Quant Ch 1 - Essential Skills

Question 1

Simplify (a/b)^2

Answer 1

a^2/b^2

Question 2

Simplify √x/y

Answer 2

√x / √y

Question 3

Simplify (ab)^x

Answer 3

(a^x)(b^x)

Question 4

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

Answer 4

If 0<x<1, then x^2 < x < √x

Question 5

Strategic number

Answer 5

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

Question 6

Squares of integers

Answer 6

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

Question 7

Simple fraction

Answer 7

Two whole numbers

Question 8

Proper fraction

Answer 8

numerator < denominator

Question 9

Improper fraction

Answer 9

numerator > denominator

Question 10

Least common denominator (LCD)

Answer 10

smallest nonzero whole number divisible by each denominator

Question 11

Distributive property of division over addition

Answer 11

a/b + c/b <–> a+c / b

Question 12

Distributive property of division over subtraction

Answer 12

a/b - c/b <–> a-c / b

Question 13

Adding and subtracting fractions with unlike denominators

Answer 13

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

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

Question 14

Subtracting a fraction from a whole number

Answer 14

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

Question 15

Simplify a/b x b/d

Answer 15

ac / bd

Question 16

Simplify a/b / c/d

Answer 16

a/b x d/c = ad/bc

aka multiply by the reciprocal

Question 17

Simplify A x b/c

Answer 17

Ab/c

Question 18

Simplify 1 / -1

Answer 18

-1

Question 19

Simplify 1 / a/b

Answer 19

b/a

Question 20

Complex fractions

Answer 20

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

Question 21

Bow tie method

Answer 21

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

Question 22

To add/subtract decimals

Answer 22

Line up the decimal points then add/subtract

Question 23

To multiply decimals

Answer 23

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

Question 24

To divide decimals

Answer 24

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

Question 25

“Percent”

Answer 25

Divide by 100

Question 26

Ellipses

Answer 26

“…” signify that decimals never terminate

Question 27

Block

Answer 27

set of numbers in a decimal that repeat (bar over that set of numbers)

Question 28

Decimal for base fraction 1/2

Answer 28

0.5

Question 29

Decimal for base fraction 1/3

Answer 29

0.33

Question 30

Decimal for base fraction 1/4

Answer 30

0.25

Question 31

Decimal for base fraction 1/5

Answer 31

0.2

Question 32

Decimal for base fraction 1/6

Answer 32

0.167

Question 33

Decimal for base fraction 1/7

Answer 33

0.143

Question 34

Decimal for base fraction 1/8

Answer 34

0.125

Question 35

Decimal for base fraction 1/9

Answer 35

0.111

Question 36

Decimal for base fraction 1/10

Answer 36

0.1

Question 37

Principal square root

Answer 37

non-negative square root of a number

Question 38

Simplify √0

Answer 38

0

Question 39

Priority of absolute value and radicals

Answer 39

Absolute value and radicals have the same priority as parentheses

Question 40

Distributive property

Answer 40

a(b+c) = ab +ac

*use for common factors and factorials

Question 41

Simplify 0!

Answer 41

0

Question 42

Average of an arithmetic sequence

Answer 42

The average is the median

Sum = average x number of numbers in sequence