Introducing
Even and Odd Numbers

Identifying even and odd numbers is an important skill that children need to
help them understand our number system and aid in their preparation to group
whole number operations. It will also help prepare them to learn division,
prime numbers, and even square roots.

Some kids really struggle with understanding even and odd numbers. This
concept is important because it helps the student see a pattern within the
numbers. It is a precursor for skip counting, division, and prime numbers. So,
making sure kids understand this early on is important.

Even Numbers are integers that are divisible by 2, with no remainders. This
means that the number can be divided into pairs or two equal groups with no
leftovers. The examples of even numbers are 2, 6, 10, 20, 50, etc.

What is The Even Number
in Math?

A number that can be divided into two halves, i.e. into two equal parts.
That is called an even number. In other words, even numbers are exactly
divisible by 2. Which means that the remainder will be 0.

What are Even Numbers in General?

Whole numbers that have the digits 0, 2, 4, 6, or 8 in there one’s place are
even numbers. Even numbers always end up with the last digit as 0, 2, 4, 6, or
8. Some examples of even numbers are 2, 4, 6, 8, 10, 12, 14, and 16.

These are even numbers as these numbers can easily be divided by 2. It
should be noted that the smallest positive even natural number is 2. If you
pick a number that cannot be divided by 2,

it will be known as an odd number For Example- 1, 3, 5, 7, 9, etc.

How to Know If a Number
is Even or Odd?

To find out whether the given number is odd or even, you need to check the
number in one’s (or unit’s) place. That particular number in one’s place
will tell you whether the number is odd or even.

  • Even
    numbers end with 0, 2, 4, 6, 8
  • Odd
    Numbers end with 1, 3, 5, 7, 9

If the unit’s digit (or one’s digit) is 1, 3, 5, 7, or 9, then the number is
called an odd number. If the unit’s
digit is 0, 2, 4, 6, or 8, then the number is called an even
number
. These are the simple tricks to identify the numbers
whether they are even or odd.

Think about the following numbers 3, 845, and 917 which end with an odd
number i.e. 3, 5, and 7. Therefore, the given numbers 3, 845, and 917 are odd
numbers. Thus, those numbers are not even numbers. In the same way, 8 and 322
are even numbers as they end with 8 and 2.

Zero

Zero is an even number because there is nothing to pair and nothing is left
over. So, it means it is even. For mathematicians, zero is an even number
because any number that can be divided by two to create another whole number is
even. Zero passes this test because if you halve zero you get zero. We should
memorize 0,2,4,6,7, and 8 as even and 1, 3,5,7, and 9 as odd.

List of Even Numbers up to 100

The even numbers’ list up to 100 is given below:

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40,
42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80,
82, 84, 86, 88, 90, 92, 94, 96, 98, 100

Properties of Even Numbers

There are three important properties of even numbers which are given below:

First
Property: Property of Addition;
Adding an even and another even number will always result in an even
number

Example: Even + Even = Even, 14 + 6 = 20

Second Property: Property of Subtraction;
Subtracting an even number from another even number will always result in
an even number.

Example: Even – Even = Even, 16 – 6 = 10

Third Property: Property of Multiplication;
Multiplying an even number with another even number will always result in an
even number.

Example: Even × Even = Even, 6 × 4 = 24

Summary of Facts

The sum
of two or more even numbers is always even

Even
numbers when divided by 2 leave no remainder

Even
numbers are multiples of two

There
are no remainder. Yes, it’s true!

Even
numbers when multiplied by any number always result in an even number

The
product of two or more even numbers is always even

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The Property of Addition

  • When
    adding an even number and an odd number (or vice-versa), the resulting
    number will always be an odd number.

Examples:

9 + 4 =13

3 + 20 =23

Adding
an even number and another even number, will result in a number that is
always even.

Examples:

14+6 =20

Adding
an odd number and another odd number, will always be resulting in a number
that is even.

Examples:

11 + 13=24

The Property of Subtraction

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The Property of
Subtraction

  • If you
    subtract an even number from an even number, the answer is an even number
  • If you
    subtract an odd number from an odd number, the answer is an even number
  • If you
    subtract an even number from an odd number, the answer is an odd number
  • If you
    subtract an odd number from an even number, the answer is an odd number
  • Subtracting
    an even number from an odd number (or vice-versa), will result in a number
    that is always odd.

Examples:

7 – 4= 3

8 – 5= 3

Subtracting
an even number from another even number, will result in a number that is
always even.

Example:

12 – 8= 4

Subtracting
an odd number from another odd number, will result in a number that is
always even.

Examples:

23 –11 = 12

The Property of Multiplication

Multiplying
an even number and another even number will always result in an even
number.

Examples:

8 × 2= 16

10 × 6= 60

Multiplying
an even number and an odd number will always result in an even number.

Examples:

4 × 5= 20

8 × 5= 40

Multiplying
an odd number and another odd number will always give you an odd number.

Examples:

3 × 5= 15

3 × 5= 15

Even numbers between 40 and 60

Let us have a look at the list of even numbers
between 40 and 60.
42, 44, 46, 48, 50, 52, 54, 56, 58
Thus, there are a total of 9 even numbers between 40 and 60.
Go through the examples and solutions of the even number given below for a
better understanding.

Example 1:

Some Even Numbers Solved Problems

Are all whole numbers even?

Solution:

No, the list of whole numbers which are exactly divisible by two is called
the even numbers.

Example 2:

Write any four consecutive even numbers between the numbers 13 to 21.

Solution:

Let A = {13, 14, 15, 16, 17, 18, 19, 20, 21}

Therefore, 14, 16, 18, 20 are 4 consecutive even numbers.

Example 3:

Choose the correct answer. The sum of two even numbers

A) Is always an even number

B) Is always an odd number

C) is sometimes odd and sometimes even

d) Maybe neither odd nor even
Solution:

The correct answer is option a). Even number + Even number = Even number

Example4:
−24, 0, 6, and 38 are all even numbers?

Yes, all numbers -24, 0, 6, and 38 are even numbers.

Example 5: Is 2 an even number?

Yes, 2 is an even number since 2 is exactly divisible by 2.

Example 6: What are the even numbers between 1
and 50?

The list of even numbers between 1 and 50 are:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42,
44, 46, 48

Example 7: Which is the even prime number?

2 is the only even prime number.

Example 8: If you add two even numbers together, the answer is:

  • Always
    even
  • Always
    odd
  • Sometimes
    even and sometimes odd
  • 0
  • Even + Even = Even
    For Example, 2 + 6 = 8. So, the answer is always even.

Example 9: Which one of the following is even?

  1. 9 × 14
  2. 15 ×17
  3. 17 × 9
  4. 11 ×19

9 × 14=126 is even because odd × even = even
15 × 17=255 is odd because odd × odd = odd
17 × 9=153 is odd because odd × odd = odd
11 × 19=209 is odd because odd × odd = odd

so, the answer is A.

Example 10: Which one of the following is even?

  1. 5+16
  2. 22+12
  3. 13+44
  4. 11+4

The answer is B. Why?

How do you write the general form of an even number?

The general form of an even number is 2k, where k is an integer.

How do you write the general form of an even number?

Worksheets on Even Numbers

  • What
    are the even numbers from 1 to 100?
  • How to
    know if a number is even?
  • Can you
    guess the first even number?
  • Name
    the smallest even number?

This was all about Even Numbers.
We hope you enjoyed it. To practice even more on even numbers and learn about
other interesting mathematics’ concepts, keep visiting LearningMole.

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