denominator
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Divisibility Rule:
A number is divisible by 2 if... |
...it is an even number.
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Divisibility Rule:
A number is divisible by 4 if... |
...the last two digits form a number divisible by 4.
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Divisibility Rule:
A number is divisible by 8 if... |
...the last three digits form a number divisible by 8.
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Divisibility Rule:
A number is divisible by 5 if... |
...it ends in 0 or 5.
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Divisibility Rule:
A number is divisible by 3 if... |
...the sum of the digits is divisible by 3.
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Divisibility Rule:
A number is divisible by 9 if... |
...the sum of the digits is divisible by 9.
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Divisibility Rule:
A number is divisible by 6 if... |
...it is divisible by both 2 and 3.
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Divisibility Rule:
A number is divisible by 12 if... |
...it is divisible by both 3 and 4.
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Divisibility Rule:
A number is divisible by 15 if... |
...it is divisible by both 3 and 5.
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Divisibility Rule:
A number is divisible by 11 if... |
...the sums of the alternating digits have a difference of 0 or 11 or 22.
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