Quant Ch 1 - Essential Skills Flashcards
Simplify (a/b)^2
a^2/b^2
Simplify √x/y
√x / √y
Simplify (ab)^x
(a^x)(b^x)
Squaring and taking the square root of a number b/t 0 and 1
If 0<x<1, then x^2 < x < √x
Strategic number
Using a number that is easier to simplify that is within the same parameters as the given nuber
Squares of integers
If a number is equal to the square of an integer, the units digit of that number will be equal to the units digit of at least 1 of the squares of the integer
Simple fraction
Two whole numbers
Proper fraction
numerator < denominator
Improper fraction
numerator > denominator
Least common denominator (LCD)
smallest nonzero whole number divisible by each denominator
Distributive property of division over addition
a/b + c/b <–> a+c / b
Distributive property of division over subtraction
a/b - c/b <–> a-c / b
Adding and subtracting fractions with unlike denominators
a/b + c/d = ad + bc / bd
a/b - c/d = ad - bc / bd
Subtracting a fraction from a whole number
A - b/c = (A x c)-b / c for proper & improper fractions
A - b/c = (A-1)c/c - b/c for proper fractions and b <c
A - b/c = (A-1)c/c - b/c for improper fractions but b/c has to be converted to a mixed number
Simplify a/b x b/d
ac / bd
Simplify a/b / c/d
a/b x d/c = ad/bc
aka multiply by the reciprocal
Simplify A x b/c
Ab/c
Simplify 1 / -1
-1
Simplify 1 / a/b
b/a
Complex fractions
Fractions with a fraction in the num, denominator, or both
Bow tie method
Used to compare the size of fractions:
Given a/b and c/d, a/b > c/d if ad > bc
To add/subtract decimals
Line up the decimal points then add/subtract
To multiply decimals
1) ignore the decimal point. Treat the # like a whole number
2) count the total number of decimal points to the right of the decimal pt. in the #’s that were multiplied
3) move the decimal point to the left the same # of spaces
To divide decimals
1) move the decimal pt of the divisor to the right until its a whole number
2) move the decimal pt of the dividend to the right the same # of spaces
3) divide by long division
“Percent”
Divide by 100
Ellipses
“…” signify that decimals never terminate
Block
set of numbers in a decimal that repeat (bar over that set of numbers)
Decimal for base fraction 1/2
0.5
Decimal for base fraction 1/3
0.33
Decimal for base fraction 1/4
0.25
Decimal for base fraction 1/5
0.2
Decimal for base fraction 1/6
0.167
Decimal for base fraction 1/7
0.143
Decimal for base fraction 1/8
0.125
Decimal for base fraction 1/9
0.111
Decimal for base fraction 1/10
0.1
Principal square root
non-negative square root of a number
Simplify √0
0
Priority of absolute value and radicals
Absolute value and radicals have the same priority as parentheses
Distributive property
a(b+c) = ab +ac
*use for common factors and factorials
Simplify 0!
0
Average of an arithmetic sequence
The average is the median
Sum = average x number of numbers in sequence
