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mathxyz

Banned

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Properties of Real Numbers...Part 6

Multiplication by Zero

Let n = a number

Then n • 0 = 0 • n = 0

If the number 0 has no value, why multiply anything by zero?

Division Properties

Let n = a number

Then 0/n = 0.

Does this also work for terms?

For example,  0/(x - 5) = 0. What if x = 5?

I can also say n/n = 1, if n does not = 0.

Does this also apply to terms?

Say we have (x + 5)/(x + 5) = 1. What if x = -5?

Zero-Product Property

Let x and y be two numbers.

If x • y = 0, then I can say x = 0, or y = 0, or both.

Does this property apply to terms? If so, can you provide an example?

Last edited by mathxyz (2024-04-28 07:22:57)

Bob

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Registered: 2010-06-20

Posts: 10,456

Re: Properties of Real Numbers...Part 6

Yes. See previous post about the denominator not being zero.

This is used to solve quadratics ...(x-3)(2x + 5) = 0 means x = 3 or x = -5/2

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Banned

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Properties of Real Numbers...Part 6

Yes. See previous post about the denominator not being zero.

This is used to solve quadratics ...(x-3)(2x + 5) = 0 means x = 3 or x = -5/2

Bob

Yes, we set each factor to 0 and solve for x. I feel so much better returning to chapter 1. Section 3.6 applications kicked my back door.