EVEN OR ODD ARITHMETIC RULES

Even Number :

An even number is an integer which is a multiple of 2.

Examples :

2, 4, 6, 8, 10

Odd Number :

An odd number is an integer which is not a multiple of 2.

Examples :

1, 3, 5, 7

Note :

In a two digit number or three digit number or four digit number, to check whether it is even or odd, look at the digit at the ones place.

If the digit at the one's place is 0 or 2 or 4 or 6 or 8, then the number is even.

Examples :

138, 28596, 325670

If the digit at the ones place is 1 or 3 or 5 or 7, then the number is odd.

Examples :

261, 39485, 150867

1. The sum or difference of two even numbers is always an even number.

4 + 8 = 12

16 - 10 = 6

2. The sum or difference of two odd numbers is always an even number.

3 + 7 = 10

13 - 7 = 6

3. The sum or difference of an odd number and an even number is always an odd number.

3 + 8 = 11

6 + 7 = 13

13 - 6 = 7

8 - 5 = 3

4. The product of two even numbers is always an even number.

2 x 6 = 12

5. The product of an even number and an odd number is always an even number.

3 x 6 = 18

4 x 7 = 28

6. The product of two odd numbers is always an odd number.

3 x 7 = 21

Addition

odd + odd = even

even + even = even

odd + even = odd

even + odd = odd

Multiplication

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

Rule :

odd + odd = even

Moreover,

9 + 49 = 58

(58 is an even number)

So, 9 + 49 is even.

Example 2 :

Is 36 + 120 even or odd?

Solution :

36 = even number

120 = even number

Rule : 

even + even = even

Moreover,

36 + 120 = 156

(156 is an even number)

So, 36 + 120 is even.

Example 3 :

Is 5 + 114 even or odd?

Solution :

5 = odd number

114 = even number

Rule :

odd + even = odd

Moreover,

5 + 114 = 119

(119 is an odd number)

So, 5 + 114 is odd.

Example 4 :

Is 146 + 289 even or odd?

Solution :

146 = odd number

289 = even number

Rule :

even + odd = odd

Moreover :

146 + 289 = 435

(435 is an odd number)

So, 146 + 289 is odd.

Example 5 :

Is 120 x 146 even or odd?

Solution :

120 = even number

146 = even number

Rule :

even x even = even

Moreover,

120 x 146 = 17520

(17520 is an even number)

So, 17520 is even.

Example 6 :

Is 121 x 14 even or odd?

Solution :

121 = odd number

14 = even number

Rule :

odd x even = even

Moreover,

121 x 14 = 1694

(1694 is an even number)

So, 121 x 14 is even.

Example 7 :

Is 151 x 17 even or odd?

Solution :

151 = odd number

17 = odd number

Rule :

odd x odd = odd

Moreover,

151 x 17 = 2567

(2567 is an odd number)

So, 151 x 17 is odd.

Example 8 :

Is 160 x 7 even or odd?

Solution :

160 = even number

7 = odd number

Rule : 

even x odd = even

Moreover,

160 x 7 = 1120

(1120 is an even number)

So, 160 x 7 is even.

Example 9 :

Is 2x2 even or odd?

Solution :

In 2x2, 'x' is a variable and it can take any value.

Whatever value we substitute for x, when x2 is multiplied by 2, it becomes a multiple of 2.

So, 2x2 is even.

Example 10 :

Is 2x2 + 3 even or odd?

Solution :

From the above example 9, it is clear that 2xis even.

And 3 is an odd number.

2x2 + 3 = even + odd

Rule :

even + odd = odd

So, 2x2 + 3 is odd.

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