**Even or odd arithmetic rules :**

Using even or odd arithmetic rules we can easily evaluate an algebraic expression.

What is odd number ?

An odd number is an integer which is not a multiple DIVISIBLE of two. Examples 1, 3, 5, 7 ..........

What is even number ?

An even number is an integer which is "evenly divisible" by two. Examples 2, 4, 6, 8 ..........

The terms “even number” and “odd number” are only used for whole numbers and their opposites (additive inverses).

- The sum of two odd numbers or even numbers is even
- The sum of odd and even numbers or even and odd numbers is odd

- The product two odd numbers is odd
- The product of two even numbers or the product even and odd number is even

Odd + Odd = Even Even + Even = Even Odd + Even = Odd Even + odd = Odd |
Odd x Odd = Odd Even x Even = even Odd x even = even Even x odd = even |

**Example 1 :**

Is 9 + 49 even or odd?

**Solution :**

9 = odd number

49 = odd number

Applying the rule,

Odd + Odd = Even

Hence, 9 + 49 is even.

We can do this problem in another way also,

9 + 49 = 58 (which is divisible by 2)

Hence, 9 + 49 is even.

**Example 2 :**

Is 36 + 120 even or odd?

**Solution :**

36 = even number

120 = even number

Applying the rule,

Even + Even = Even

Hence, 36 + 120 is even.

We can do this problem in another way also,

36 + 120 = 156 (which is divisible by 2)

Hence, 36 + 120 is even.

**Example 3 :**

Is 5 + 114 even or odd?

**Solution :**

5 = odd number

114 = even number

Applying the rule,

Odd + Even = odd

Hence, 5 + 114 is odd.

We can do this problem in another way also,

5 + 114 = 119 (which is not divisible by 2)

So, 5 + 114 is odd.

**Example 4 :**

Is 146 + 289 even or odd?

**Solution :**

146 = odd number

289 = even number

Applying the rule,

Even + Odd = odd

Hence, 146 + 289 is odd.

We can do this problem in another way also,

146 + 289 = 435 (which is not divisible by 2)

So, 146 + 289 is odd.

**Example 5 :**

Is 120 x 146 even or odd?

**Solution :**

120 = even number

146 = even number

Applying the rule,

Even x Even = Even

Hence, the product of 120 x 146 is even.

By applying the rule, we got the answer easily. If we want to use the alternate method then we have to multiply 120 and 146 and check whether the answer is divisible 2 or not.

Since this is the longer way, we may do this kind of problem using the above rule.

**Example 6 :**

Is 121 x 14 even or odd?

**Solution :**

121 = odd number

14 = even number

Applying the rule,

Odd x Even = Even

Hence, the product of 121 x 14 is even.

**Example 7 :**

Is 5 x 7 even or odd?

**Solution :**

5 = odd number

7 = odd number

Applying the rule,

Odd x Odd = Odd

Hence, the product of 5 x 7 is odd.

**Example 8 :**

Is 160 x 7 even or odd?

**Solution :**

160 = even number

7 = odd number

Applying the rule,

Even x Odd = Even

Hence, the product of 160 x 7 is even.

After having gone through the stuff given above, we hope that the students would have understood "Even or odd arithmetic rules".

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