PROPERTIES OF ZERO

Multiplication by Zero

Words :

The product of any number and zero is zero. 

Numbers : 

(1/5) ⋅ 0  =  0

0 ⋅ (-2)  =  0

Algebra : 

a ⋅ 0  =  0

0 ⋅ a  =  0

Zero Divided by Number

Words : 

The quotient of zero and any nonzero number is zero.

Numbers : 

0/5  =  0

0 ÷ (2/3)  =  0

Algebra : 

0/a  =  0    (a ≠ 0)

Division by Zero

Words : 

Division by zero is undefined. 

Numbers : 

8 ÷ 0  =  Undefined

-3/0  =  Undefined

Algebra : 

a ÷ 0  =  Undefined

a/0  =  Undefined

Additive Identity

If zero is added to any real number, the result is the same real number.

Examples :

7 + 0  =  5

-2 + 0  =  -2

0 + 3  =  0

0 + (-5)  =  0

In general, for any real number a,

a + 0  =  a

0 + a  =  0

Therefore, zero is the additive identity for real numbers.

Multiplying and Dividing with Zero

Multiply or divide if possible.

Example 1 :

0 ÷ 15.238 

Solution :

=  0 ÷ 15.238

Here, zero is divided by a nonzero number. 

The quotient of zero and any non zero number is zero. 

=  0

Example 2 :

259¼ ÷ 0

Solution :

=  259¼ ÷ 0

Here, nonzero number is divided zero. 

Division by zero is undefined.

=  undefined

Example 3 :

5 ⋅ 0

Solution :

=  5 ⋅ 0

Here, a number is multiplied by zero.

The product of any number and zero is zero.

=  0

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