Quant Ch 1 - Essential Skills Flashcards

1
Q

Simplify (a/b)^2

A

a^2/b^2

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2
Q

Simplify √x/y

A

√x / √y

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3
Q

Simplify (ab)^x

A

(a^x)(b^x)

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4
Q

Squaring and taking the square root of a number b/t 0 and 1

A

If 0<x<1, then x^2 < x < √x

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5
Q

Strategic number

A

Using a number that is easier to simplify that is within the same parameters as the given nuber

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6
Q

Squares of integers

A

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

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7
Q

Simple fraction

A

Two whole numbers

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8
Q

Proper fraction

A

numerator < denominator

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9
Q

Improper fraction

A

numerator > denominator

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10
Q

Least common denominator (LCD)

A

smallest nonzero whole number divisible by each denominator

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11
Q

Distributive property of division over addition

A

a/b + c/b <–> a+c / b

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12
Q

Distributive property of division over subtraction

A

a/b - c/b <–> a-c / b

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13
Q

Adding and subtracting fractions with unlike denominators

A

a/b + c/d = ad + bc / bd

a/b - c/d = ad - bc / bd

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14
Q

Subtracting a fraction from a whole number

A

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

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15
Q

Simplify a/b x b/d

A

ac / bd

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16
Q

Simplify a/b / c/d

A

a/b x d/c = ad/bc

aka multiply by the reciprocal

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17
Q

Simplify A x b/c

18
Q

Simplify 1 / -1

19
Q

Simplify 1 / a/b

20
Q

Complex fractions

A

Fractions with a fraction in the num, denominator, or both

21
Q

Bow tie method

A

Used to compare the size of fractions:
Given a/b and c/d, a/b > c/d if ad > bc

22
Q

To add/subtract decimals

A

Line up the decimal points then add/subtract

23
Q

To multiply decimals

A

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

24
Q

To divide decimals

A

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

25
"Percent"
Divide by 100
26
Ellipses
"..." signify that decimals never terminate
27
Block
set of numbers in a decimal that repeat (bar over that set of numbers)
28
Decimal for base fraction 1/2
0.5
29
Decimal for base fraction 1/3
0.33
30
Decimal for base fraction 1/4
0.25
31
Decimal for base fraction 1/5
0.2
32
Decimal for base fraction 1/6
0.167
33
Decimal for base fraction 1/7
0.143
34
Decimal for base fraction 1/8
0.125
35
Decimal for base fraction 1/9
0.111
36
Decimal for base fraction 1/10
0.1
37
Principal square root
non-negative square root of a number
38
Simplify √0
0
39
Priority of absolute value and radicals
Absolute value and radicals have the same priority as parentheses
40
Distributive property
a(b+c) = ab +ac *use for common factors and factorials
41
Simplify 0!
0
42
Average of an arithmetic sequence
The average is the median Sum = average x number of numbers in sequence