Arithmetic

Question 1

When integers are added, subtracted, or multiplied, the result is always…

Answer 1

an integer.

When divided, the result may also be a fraction.

Question 2

Subtracting a negative number is the same as…

Answer 2

adding it.

7– -1=8

Question 3

The product of two positive integers is…

Answer 3

a positive integer.

(5)(6)=30

Question 4

The product of 2 negative integers is…

Answer 4

a positive integer

(-5)(-6)=30

Question 5

A positive integer times a negative integer is…

Answer 5

a negative integer

(-5)(6)=30

Question 6

Factors

Answer 6

Positive or negative numbers that can be multiplied to get an integer.

1,2,3,4,6,12 are factors of 12

Question 7

Multiple

Answer 7

A number divisible by integer x

60 is a multiple of 2

Question 8

1 is a factor of…

Answer 8

Every integer

Question 9

1 is a multiple of…

Answer 9

1 and -1

Question 10

0 is a multiple of…

Answer 10

Every integer

Question 11

0 is a factor of…

Answer 11

1

Question 12

Lowest common multiple of c and d

Answer 12

C and D are non zéro integers and the least positive integer that is a multiple of c AND d

Question 13

Greatest common factor (divisor) of C and D

Answer 13

The greatest positive integer divisible by both C AND D

Question 14

If C and D are not both divisors of integer x, the result is represented as a…

Answer 14

Fraction, decimal, or quotient with remainder where both are integers

Question 15

The sum of two even integers is…

Answer 15

an even integer

Question 16

The sum of two odd integers is…

Answer 16

an even integer

Question 17

The sum of an even and an odd integer is…

Answer 17

an odd integer

Question 18

The product of two even integers is…

Answer 18

An even integer

Question 19

The product of two odd integers is…

Answer 19

An odd integer

Question 20

The product of an even integer and an odd integer is…

Answer 20

An even integer

Question 21

Prime number

Answer 21

Integer greater than one divisible only by 1 and itself

Question 22

The first ten prime numbers

Answer 22

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Question 23

Prime factorization for 12

Answer 23

(2)(2)(3) = (2^2)(3)

Question 24

Fraction

Answer 24

c/d where c (numerator) and d (denominator) are integers and d is NOT equal to 0

Question 25

Rational number

Answer 25

A number that can be turned into a fraction where d is NOT 0. All integers are rational numbers because all integers can be n/1.

Question 26

Equivalent fractions

Answer 26

Any fraction can be multiplied by the same nonzero integer to create an equivalent fraction. Any fraction can have the same common factor factored out to be reduced to an equivalent fraction.

Question 27

Adding and subtracting fractions with same denominator | 3/11 + 2/11

Answer 27

Add straight across. Keep the denominator the same. | 3/11 + 2/11 = 5/11

Question 28

Adding and subtracting fractions with different denominators | 1/3 + -2/5

Answer 28

Find a common denominator. Convert both fractions to equivalent fractions with the same denominator. Add numerators and keep common denominator. 1/3 + -2/5 1/3 = 5/15 and -2/5 = -6/15 5/15 + -6/15 = -1/15

Question 29

Multiplying fractions | 8/7)(7/3

Answer 29

Multiply the two numerators. Multiply the two denominators. | (8/3)(7/3) = 56/9

Question 30

Dividing fractions | 17/8 \ 3/5

Answer 30

Invert the second fraction (find the reciprocal). Multiply the first fraction by the inverted fraction. 17/8 * 5/3 = 85/24

Question 31

Mixed number

Answer 31

Integer plus a fraction

Question 32

Converting a mixed number to a fraction | 4 3/8

Answer 32

Convert the integer part to an equivalent fraction. Add the fraction. 4 = 32/8 + 3/8 = 35/8

Question 33

Base and exponent | 3ˆ4

Answer 33

``` 3 = base 4 = exponent ```

Question 34

A negative number raised to an even power is always... | (-3)ˆ2

Answer 34

Even | 9

Question 35

A negative number raised to an odd power is always... | (-3)ˆ3

Answer 35

Odd | -27

Question 36

(-3)ˆ2= | -3ˆ2

Answer 36

``` (-3)ˆ2 = 9 -3ˆ2 = -(3)(3) = -9 ```

Question 37

aˆ0=

Answer 37

1

Question 38

0ˆ0

Answer 38

undefined

Question 39

aˆ-1=

Answer 39

1/a

Question 40

aˆ-2=

Answer 40

1/aˆ2

Question 41

(√a)ˆ2 = | (√3)ˆ2 =

Answer 41

a | 3

Question 42

√(aˆ2)= | √4=

Answer 42

a | √4 = √(2ˆ2) = 2

Question 43

√a √b= | √3√10

Answer 43

√ab | √30

Question 44

√a/√b = | √5/√15=

Answer 44

√ab | √5/√15 = √5/15 = √1/3

Question 45

For odd order roots

Answer 45

There is exactly ONE root for EVERY number n, even when n is negative

Question 46

For even order roots

Answer 46

There are exactly TWO roots for every POSITIVE number and NO roots for any NEGATIVE number

Question 47

3√8 (cube root)= 4√8 (4th root)= -4√8 (- 4th root)= 4√-8 (4th root of a negative number) =

Answer 47

1 cube root (2) 8 is positive so has two 4th roots-- 4 and -4 -8 is negative, so no 4th root because the root is positive and the number is negative (imaginary numbers)

Question 48

irrational number

Answer 48

a number whose decimal does not terminate or repeat; cannot be written as a fraction

Question 49

The set of real numbers consists of...

Answer 49

all rational and irrational numbers

Question 50

Organize the sets from smallest to largest: Imaginary numbers Rational numbers Integers Real numbers

Answer 50

Integers Rational numbers Real numbers Imaginary numbers (separate set)

Question 51

Absolute value

Answer 51

The distance between the number X and zero on the number line.

Question 52

r(s + t) =

Answer 52

(rs) + (rt)

Question 53

if rs = 0, then... ex: -2s=0

Answer 53

either r is 0, s is 0, or both are 0 -2s=0, s=0

Question 54

|r + s| is... | ex: |3+ -6|

Answer 54

less than or equal to |r| + |s| |3+-6| = |-3| = 3 |3| + |-6| = 3 + 6 = 9

Question 55

|r||s| = | |5||-2|

Answer 55

|rs| | |(5)(-2)| = |-10| = 10

Question 56

If r is greater than 1, then rˆ2 is... If r is between 0 and 1, then rˆ2 is...

Answer 56

greater than r (5, 5ˆ2=25) less than r (1/25 is less than 1/5)

Question 57

2 apples and 3 oranges in a basket | What is the ratio?

Answer 57

2 apples to 3 oranges or 2/3 | Can be reduced like a fraction

Question 58

Proportion and how to solve

Answer 58

``` An equation relating two ratios: 9/12 = X/4 Solve by cross multiplying: 9x = 36 x = 36/9 = 4 ```

Question 59

Solving for percents proportion

Answer 59

part / whole = percent / 100

Question 60

Percent increase/decrease formula

Answer 60

amount of increase/decrease over base (original amount)