Why is 10-0 equals 10 but 0 divided by 10 equal 0?

Answer 1

0 is something called the additive identity: If you add (or subtract) it from something, the something remains unchanged.

It is also something called the multiplicative zero (sounds obvious doesn't it) in that multiplying something by it makes it equal to zero. Dividing 0 by 10 is the same as multiplying 0 with 1/10 . Therefore it makes it zero, just like anything else multiplied by zero. Simple!

Especially "

The following are some basic (elementary) rules for dealing with the number 0. These rules apply for any real or complex number x, unless otherwise stated.

• Addition: x + 0 = 0 + x = x. That is, 0 is an identity element (or neutral element) with respect to addition.
• Subtraction: x − 0 = x and 0 − x = −x.
• Multiplication: x · 0 = 0 · x = 0.
• Division: 0⁄x = 0, for nonzero x. But x⁄0 is undefined, because 0 has no multiplicative inverse (no real number multiplied by 0 produces 1), a consequence of the previous rule; see division by zero.
• Exponentiation: x0 = x/x = 1, except that the case x = 0 may be left undefined in some contexts; see Zero to the zero power. For all positive real x, 0x = 0.

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