Arithmetic

Question 1

The product of a positive integer and a negative integer

Answer 1

Negative integer

Question 2

The product of an even integer and an odd integer

Answer 2

Even integer

Question 3

The product of two odd integers

Answer 3

Odd integer

Question 4

The product of two even integers

Answer 4

Even integer

Question 5

The sum of an even integer and an odd integer

Answer 5

Odd integer

Question 6

The sum of two odd integers

Answer 6

Even integer

Question 7

The sum of two even integers

Answer 7

Even integer

Question 8

What is a prime number

Answer 8

an integer greater than 1 that has only two positive divisors: 1 and itself.

Question 9

The first ten prime numbers

Answer 9

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

Question 10

An integer greater than 1 that is not a prime number

Answer 10

Composite number

Question 11

If both the numerator and denominator of a fraction have a common factor, then

Answer 11

the numerator and denominator can be factored and the fraction can be reduced to an equivalent or simplified fraction.

Question 12

What is a fraction?

Answer 12

a number of the form c/d , where c and d are integers and d (the denominator) does NOT equal 0.

Every integer is a fraction or rational number; e.g. 3 = 3/1

Question 13

What are the equivalent fractions for integers c and d?

Answer 13

c/d

-c/d

c/-d

-(c/d)

Question 14

How do you add two fractions with the same denominator?

Answer 14

add the numerators and keep the same denominator.

3/11 + 2/11 = 5/11

-8/11 + 5/11 = -3/11 or -(3/11)

Question 15

How do you add or subtract two fractions with different denominators?

Answer 15

First, find a common denominator. Second, convert both fractions so that they have the same denominator. Third, add or subtract the numerators.

Ex. 1/3 + 2/5
1. The common denominator is 15.

2. 1/3 x 5/5 = 5/15 AND 2/5 x 3/3 = 6/15
3. 5/15 + 6/15 = 11/15

Question 16

How do you multiply two fractions?

Answer 16

multiply the two numerators and multiply the two denominators.

Ex. 10/7 x -1/3 = -10/21

Question 17

How do you divide two fractions?

Answer 17

To divide one fraction by another, first invert the second fraction (that is, find its reciprocal), then multiply the first fraction by the inverted fraction.

Ex. (3/10) / (7/13) = 3/10 x 13/7 = 39/70

Question 18

What is a mixed number?

Answer 18

It consists of an integer part/whole number and a fraction part, where the fraction part has a value between 0 and 1

Ex 4(1/3) means 4 + 1/3

Question 19

How do you convert a mixed number to a fraction?

Answer 19

To convert a mixed number to a fraction, convert the integer part to an equivalent fraction with the same denominator as the fraction, and then add it to the fraction part.

Ex. 4 3/8 = 4/1 x 8/8 = 32/8;
32/8 + 3/8 =35/8;
Thus 4 3/8 is equivalent to 35/8

OR Multiply the denominator (8) times the whole number (4) then add the numerator (3), place the answer over the denominator to create the improper or equivalent fraction.

Ex to convert 4 3/8…
8 x 4 + 3 = 35;
Thus the new fraction is 35/8

Question 20

What are fractional expressions?

Answer 20

Numbers of the form c/d, where either c or d is not an integer and d is NOT 0, are called fractional expressions. Fractional expressions can be manipulated just like fractions.

Question 21

A negative number raised to an even power is always

Answer 21

Positive

Question 22

a negative number raised to an odd power is always

Answer 22

Negative

Question 23

What is the difference between (-3)^2 and -3^2?

Answer 23

(-3)^2 = 9
-3^2 = -9

Question 24

For all nonzero numbers a, a^0 =

Answer 24

1

Question 25

For all nonzero numbers a,

a^-1 =
a^-2 =
a^-3 =
….

