SOLUTION: why is it when a odd number is added to an odd number its always even, and when a odd number is multilied by a odd number its always odd.

Question 225400: why is it when a odd number is added to an odd number its always even, and when a odd number is multilied by a odd number its always odd.
Answer by RAY100(1637) (Show Source): You can put this solution on YOUR website!
Lets just look at the visual representations
.
Addition,,,,0+0=00,,000+000=000000,,00000+00000=0000000000,, in short when we increment an odd number on top of an odd number ,,,it will be even.
.
If this was multiplication this would be an odd number taken an even number of times,,,(2)
.
.
.
Multiplication,,,,is repeated addition,,,but
.
1*1 = 0,,,,,
.
.
3*3 = 000
,,,,,,000
,,,,,,000,,,,,,,,,or the summation of an odd number by and odd number of sets.
.
.
5*5,,,,=,,,,00000
,,,,,,,,,,,,00000
,,,,,,,,,,,,00000
,,,,,,,,,,,,00000
,,,,,,,,,,,,00000,,,,,again an odd number taken an odd number of times
.
.
Hopefully this "adds" some insight... Please review several times.
RELATED QUESTIONS
If a is an odd number, b an even number, and c an odd number, which expression will... (answered by Edwin McCravy,ikleyn)

What is the smallest number when added to an odd number makes it an even number ? (answered by ikleyn)

when a odd number is added to the product of two even numbers, the answer is even. what... (answered by stanbon)

Why is this statement true. The sum of an even and odd number is always an odd number.... (answered by CubeyThePenguin)

An odd number which when multiplied by 4 and added to the next odd number produces a... (answered by checkley79)

What is the smallest number which when added to an odd number makes the sum an even... (answered by richwmiller)

6*3*a=an even number. What is a? 1. an even number 2. an odd or even number (answered by Alan3354)

The product of a negative even number raised to an odd power and a positive odd number (answered by palanisamy)

when y is an odd number in an algebraic equation why does the always equal an even number (answered by Alan3354)