Elementary Algebra_Chapter 1

Question 1

Real Numbers are made up by what types of numbers?

Answer 1

Rational Numbers and Irrational Numbers

Question 2

Natural Numbers

Answer 2

AKA Counting Numbers = 1, 2, 3, 4

Question 3

Ellipsis

Answer 3

The dots in braces that mean the pattern repeats forever. {1,2,3,4,….}

Question 4

Whole Numbers

Answer 4

Adding ZERO (0) to the natural numbers gives you a set of whole numbers {0, 1, 2, 3, 4, …}

Question 5

What is the only difference between NATURAL numbers and WHOLE numbers?

Answer 5

You added a ZERO (0) to the set

Question 6

Integers

Answer 6

Adding the opposites of each natural number to the natural numbers. Ex. {3 + (-3) = 0

Question 7

What is the Set of Integers for 3?

Answer 7

Ex. ( ..-3, -2, -1, 0, 1, 2, 3,…)

Question 8

Define Rational Numbers

Answer 8

A number that can be written as a QUOTIENT of 2 integers, or as a fraction. Ex. an integer can be written as a fraction by placing a 1 in the denominator.

Question 9

Quotient

Answer 9

The answer after you divide one number by another
dividend ÷ divisor = quotient
Example: in 12 ÷ 3 = 4, 4 is the quotient

Question 10

Dividend

Answer 10

The amount that you want to divide up.
dividend ÷ divisor = quotient
Example: in 12 ÷ 3 = 4, 12 is the dividend

Question 11

Divisor

Answer 11

A number that divides the integer evenly (no remainder).

Example: 3 is a divisor of 12, because 12/3 = 4
But 5 is NOT a divisor of 12, because 12/5 = 2 with a remainder of 2

The divisor must also be an integer (no fractional part).

A divisor is also a factor of the original integer.

Question 12

ALL FRACTIONS that can’t be reduced to INTEGERS are also RATIONAL NUMBERS. T or F

Answer 12

TRUE (Ex. (-4)/3, 1/5, 97/98)

Question 13

Terminating Decimal

Answer 13

A number in which the decimal ends or terminates (ex. 5.0, -3.25, 4.6789, etc)

Question 14

Repeating Decimal

Answer 14

Number in which the decimal keeps repeating a pattern (ex. 1.3333 also written as 1.3 with line over the 3)

Question 15

Rational Numbers also include positive and negative fractions that do not reduce to integers. Do you include fractions that have Zero (0) in their respective denominators?

Answer 15

No (Will be understood later pg 4)

Question 16

Which numbers are included in RATIONAL NUMBERS?

Answer 16

Integers, Fractions, Decimal Representations of Integers and Fractions

Question 17

Define Irrational Numbers

Answer 17

Any NON repeating, NON Terminating Decimal (Ex. 3.14159265358979 Pi)

Question 18

Pi = π

Answer 18

3.14159265358979 (3.14) known as the most famous irrational number

Question 19

Define and give example of an EXPONENT.

Answer 19

The exponent of a number says how many times to use the number in a multiplication.

In 82 the “2” says to use 8 twice in a multiplication,
so 82 = 8 × 8 = 64

Question 20

What term _________ is also known as Powers or Indices?

Answer 20

AKA..EXPONENTS

Question 21

Word example for an Exponent.

Answer 21

53 could be called “5 to the third power”, “5 to the power 3” or simply “5 cubed”

Question 22

What is 2^4?

Answer 22

An exponent_ it is the same as 2 to 4th power

Question 23

Square Roots of NON Perfect Squares are examples of ________ ___________.

Answer 23

Irrational Numbers

Question 24

Give an example of a Square root of a non perfect square that are Irrational Numbers

Answer 24

√5, √10, √31 are examples (They never repeat and or terminate which means they are irrational numbers and an example of this.

Question 25

Give an example of perfect Square Roots that are Rational Numbers

Answer 25

√4=2, √9 = 3, √25 =5 because they become whole numbers so the are ____ and ____ square roots

Question 26

Define RADICAL.What symbol is used for this term?