Answer 25

a^-1 = 1/a
a^-2 = 1/a^2
a^-3 = 1/a^3

Question 26

(a)(a^-1) =

Answer 26

(a) (a^-1) =

(a) (1/a) = 1

Question 27

A square root of a nonnegative number n is

Answer 27

a number r such that r^2 = n

Ex. 4 is a square root of 16 because 4^2 = 16.

Another square root of 16 is −4, since (-4)^2 = 16.

All positive numbers have two square roots, one positive and one negative.

Question 28

What are the four important rules of square roots?

Answer 28

(✔️a)^2 = a; (✔️3)^2 = 3

✔️a^2 = a; ✔️2^2 = 2

✔️a✔️b = ✔️ab; ✔️3✔️10 = ✔️30

✔️a/✔️b = ✔️a/b; ✔️5/✔️15 = ✔️5/15 =✔️1/3

Question 29

For odd order roots, there is/are________ root(s) for every number n, even when n is negative.

Answer 29

For odd order roots, there is exactly one root for every number n, even when n is negative.

Question 30

For even order roots, there is/are _______ roots for every positive number n and _____ roots for any negative number n.

Answer 30

For even order roots, there are exactly two roots for every positive number n and no roots for any negative number n.

For example, 8 has exactly one cube root, 3✔️8 = 2, but 8 has two fourth roots, 4✔️8 and -4✔️8, whereas -8 has exactly one cube root, 3✔️-8 = -2, but -8 has no fourth root, since it is negative.

Question 31

Convert 2.3 to an equivalent fraction

Answer 31

2.3 =
2/1 + 3/10 =
(2/1 x 10/10) + 3/10 =
20/10 + 3/10 =
23/10

Question 32

Convert 90.17 to an equivalent fraction

Answer 32

90.17 = 90/1+ 17/100 =
(90/1 x 100/100) + 17/100 =
9,000/100 + 17/100 =
9, 017/100

Question 33

Convert 0.612 to an equivalent fraction

Answer 33

0.612 = 612/1000

Question 34

What are irrational numbers?

Answer 34

Decimals that do not terminate (ex. 0.375) or repeat (0.1111…)

Ex. 1.41421356237

Question 35

What are real numbers?

Answer 35

All rational numbers and all irrational numbers. The real numbers include all integers, fractions, and decimals.

Question 36

What does absolute number mean?

Answer 36

The distance between a number x and 0 on the number line.

Ex. |-3| = 3
|9| = 9

Question 37

R(s + t) =

Answer 37

r(s + t) = Rs + rt

Question 38

If rs = 0, then

Answer 38

If rs = 0, then r = 0 OR s = 0, OR both

Question 39

Division by 0 is

Answer 39

Division by 0 is undefined

Ex. 5/0 is undefined

Question 40

If both r and s are negative, then

Answer 40

If both r and s are negative, then

R + S is negative and RS is positive

Question 41

If R is negative and S is positive, then

Answer 41

If R is negative and S is positive, then RS is negative

Question 42

Triangle inequality

Answer 42

|r + s| is less than or equal to |r| + |s|

Question 43

When expressing a ratio as a fraction, which number is the numerator and which is the denominator?

Answer 43

the first quantity is the numerator and the second quantity is the denominator.

For example, if there are 2 apples and 3 oranges in a basket, we can say that the ratio of the number of apples to the number of oranges is 2/3 , or that it is 2 to 3, or
that it is 2 : 3.

Question 44

What is a proportion?

Answer 44

A proportion is an equation relating two ratios.

for example, 9/12 = 3/4

Question 45

How do you solve an equation with ratios?

Answer 45

Write a proportion and cross multiply.

Example: To find a number x so that the ratio of x to 49 is the same as the ratio of 3 to 21, you can first write the following equation.
X/49 = 3/21

You can then cross multiply to get
21x = (3)(49) and finally you can solve for x to get x = 147/21 = 7

Question 46

Define percent

Answer 46

The term percent means per hundred, or hundredths. Percents are ratios that are often used to represent parts of a whole, where the whole is considered as having 100 parts. Percents can be converted to fraction or decimal equivalents.