Even and Odd

Even and odd are two ways of classifying whole numbers according to whether they can be divided into two equal groups without a remainder. An even number can be written as 2 multiplied by a whole number. Examples include 0, 2, 4, 6, 8, and 10. If we have 8 objects, we can arrange them into two groups of 4, so 8 is even. An odd number cannot be divided into two equal groups of whole objects without leaving one object over.

Numbers such as 1, 3, 5, 7, and 9 are odd. Looking at the last digit is a quick way to identify the type of a whole number written in the usual decimal system: numbers ending in 0, 2, 4, 6, or 8 are even, while those ending in 1, 3, 5, 7, or 9 are odd. These two categories follow a regular pattern as we count: even and odd numbers alternate.

Adding two even numbers gives an even number, and adding two odd numbers also gives an even number. When an even number and an odd number are added, the result is odd. Multiplying an even number by any whole number gives an even result, while multiplying two odd numbers gives an odd result. These patterns help children recognize numbers and check calculations.

Objects such as counters can make the idea easy to see: pairs can be formed for every object in an even group, whereas an odd group always has one object without a partner. Zero is an even number because it can be written as 2 × 0. Understanding even and odd numbers provides a useful foundation for arithmetic, patterns, multiplication, division, and later mathematical reasoning.