What are the properties of real numbers? these abbreviations for the properties of real numbers and...
Transcript of What are the properties of real numbers? these abbreviations for the properties of real numbers and...
Aim #6: What are the properties of real numbers?Homework: pg 18-19 #1-20Do Now: Simplify the following:
a) 3(x + 4) b) (x - 4)(2x - 1) c) (3x - 5y) 2
The order of the numbers
does NOT affect the sum.
The order of the numbers
does NOT affect the product.
The way the numbers are
paired does NOT affect the
sum.
The way the numbers are
paired does NOT affect the
product.
When zero is added to any
number, the number remains
unchanged.
Any number multiplied by 1
remains unchanged.
The sum of a number and its
additive inverse (also called
its opposite) is zero.
The product of any number
and its multiplicative inverse
(its reciprocal) is 1.
The product of zero and any
number is zero.
Multiplication can be
distributed over addition
or subtraction.
9-15-16
State the property illustrated in each example.
11. (3 + 5) - 3 = (5 + 3) - 3 12.
17. Fill in the circles with the correct property:
14. ab + cd = ab + dc 15. 1a = a 16. 0.5(2) = 1
13. π(0) = 0
Use these abbreviations for the properties of real numbers and complete the flow diagram.C+ for the commutative property of additionC× for the commutative property of multiplicationA+ for the associative property of additionA× for the associative property of multiplicationD for distributive property
Now, show a mathematical proof of the statement that (x + y) + z = (z + y) + x are equivalent expressions:
(x + y) + z Givenz + (x + y) _____________________________z + (y + x) ________________________
(z + y) + x ________________________
Is it true for all real numbers x, y, and z that (x + y) + z should equal (z + y) + x? Lets prove that (x + y) + z = (z + y) + x using a flow diagram and the commutative and associative properties.
(x + y) + z
The Distributive, Associative and Commutative Properties can be applied to algebraic expressions using variables that represent real numbers.
Two algebraic expressions are equivalent if we can convert one expression into the other by repeatedly applying the Commutative, Associative, and Distributive Properties and the properties of rational exponents to components of the first expression.
Sum It Up!