Answer 26

An expression that has a square root, cube root, etc. The symbol is √ (ex. √1, √4)

Question 27

Define SQUARE ROOT.

Answer 27

The square root of a number is a value that, when multiplied by itself, gives the number.

Example: 4 × 4 = 16, so the square root of 16 is 4.

The symbol is √

Another example: √36 = 6 (because 6 x 6 = 36)

Question 28

Define CUBE ROOT.

Answer 28

The cube root of a number is a special value that, when used in a multiplication three times, gives that number.

Example: 3 × 3 × 3 = 27 so the cube root of 27 is 3

Question 29

If a Radical isn’t a perfect square then it is known as a Rational Number. T or F

Answer 29

False

Question 30

*If a perfect square appears under a Radical, then we have a __________ __________.

Answer 30

Rational Number (ex. 1, 4, 9, 16, 25, 36,…)

Question 31

Identify whether the following is a member of the set of natural numbers, whole numbers, integers, rational numbers, irrational numbers or real numbers: (-10)

Answer 31

-10 is a member of the set of integers, rational numbers and real numbers

Question 32

Identify whether the following is a member of the set of natural numbers, whole numbers, integers, rational numbers, irrational numbers or real numbers: (-3.5)

Answer 32

-3.5 is a member of the rational and real numbers

Question 33

Identify whether the following is a member of the set of natural numbers, whole numbers, integers, rational numbers, irrational numbers or real numbers: 10

Answer 33

10 is a member of natural numbers, whole numbers, integers, rational and real numbers

Question 34

Identify whether the following is a member of the set of natural numbers, whole numbers, integers, rational numbers, irrational numbers or real numbers: 5/3

Answer 34

The fraction 5/3 is a member of the rational and real numbers

Question 35

Identify whether the following is a member of the set of natural numbers, whole numbers, integers, rational numbers, irrational numbers or real numbers: √50

Answer 35

√50 is an irrational number since 50 is not a perfect square and it is a real number

Question 36

AKA Opposites (re: Absolute Values)

Answer 36

Additive Integers (same number with the opposite sign)

Question 37

______, ________, and ________ can have opposites.

Answer 37

Decimals, Fractions and Irrational Numbers can have Opposites

Question 38

What would be the answer? - |-5|

Answer 38

= -5

Question 39

Absolute Value

Answer 39

means… only how far a number is from zero:

Question 40

What is the rule for Adding Integers (any natural number with (0) added to it)

Answer 40

With Different Signs (Use Subtraction)

With SAME Signs (Add and keep signs)

Question 41

What is the rule for Subtracting Integers (any natural number with (0) added to it)

Answer 41

1) write the first number 2) Change the subtraction sign to an additional sign 3) Change the sign of the number that follows the subtraction sign..if positive change to negative and vice verse! 4) Add the numbers if signs are same and subtract if different (rules for addition) 5) KEEP THE SIGN OF THE LARGER NUMBER

Question 42

RULE: for adding and subtracting multiple integers

Answer 42

1) Convert all SUBTRACTION signs to ADDITION signs and then CHANGE the sign of the number that follows them 2) ADD all of the POSITIVE numbers 3) ADD all of the NEGATIVE numbers 4) SUBTRACT the two remaining numbers 5) KEEP the answer the sign of the LARGER number

Question 43

When ABSOLUTE VALUE numbers are integrated into adding and subtracting MULTIPLE integers what is the first rule? ex |6|

Answer 43

Switch the signs/opposite of the value therefore:

|-6| = 6

Question 44

A negative times a negative equals a ______number

Answer 44

POSITIVE

Question 45

(-) x (-) =

Answer 45

+

Question 46

An even number of NEGATIVE signs when Multiplying or Dividing Integers = _______ sign

Answer 46

POSITIVE (answer will be positive if there are 2,4,6.. number of negative signs)

Question 47

An odd number of NEGATIVE signs when Multiplying or Dividing Integers = ________ sign

Answer 47

NEGATIVE (answer will be negative if there are 1,3,5…number of negative signs)