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Arithmetic With Even and Odd Numbers (Mathematics Lesson)

What Are Even and Odd Numbers?

A whole number (called an integer) is either an even or an odd number.
  • An even number is a whole number that can be divided exactly by 2.
  • An odd number is a whole number that cannot be divided exactly by 2.
The image below shows even and odd numbers on a number line.

Arithmetic With Even and Odd Numbers

Arithmetic means adding, subtracting, multiplying and dividing numbers.

Adding, subtracting, multiplying and dividing are examples of operations. They operate on two numbers.

The number that results from an operation will be even or odd depending on whether the two numbers we operate on are both even, both odd or one of each.

In this lesson, we are going to look at:

Adding Numbers

When both numbers are even or odd, the sum of the numbers is even.


2 (even) + 4 (even) = 6 (even)

1 (odd) + 3 (odd) = 4 (even)
When one number is even and the other odd, the sum of the numbers is odd.


2 (even) + 1 (odd) = 3 (odd)

3 (odd) + 4 (even) = 7 (odd)

Subtracting Numbers

When both numbers are even or odd, the difference of the numbers is even.


6 (even) - 4 (even) = 2 (even)

5 (odd) - 3 (odd) = 2 (even)
When one number is even and the other odd, the difference of the numbers is odd.


4 (even) - 3 (odd) = 1 (odd)

3 (odd) - 2 (even) = 1 (odd)

Multiplying Numbers

When at least one number is even, the product of the numbers is even.


2 (even) × 4 (even) = 8 (even)

2 (even) × 3 (odd) = 6 (even)

1 (odd) × 2 (even) = 2 (even)
Only when both numbers are odd is the product of the numbers odd.


3 (odd) × 5 (odd) = 15 (odd)

Dividing Numbers

When dividing two numbers, there is no guarantee that one number will divide exactly into the other. If it does not divide exactly, the result of the division (called the quotient) will not be a whole number and so will be neither even nor odd.

Even when a number does divide exactly into the other, so the quotient is a whole number, there are no simple rules, like that for adding, subtracting and multiplying.
  • An even number divided by an even number may be even or may be odd.


    8 (even) ÷ 4 (even) = 2 (even)
    6 (even) ÷ 2 (even) = 3 (odd)

  • An even number divided by an odd number is even.


    10 (even) ÷ 5 (odd) = 2 (even)

  • An odd number divided by an odd number will always be odd.


    21 (odd) ÷ 7 (odd) = 3 (odd)

  • An odd number cannot be divided by an even number to give a whole number. The quotient will be a fraction, which is neither even nor odd.
Interactive Test
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Here's a second test on arithmetic with even and odd numbers.
Here's a third test on arithmetic with even and odd numbers.
Top Tip

A Quick Way to See If a Number Is Even

A number is even if its last digit is 0, 2, 4, 6 or 8.

A Quick Way to See If a Number Is Odd

A number is odd if its last digit is 1, 3, 5, 7 or 9.