Table of Contents
- 1 Why is the product of two odd numbers an odd number?
- 2 Is the product of any two odd numbers an odd number is it true for any two even numbers?
- 3 Is the product of two consecutive numbers odd even or sometimes odd and sometimes even why?
- 4 How do you find the product of two odd numbers?
- 5 How can I conclude that q × r results in an odd number?
- 6 Is 2 m + 1 even or odd?
Why is the product of two odd numbers an odd number?
When two odd numbers are multiplied together, the result is always an odd number. Because n and m are even, when we multiply two even numbers together, we always get an even number. Thus nm is even. However, when we then add one to an even number, the result will be an odd number.
Is the product of any two odd numbers an odd number is it true for any two even numbers?
Answer: For the product to be even, it has to have a factor of 2. Since you say the original numbers are odd, there is no factor of two in either of them, so the product cannot be even, and so must be odd.
Why is the product of 2 times any number is an even number?
EVEN NUMBERS can be looked at as any number (call it “n”), multiplied by 2. Therefore, all even numbers can be described as 2n. Therefore, any even number plus any other even number will always equal an even number (as the answer you get will always be some number multiplied by two).
Is the product of two consecutive numbers odd even or sometimes odd and sometimes even why?
Given two consecutive numbers, one must be even and one must be odd. Since the product of an even number and an odd number is always even, the product of two consecutive numbers (and, in fact, of any number of consecutive numbers) is always even.
How do you find the product of two odd numbers?
An odd number can be written in the form 2x + 1, where x is an integer. So two odd numbers can be represented by 2a +1 and 2b +1, the product would be: (2a + 1) (2b +1) = 4ab + 2a + 2b + 1 = which can be written as 2 (2ab + a +b) + 1, but 2ab +a + b represents some integer, so 2ab + a + b = x.
How do you prove two odd integers are consecutive?
For any Integer to be odd, it is not exactly divisible le by 2 and it can be described by the formula “ 2n + 1 “ where “ n “ is any integer. Let us therefore consider two odd integers, being ( 2n + 1 ) and ( 2n + 3 ). In this case, the two numbers are both odd and are consecutive.
How can I conclude that q × r results in an odd number?
I would then conclude that q × r results in an odd number, because 2 times an integer with one added to it is, by definition, an odd number. However, how can I conclude this? Is ( 2 m k + k + m) in fact an integer? How do I know if the product of any two integers is an integer; similarly, does adding any two integers yield another integer?
Is 2 m + 1 even or odd?
In order for 2 n to be even, n must be an integer which means that m cannot be an integer, and so 2 m + 1 cannot be odd. If it is an odd number, then m must be an integer, and so n cannot be an integer, and 2 n cannot be even.