Arithmetic Review

Question 0

Neg x neg

Answer 0

Pos

Question 1

Pos. x pos.

Answer 1

Pos.

Question 2

Pos x neg

Answer 2

Neg

Question 3

When using quotient/remainder result, 6/24=

Answer 3

0 remainder 6

Question 4

Even + even

Answer 4

Even

Question 5

Odd + odd

Answer 5

Even

Question 6

Even + odd

Answer 6

Odd

Question 7

Even x even

Answer 7

Even

Question 8

Odd x odd

Answer 8

Odd

Question 9

Even x odd

Answer 9

Even

Question 10

T/F: 1 is the first prime number

Answer 10

FALSE. 1 is not counted as a prime number. 2 is the first prime number.

Question 11

How many even prime numbers?

Answer 11

Only one. 2 is the only even prime.

Question 12

Not a prime number?

Answer 12

“Composite number”

Question 14

0 can never be the ________ in a fraction.

Answer 14

Denominator

Can NEVER be 0

Question 15

To divide fractions

Answer 15

invert second fraction –> multiply

Question 16

Neg number to an even power is always _________, and a neg number with an odd exponent is always __________.

Answer 16

Neg number to an even power is always positive, and a neg number with an odd exponent is always negative.

Question 17

All positive numbers have two square roots:

Answer 17

one pos and one neg (except 0; square root of 0 is 0)

Question 18

PENMDAS

Answer 18

Parentheses, Exponents, NEGATION… M/D, A/S

Question 19

• √100

Answer 19

-10

Question 20

Square root of neg. number

Answer 20

undefined by the real number system

Question 21

(√a)(√b)

Answer 21

√(ab)

Question 22

(√a)/(√b)

Answer 22

√(a/b)

Question 23

For odd-order roots, there is/are __________ for every number “n”, even when “n” is negative.

Answer 23

exactly ONE

Question 24

For even-order roots, there is/are ___________ for every positive number “n”, and ________ roots for any negative number “n”.

Answer 24

exactly two for every positive number “n”

and NO roots for any neg. number “n”

Question 25

Irrational numbers

Answer 25

decimals that do not repeat or terminate

Question 26

Real numbers

Answer 26

include rational and irrational (do not terminate or repeat) numbers

Question 27

absolute value

Answer 27

distance between x and 0
x = | x |
-x = | x |

Question 28

Division by 0 is

Answer 28

undefined.

Question 29

Triangle inequality

Answer 29

a+b | ≤ | a | + | b |

Question 30

a | | b | =

Answer 30

ab |

Question 31

If 0 < b < 1, then b^2

Answer 31

< b

For ex. (1/5)^2 = (1/25) which is less than (1/5)

Question 32

Rations, like fractions, can be

Answer 32

reduced. Ex. The ratio 9:12 apples to oranges can be reduced to 3:4, or 3/4, or “3 to 4”

Question 33

To solve a proportion (equation relating two ratios)…

Answer 33

Cross multiply to solve. Ex. x/49=3/21 –> 21x=(3)(49)

Question 34

When asked “x is y% of what number?”…

Answer 34

set up equation: y%(z) = x
Example: 15 is 60% of what? 0.6z = 15 so z = 15/0.6
OR… set up proportion 15/z=60/100, then 60z=(15)(100)

Question 35

300% equals… (fraction)

Answer 35

300/100

Question 36

To calculate percent change…

Answer 36

larger number - smaller number divided by the base (or first/original) number
End up calculating change/base (multiply by 100 for percent)