Even numbers

Here you will learn about even numbers, including examples of even numbers, even numbers on a number line and a number chart, and properties of even numbers.

Students will first learn about even numbers as part of operations and algebraic thinking in 2nd grade. They expand upon their knowledge of even numbers in 3rd grade when they identify arithmetic patterns and properties of numbers.

What are even numbers?

Even numbers are whole numbers that are multiples of 2. This means that every even number is divisible by 2 with no remainders.

The last digit of an even number (the digit in the ones place), is always 0, 2, 4, 6, or 8. The smallest even number is zero.

Even numbers are the opposite of odd numbers, which are not divisible by 2 without remainders. An odd number’s last digit is 1, 3, 5, 7, or 9.

For example,

To identify an even number, you can look at the last digit, use a number line, or use a number chart.

Last digit	The last digit of a number, or the digit in the ones place, will tell you if it is even or odd. The last digit of an even number will always be \bf{0, 2, 4, 6,} or \bf{8} . 1,597,631,58\underline{6} In this number, the last digit is 6, so it is an even number.
Number line	Start with a number whose last digit is 0, 2, 4, 6, or 8 and jump every other number, or count by twos.
Number chart	On a number chart each column that begins with 2, 4, 6, 8, or 10 includes even numbers. This chart shows a list of even numbers between 1 and 100.

Properties of even numbers and odd numbers

• Property of addition
  • If you add an even number to an even number, the sum will always be an even number. For example, 8 + 4 = 12 .
  • If you add an even number to an odd number, the sum will always be an odd number. For example, 8 + 3 = 11 .
  • If you add an odd number to an odd number, the sum will always be an even number. For example, 5 + 3 = 8 .

• Property of subtraction
  • If you subtract an even number from an even number, the difference will always be an even number. For example, 16-10 = 6 .
  • If you subtract an even number from an odd number or an odd number from an even number, the difference will always be an odd number. For example, 16-9 = 7; 17-10 = 7 .
  • If you subtract an odd number from an odd number, the difference will always be an even number. For example, 9-5 = 4 .

• Property of multiplication
  • If you multiply an even number by an even number, the product will always be an even number. For example, 4 \times 2 = 8.
  • If you multiply an even number by an odd number, the product will always be an even number. For example, 4 \times 5 = 20.
  • If you multiply an odd number by an odd number, the product will always be an odd number. For example, 3 \times 5 = 15.

Groups of objects

• To determine if a group of objects has an even number of objects or an odd number of objects, group the objects into pairs or equal groups of 2. If each object can be grouped into a pair, there is an even number of objects. If there is one object left over after pairing, there is an odd number of objects.

For example,

Since all of the objects in this group can be grouped into pairs, there is an even number of objects.	After grouping the objects into pairs, there is one left over. Therefore, there is an odd number of objects in this group.

What are even numbers?

Common Core State Standards

How does this relate to 2nd grade and 3rd grade math?

• Grade 2 – Operations and Algebraic Thinking (2.OA.3)
  Determine whether a group of objects (up to 20 ) has an odd or even number of members, for example, by pairing objects or counting them by 2 s; write an equation to express an even number as a sum of two equal addends.

• Grade 3 – Operations and Algebraic Thinking (3.OA.9)
  Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

How to identify even numbers

In order to identify even numbers:

1. Look at the last digit, or the digit in the ones place. If the digit is \bf{0, 2, 4, 6,} or \bf{8,} the number is even.
2. Use this strategy to answer the question.

In order to determine if the answer to an equation will be an even number:

1. Recall the properties of addition, subtraction, or multiplication for even numbers.
2. Apply the correct property.

In order to determine if there is an even number of objects in a group:

1. Group the objects into pairs.
2. If all objects can be grouped into pairs, there is an even number of objects. If there is one left over, there is an odd number of objects.

Even numbers examples

Example 1: identifying even numbers

True or false: 754 is an even number.

1. Look at the last digit, or the digit in the ones place. If the digit is \bf{0, 2, 4, 6,} or \bf{8,} the number is even.

The last digit, or the digit in the ones place, is 4.

2Use this strategy to answer the question.

Since the last digit in 754 is 4, it is an even number, so the statement is true.

Example 2: identifying even numbers

List all even numbers between 45 and 55.

Example 3: identifying even numbers

Look at the list of numbers. Which numbers are even?

95, 236, 148, 300, 721, 688, 177, 533, 339, 410

Look at the last digit, or the digit in the ones place. If the digit is \bf{0, 2, 4, 6,} or \bf{8,} the number is even.

Example 4: apply properties of even numbers

Lincoln is subtracting an even number from an even number. He thinks the difference will be an even number, but his friend Beth says it will be odd. Who is correct?

Recall the properties of addition, subtraction, or multiplication for even numbers.

Example 5: apply properties of even numbers

Maria solves the following equation:

725,984 + 539,046 = 1,265,031

Her friend glances at the equation and tells her it’s incorrect. How does her friend know this is incorrect?

Recall the properties of addition, subtraction, or multiplication for even numbers.

Example 6: determine if a group of objects is even

Look at the objects in the square. Is there an even number of objects?

Group the objects into pairs.

Teaching tips for even numbers

• Hang a number chart, or hundreds chart, in your classroom with even numbers highlighted.

• Provide worksheets that require students to find even numbers between any given numbers. For example, instead of always starting at 0, give them a starting number of 76 and ask them to find the even numbers through 100.

Easy mistakes to make

• Thinking that zero is not an even number
  Zero and all numbers ending in zero are even numbers. This is because if you divide zero by 2, the quotient is zero, which is an integer. Therefore, it fits the definition of an even number. There are also many multiples of 2 that end in zero such as 10, 20, 30, and so on.

• Thinking that fractions and decimals can be even numbers
  Only integers (whole numbers and their corresponding negative numbers) can be even numbers. Students may think that a number such as 1.52 is an even number because its last digit is a 2. However, this is not the case as fractions and decimals can not be even numbers or odd numbers.

Related types of numbers lessons

• Types of numbers
• Irrational numbers
• Absolute value
• Prime numbers
• Natural numbers
• Rational numbers
• Odd numbers
• Number sets
• Prime and composite numbers
• Integers
• Whole numbers

The next lessons are

• Rounding numbers
• Factors and multiples
• Fractions
• Number patterns

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