Unit 1 Test Flashcards
Natural (Numbers)
The set of natural numbers is compromised of the counting numbers. (1, 2, 3, 4, 5,..)
Whole (Numbers)
The set of whole numbers included the counting numbers and zero. (0, 1, 2, 3, 4 , 5,..)
Integers
The set of integers included whole numbers and their opposites. (…, -3, -2, -1, 0, 1, 2, 3..)
-No decimals and no fractions (Integers are rational)
Rational
A rational number is a number that can be expressed as a fraction, a divided by b a/b where a and b are both integers. Repeating decimals and terminating decimals (decimals that end) are rational. 5/1 10/2 30/6- 5 is rational!
Irrational
Irrational Numbers cannot be expressed as a fraction. These numbers will be non-terminating and non-repeating decimals. Ex, pie and 0.12345678910.. square root of a non perfect square.
What is the sum of two rational numbers? What is the sum of two irrational numbers? What is the sum of one irrational number and one rational number? What is the product of two irrational numbers? What is the product of two rational numbers? What is the product of one irrational number and one rational number?
The sum of two rational numbers is always a rational number. The sum of two irrational numbers is either a rational number or an irrational number. The sum of one irrational number and one rational number is an irrational number. The product of two irrational numbers is a rational number or an irrational number. The product of two rational numbers is a rational number. The product of one irrational number and one rational number is an irrational number.
What are “perfect numbers”? List the first 15 perfect squares and the first 5 perfect cubes.
“Perfect numbers” are when you multiply a counting number by itself a certain amount of times. The first 15 perfect squares are one, four, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225. The first five perfect cubes are one, 8, 27, 64, 125.
Square Root
The square root of a number is the number that will multiply by itself gives you the original number. For example the square root of 25 is 5. You know the symbol!
Cube Root
The cube root of a number is the the number that when used as a factor three times gives us the original number. For example the cube root of 8 is 2! You know the symbol!
Radical Expressions
An expression that uses a root, such as a sqaure root, cube root, etc..
Index
The index is the number that goes on the left side of the radical symbol.
Radicand
The radicand is the number inside the radical symbol.
If the index is not written, what is the index?
If the index is not written, the index is automatically a 2.
Commutative Property and ex
The commutative property of addition and a multiplication states that changing the order does not change the value. a + b = b + a, ab=ba
Associative Property and ex
The associative property of addition and multiplication states that changing the grouping does not change the value. (a + b)+ c = a + (b + c)
(ab)c = a(bc)
The Identity Property Of Addition and Multiplication and ex
The identity property of addition states that adding zero and any number does not change the value of the number. You get the identical problem you start with and zero is known as the identity element for addition. The identity property of multiplication states that when you multiply any number by one you will get the original number and one is known as the identity element for multiplication. a + 0 = a
(a)(1) = a
The Inverse Property Of Addition and Multiplication and ex
The inverse property of addition is the sum of any number and its additive inverse is 0, which is adding opposites. (The additive inverse are 0 pairs on an Expression mat) Ex, A+ (-A)= 0. The inverse property of multiplication is multiplying reciprocals. Ex, a x 1/a =1 and a+ (-a) = 0.
The Distributive Property
A sum can be multiplied by a factor by multiplying each addend
separately and then adding the products. (Simplifying and combine like terms) a(b + c) = ab + ac and a(b – c) = ab – ac
Equivalent Expressions
Equivalent expressions represent the same value for any value(s) substituted for the variables that they contain and look exactly the same one simplified.
Zero Product
Any term or number multiplied by zero is always zero. Ex, (a)(0) = 0.
What are like terms?
Like terms of an expression are terms that contain the same variable(s) raised to the same power.
