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How do you use inductive reasoning to prove the product of an odd integer and an even integer will always be even?
The product of an odd and even number will always have 2 as a factor. Therefore, it will always be even.
Is the product of an odd integer and an even integer even?
Yes, the product of an odd integer and an even integer is always even. This is because an even integer can be expressed as 2 times some integer, and when multiplied by any other integer (odd or even), the result will still be a multiple of 2, thus making it even. For example, multiplying 3 (odd) by 4 (even) gives 12, which is even.
Can you prove The product of two integers is even if and only if at least one integer is even?
To prove this, we need to be able to prove two things:The product of two integers is always even if at least one integer is evenThe product of two integers is never even if neither integer is evenFirst, let's prove that the product of two integers is always even if at least one integer is even:Let's say that n is an even integer, and that k is some integer (even or odd). We want to prove that k*n has to be even. Since even is even, we can think of it as 2m, where m is some integer. In other words, n is equal to (2 + 2 + 2 + 2 ...) for however many twos it takes to get there.We can re-write k*n as k*2m. We can factor out a 2 to get:2*k*2m-1.Since we are multiplying an integer quantity by two, this proves that the quantity has to be divisible by 2, which, by definition, means that the number must be even.Now let's prove that the product of two integers is never even if neither integer is even. Let's call the two integers k and n. Since nither k and n are even, they must both be odd.k*n can be re-written as k*n - n + n, which can be factored into (k-1)n + n.Now we know that (k-1)n has to be even, since k-1 is even, and we have proved that a number times an even number is even above.So now we have an even number plus and odd number. We can re-write n as 2m + 1, where m is an integer. Since (k-1)n is even, that quantity can be written as 2p, where p is an integer.To recap so far, this means that we can say that if k and n are both odd:k*n = (k-1)n + n = 2p + 2m + 1.This can be re-written as 2p+m + 1. Since 2p+m is a multiple of two, it must be even, and an even number plus one must be odd, so the product of two odd numbers must be odd.
Is the product of two odd integers odd?
Yes the product of two odd integers is odd. The proof lies in recognizing that 2 times an integer is an even integer. Like, given two arbitrary integers a and b, 2a+1 and 2b+1 are odd. And the product of (2a+1)(2b+1) can be represented as 2c+1, where c might be even or odd - it doesn't matter. c = 2ab+a+b, in fact (check it out.) However, 2c+1 is clearly an odd integer.
What is the product of any two even integers?
Another even integer.
What is the product of an even number of negative integers?
A positive integer.
Is 3320 an even number?
Yes 3320 is an even number as the product of dividing it by 2 is an integer.
How is even times odd equal even?
In mathematics, an even number is defined as any integer that can be expressed as (2n), where (n) is an integer, while an odd number can be expressed as (2m + 1) for some integer (m). When you multiply an even number by any integer (even or odd), the result is still even, because the product will still have a factor of 2. Therefore, when you multiply an even number by an odd number, the product remains an even number. Thus, even times odd equals even.
Is it possible to prove the square of even number is a even number using direct proof?
Yes. Any even number can be expressed as 2x (where x is an integer). (2x)2 = 4x2. We don't know exactly what x2 is, and we don't need to know, because we know that the square of any integer is also an integer, and any integer multiplied by 4 is an even number.
What is The sum of an even integer and an even integer is?
Another even integer.
What category do the numbers 581116 all fit in to?
581116 is an even integer.581116 is an even integer.581116 is an even integer.581116 is an even integer.
Is -2 even integer or odd integer?
even integer.
