Math #2 Questions with Rationale
Real Numbers
numbers that appear on the number line.
Integer
whole number; no fractions or decimals
Zero
is an EVEN integer but is NEITHER positive nor negative
Negative fractions and exponents
Negative fractions between 0 and -1 become an ...
Real Numbers - answer numbers that appear on the number line.
Integer - answer whole number; no fractions or decimals
Zero - answer is an EVEN integer but is NEITHER positive nor negative
Negative fractions and exponents - answer Negative fractions between 0 and -1
become an increasingly smaller positive fraction when raised to increasingly larger,
even integer exponents. A fraction between 0 and -1 become an increasingly larger
negative fraction when raised to increasingly larger, odd integer exponents.
PEMDAS - order of operations - answerPEMDAS = Please Excuse My Dear Aunt Sally
-Parentheses = grouping symbols like brackets and absolute value
-Exponents include radicals
-Multiply and Divide together from left to right
-Add and Subtract together from left to right
Dealing with fractions - answer1) You need a common denominator to add and subtract
fractions.
2) To add or subtract fractions, you need a "common denominator." When you add or
subtract, only perform the operation on the numerators, NOT the denominators.
3) Multiply fractions straight across.
4) When dividing fractions, divide the numerator by the reciprocal of the denominator.
(flip and multiply)
5) In positive fractions, a smaller denominator (with a consistent numerator) = larger
value
Factors - answerFactors = numbers that can divide evenly into the larger number
The quickest way to find the factors of a number is to make a factor T or a prime
factorization TREE.
Average Formula - answerThe Average Formula: average = sum of terms / number of
terms
Ratios - answerThe GRE will often give you a part:part ratio but ask you a question that
requires a part:whole ratio
Ratios can be written as "x to y" "x/y" or "x : y" They all mean the same thing.
Writing ratios in fraction format is often the first step to attacking ratio problems.
, When you convert ratios to fractions, you can solve them just like any fraction problem.
*To combine ratios, line up the common term, get a common multiple, and convert.
Percents - answerPercent = (part/whole) x 100%
Convert %s and decimals to common fractions to compare.
Absolute Value - answerWhen your variable is inside the absolute value, set the portion
inside the sign to the positive and negative version. lxl = -x or x
Radicals - answerBEWARE! You cannot add/subtract radX + radY to get rad(X +/- Y). It
doesn't work!!!
• 4^(1/2) = square root of 4 = 2
• Square roots with the same base can be added or subtracted
o Ex. 4(root 3) + 7(root 3) = 11(root 3)
• When you multiply square roots or divide square roots, you multiply or divide them
underneath the square root sign
• When taking the square root of a fraction between 0 and 1, the result will always be
larger than the fraction itself
o Ex. Square root of ¼ = ½
o The square root of a fraction is always larger than the fraction itself, just as a fraction
is always larger than its square
Square roots are always positive. (For example, rad4 is ONLY 2, not 2 OR -2.)
The square root of x is the same as (x)^1/2.
When both columns contain solitary radicals, doing the same thing to both columns by
squaring the values quickly rids the question of the radical and makes comparison
easier.
In its simplest form, the number under the radical won't contain any factors that are
perfect squares.
Negative exponents - answerWhen a number is raised to a negative exponent, you
must rewrite the expression so that you have one over the number raised to the positive
version of the exponent
example. x^-1 = 1/x
Exponent rules - answerTo multiply powers with the same base, add the exponents
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