Question

Multiply:\[0\] by\[ - 23\].

Answer 1

Hint: Here, in the given question, we are asked to multiply \[0\] by \[ - 23\]. We will first understand the number zero in detail. Because zero is something special, it has unique properties than other numbers. And then we will use the zero property of multiplication to reach the final answer.

Complete step-by-step solution:
Given problem: multiply: \[0\] by \[ - 23\]
Zero: It is a special number. If we say, there are zero things; it means there are no things at all. It is the only number that is neither positive nor negative, neither prime number nor composite number. It is not a unit but a neutral number.
Peano arithmetic gives an axiom for multiplication:
\[x \times 0 = 0\]
According to this axiom, the product of any real number and zero will always be zero.
Hence, using this axiom, we get,
\[0 \times \left( { - 23} \right) = 0\]
Additional information: Brahmagupta proposed the rules for arithmetic involving zero and negative numbers in the seventh century. Rules given by him for addition which involve zero:- “The sum of zero and a negative number is negative, the sum of zero and a positive number is positive and the sum of zero and zero is zero.” Rules given by him for subtraction which involve zero:- “A negative number subtracted from zero is positive, a positive number subtracted from zero is negative, zero subtracted from a positive number is positive, zero subtracted from a negative number is negative, and zero subtracted from zero is zero.”

Note: Zero is the one and only number having so many names such as nought, naught, nil, zilch and zip. No doubt, zero means nothing but in today’s world it’s difficult to imagine mathematics without zero. Without the concept of zero as a number or as a digit, none of mathematics would be possible.