Even numbers are integers that can be divided by 2 without leaving a remainder. This means that when you divide an even number by 2, the result is always a whole number.

Examples of even numbers include 0, 2, 4, 6, 8, 10, and so on.

Characteristics of Even Numbers:

1. Divisibility by 2: If you can divide a number by 2 and get another whole number, then the number is even. For instance, 8 divided by 2 equals 4, which is a whole number, so 8 is even.
2. Last Digit: In the decimal system, a number is even if its last digit is 0, 2, 4, 6, or 8.
3. For example, 14 ends in 4, so it is even.

Visual Representation of Even Numbers:

Let’s use images to make this clearer. Imagine you have a certain number of objects, and you want to see if you can split them into two equal groups.

Example 1: 6 Objects

• 6 Objects:
• 🍎🍎🍎🍎🍎🍎
• Split into two equal groups:
• 🍎🍎🍎 🍎🍎🍎

Since you can split 6 objects into two equal groups of 3, 6 is an even number.

Example 2: 7 Objects

• 7 Objects:
• 🍏🍏🍏🍏🍏🍏🍏

• Attempt to split into two equal groups:
• 🍏🍏🍏🍏 🍏🍏🍏

Here, you have one leftover object when you try to split 7 into two equal groups, so 7 is not an even number; it’s odd.

Number Line Representation:

On a number line, even numbers are evenly spaced and always occur every second number. Here is a number line showing some even numbers:

0 1 2 3 4 5 6 7 8 9 10
|–|–|–|–|–|–|–|–|–|–|

The even numbers on this line are 0, 2, 4, 6, 8, and 10.

More Examples:

• 10 Objects:
• 🍓🍓🍓🍓🍓🍓🍓🍓🍓🍓
• Split into two equal groups:
• 🍓🍓🍓🍓🍓 🍓🍓🍓🍓🍓

10 is an even number because it can be split into two equal groups of 5.

• 12 Objects:
• ⚽⚽⚽⚽⚽⚽⚽⚽⚽⚽⚽⚽
• Split into two equal groups:
• ⚽⚽⚽⚽⚽⚽ ⚽⚽⚽⚽⚽⚽

12 is an even number because it can be split into two equal groups of 6.

Conclusion:

Even numbers are those that can be divided into two equal parts without leaving any remainder. They have distinctive properties and patterns that make them easy to identify. With the above visual and numerical explanations, understanding even numbers becomes straightforward and engaging.