Elementary Algebra_Chapter 1 Flashcards
Real Numbers are made up by what types of numbers?
Rational Numbers and Irrational Numbers
Natural Numbers
AKA Counting Numbers = 1, 2, 3, 4
Ellipsis
The dots in braces that mean the pattern repeats forever. {1,2,3,4,….}
Whole Numbers
Adding ZERO (0) to the natural numbers gives you a set of whole numbers {0, 1, 2, 3, 4, …}
What is the only difference between NATURAL numbers and WHOLE numbers?
You added a ZERO (0) to the set
Integers
Adding the opposites of each natural number to the natural numbers. Ex. {3 + (-3) = 0
What is the Set of Integers for 3?
Ex. ( ..-3, -2, -1, 0, 1, 2, 3,…)
Define Rational Numbers
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.
Quotient
The answer after you divide one number by another
dividend ÷ divisor = quotient
Example: in 12 ÷ 3 = 4, 4 is the quotient
Dividend
The amount that you want to divide up.
dividend ÷ divisor = quotient
Example: in 12 ÷ 3 = 4, 12 is the dividend
Divisor
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.
ALL FRACTIONS that can’t be reduced to INTEGERS are also RATIONAL NUMBERS. T or F
TRUE (Ex. (-4)/3, 1/5, 97/98)
Terminating Decimal
A number in which the decimal ends or terminates (ex. 5.0, -3.25, 4.6789, etc)
Repeating Decimal
Number in which the decimal keeps repeating a pattern (ex. 1.3333 also written as 1.3 with line over the 3)
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?
No (Will be understood later pg 4)
Which numbers are included in RATIONAL NUMBERS?
Integers, Fractions, Decimal Representations of Integers and Fractions
Define Irrational Numbers
Any NON repeating, NON Terminating Decimal (Ex. 3.14159265358979 Pi)
Pi = π
3.14159265358979 (3.14) known as the most famous irrational number
Define and give example of an EXPONENT.
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
What term _________ is also known as Powers or Indices?
AKA..EXPONENTS
Word example for an Exponent.
53 could be called “5 to the third power”, “5 to the power 3” or simply “5 cubed”
What is 2^4?
An exponent_ it is the same as 2 to 4th power
Square Roots of NON Perfect Squares are examples of ________ ___________.
Irrational Numbers
Give an example of a Square root of a non perfect square that are Irrational Numbers
√5, √10, √31 are examples (They never repeat and or terminate which means they are irrational numbers and an example of this.
Give an example of perfect Square Roots that are Rational Numbers
√4=2, √9 = 3, √25 =5 because they become whole numbers so the are ____ and ____ square roots
Define RADICAL.What symbol is used for this term?
An expression that has a square root, cube root, etc. The symbol is √ (ex. √1, √4)
Define SQUARE ROOT.
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)
Define CUBE ROOT.
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
If a Radical isn’t a perfect square then it is known as a Rational Number. T or F
False
*If a perfect square appears under a Radical, then we have a __________ __________.
Rational Number (ex. 1, 4, 9, 16, 25, 36,…)
Identify whether the following is a member of the set of natural numbers, whole numbers, integers, rational numbers, irrational numbers or real numbers: (-10)
-10 is a member of the set of integers, rational numbers and real numbers
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)
-3.5 is a member of the rational and real numbers
Identify whether the following is a member of the set of natural numbers, whole numbers, integers, rational numbers, irrational numbers or real numbers: 10
10 is a member of natural numbers, whole numbers, integers, rational and real numbers
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
The fraction 5/3 is a member of the rational and real numbers
Identify whether the following is a member of the set of natural numbers, whole numbers, integers, rational numbers, irrational numbers or real numbers: √50
√50 is an irrational number since 50 is not a perfect square and it is a real number
AKA Opposites (re: Absolute Values)
Additive Integers (same number with the opposite sign)
______, ________, and ________ can have opposites.
Decimals, Fractions and Irrational Numbers can have Opposites
What would be the answer? - |-5|
= -5
Absolute Value
means… only how far a number is from zero:
What is the rule for Adding Integers (any natural number with (0) added to it)
With Different Signs (Use Subtraction)
With SAME Signs (Add and keep signs)
What is the rule for Subtracting Integers (any natural number with (0) added to it)
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
RULE: for adding and subtracting multiple integers
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
When ABSOLUTE VALUE numbers are integrated into adding and subtracting MULTIPLE integers what is the first rule? ex |6|
Switch the signs/opposite of the value therefore:
|-6| = 6
A negative times a negative equals a ______number
POSITIVE
(-) x (-) =
+
An even number of NEGATIVE signs when Multiplying or Dividing Integers = _______ sign
POSITIVE (answer will be positive if there are 2,4,6.. number of negative signs)
An odd number of NEGATIVE signs when Multiplying or Dividing Integers = ________ sign
NEGATIVE (answer will be negative if there are 1,3,5…number of negative signs)
