Is the product of an odd and an even numbers odd or even?
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To determine whether the product of an odd number and an even number is odd or even, we need to understand the properties of odd and even numbers.
An even number is any integer that is divisible by 2. These numbers can be expressed in the form of 2n, where n is an integer. For example, 2, 4, 6, and 8 are even numbers.
On the other hand, an odd number cannot be divided evenly by 2. Odd numbers can be written in the form of 2n + 1, where n is an integer. For example, 1, 3, 5, and 7 are odd numbers.
Now, let's consider the product of an odd number and an even number:
Odd number * Even number = (2n + 1) * (2m)
If we expand this equation, we get:
2n * 2m + 1 * 2m
Since both 2n and 2m are divisible by 2, we can rewrite the equation as:
(2 * n * 2 * m) + 1 * 2 * m
Simplifying further:
4(n * m) + 2m
Both terms in this equation are even numbers because they can be divided evenly by 2. Therefore, the product of an odd number and an even number is always an even number.