Even or odd: arithmetic rules

key notes:

Even Number:

An even number is any integer that is exactly divisible by 2, meaning there is no remainder when divided by 2.

Examples of even numbers: 2, 4, 6, 8, 10, …

Odd Number:

An odd number is any integer that is not divisible by 2 without leaving a remainder

Examples of odd numbers: 1, 3, 5, 7, 9, …

A simple addition or subtraction may reveal whether the resulting total or difference is odd or even, provided you are familiar with the Even or Odd arithmetic rules.

even − even = even
odd − odd = even
even − odd = odd
odd − even = odd
even+even = even
odd + odd = even
even+odd = odd
odd+even = odd
even × even = even
odd × odd = odd
even × odd = even
odd × even = even
even ÷ odd = even
odd ÷ odd = odd
Examplearithmetic rules
56+8 even + even = even [64]
79+10odd + even = odd [89]
55+5odd + odd = even [60]
12+5even + odd = odd [17]
10-2even – even = even [8]
88-5even – odd = odd [83]
97-17odd – odd = even [80]
77-12odd – even = odd [65]
86+0even + 0 = even [80]
86-0even – 0 = even [80]
55+0odd + 0 = odd [55]
55-0odd – 0 = odd [55]
12×2even × even = even [24]
7×5odd × odd = odd [35]
10×7even × odd = even [70]
5×4odd × even = even [20]
10÷5even ÷ odd = even [2]
15÷3odd ÷ odd = odd [3]

Learn with an example

▶️ Is 6 + 90 even or odd?

  • even
  • odd

6 is even. 90 is even.

Use the rule:
even + even = even

6 + 90 is even.

Now check your answer by doing the maths.

6 + 90 = 96

Yes, the answer is even. 96 ends in a 6, which makes it even.

▶️ When you divide 21 by 7, you get a whole number. Is this number even or odd?

  • even
  • odd

21 is odd. 7 is odd.

Use the rule:
odd ÷ odd = odd

21 ÷ 7 is odd.

Now check your answer by doing the maths.

21 ÷ 7 = 3

Yes, the answer is odd. 3 is an odd number.

▶️ Is 85 − 13 even or odd?

  • even
  • odd

85 is odd. 13 is odd.

Use the rule:
odd − odd = even

85 − 13 is even.

Now check your answer by doing the maths.

85 − 13 = 72

Yes, the answer is even. 72 ends in a 2, which makes it even.

Let’s practice!