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### Course: 3rd grade (Eureka Math/EngageNY)>Unit 3

Lesson 4: Topic D: Multiplication and division using units of 9

# Intro to even and odd numbers

This video explains the difference between even and odd numbers, and how they interact when added together. Even numbers are multiples of two and can be divided evenly, while odd numbers are not divisible evenly by two. You can easily identify whether a number is even or odd by looking at the ones place.

## Want to join the conversation?

• @ , Khan states that 0 is a multiple of two. Is zero not a multiple of every number?
• Yes, zero is a multiple of every number. That means that you get an even number whenever you multiply by zero, because you get zero.
Be careful though! You cannot say it the other way around and be correct. Two is not a multiple of zero. There is no way to multiply by zero and get two as a result.
• Does even and odd only apply to integers?
• In the context of real numbers, the answer to your question is yes -- the descriptions of "even" and "odd" apply only to integers.
A number n is even if and only if n = 2k, where k is an integer. This definition implies that if n is even then n is an integer, because if k is an integer, then 2k will be an integer.
A number n is odd if and only if n = 2k + 1, where k is an integer. This definition implies that if n is odd then n is an integer, because if k is an integer, then 2k + 1 will be an integer.

Example of an even number --
Consider the number 8
8 = 2*4
4 is an integer. Since 8 can be expressed as 2*4, this means 8 is even.

Example of a number that is not even --
Consider the number 2.2
2.2 = 2*(1.1)
1.1 is not an integer. Since 2.2 cannot be expressed as 2k, where k is an integer, this means 2.2 is not even.

Example of an odd number --
Consider the number -7
-7 = 2*(-4) + 1
-4 is an integer. Since 7 can be expressed as 2*(-4) + 1, this means 7 is odd.

Example of a number that is not odd --
Consider the number 13/10
13/10 = 2*(3/20) + 1
3/20 is not an integer. Since 13/10 cannot be expressed as 2k + 1, where k is an integer, this means 13/10 is not odd.

The concept of parity (the property of being even or odd) can apply to other objects in math as well. For instance, certain functions can be described as odd or even.
• How is 0 an even number?
(1 vote)
• Can't an Even + Odd become a even too?
• No, an even number added to an odd number is always an odd number. Try counting out in small numbers by yourself, and you'll notice the result.
• Sal said zero is a multiple of two but, it's also a multiple of 1 so, doesn't that make it odd and even?
• Yes, zero is a multiple of one, but it's considered even because (according to math's principles) all even numbers are two more than the last, and since one is one more than zero, it is not even, so you are half-right,Arbaaz.
• Will 190,398,928 be even?
• Just take a look at the last number. If it is 2, 4, 6, 8, or 0 the number is even. If it is 1, 3, 5, 7, or 9, then the number is odd. So in this case, the number is 8 so the number is even.
• Is 2.3 an even or an odd number? Is 3.2 even?
• Good question! We only talk about even and odd for whole numbers. Numbers like 2.3 and 3.2 are not whole numbers, they're decimals. So, they're neither even nor odd.
• is a negative number even if its multiple by 2 like -68?
• Yes, negative numbers can be even, because they are multiples of 2. Zero is also an even number.
• I have a questions that troubles me. You have made a reasonable case for claiming that the number '0' is even. You present your proof in in a rather mechanical way. On a deeper level however, that seems wrong. the symbol '0' represents 'Nothing'. How can 'nothing' be either even or odd? It is the absence of anything, if you have 0 apples, do you have an even or an odd number of apples? the answer is obvious, you have neither an even nor an odd number of apples, you have NO apples.
On the surface '0' can be classified as an even number but on a conceptual level I don't see how it can be even or odd.
what am I not understanding? Jim
• Well, it isn't really the case like the number 1, where it is neither prime nor composite, but rather because 0 is simply divisible by 2 (the definition of "even") and that it is also in between 2 odd numbers, so it just comes down to logic.
• Are Irrational numbers odd or even?