Recognizing Zero and One

SPECIAL PROPERTIES OF $\,0\,$ and $\,1$

For all real numbers $\,x\,$, $\,x + (-x) = 0\,$.
A number added to its opposite always gives zero.
The opposite of a number is also called the additive inverse.

For all real numbers $\,x\,$, $\,x\cdot 0 = 0\,$.
Any number multiplied by zero gives zero.

For all nonzero real numbers $\,x\,$, $\,\displaystyle\frac{x}{x} = x\cdot\frac{1}{x} = 1\,$.

A nonzero number divided by itself (or multiplied by its reciprocal) always gives one.

The number $\,\frac{1}{x}\,$ is called the reciprocal of $\,x\,$ or the multiplicative inverse of $\,x\,$.
Multiplying a number by its reciprocal gives the number $\,1\,$.
Every nonzero number has a reciprocal; zero does not have a reciprocal.

Be on the lookout for these special names for zero and one!

EXAMPLES:

Decide if the given number is $\,0\,$, $\,1\,$, or a different number:

$\displaystyle\frac13 + (-\frac 13)$	Answer: $\,0\,$
$\displaystyle 0\cdot\frac 13$	Answer: $\,0\,$
$\displaystyle -2\cdot \frac{-1}2$	Answer: $\,1\,$
$\displaystyle\frac{1/7}{1/7}$	Answer: $\,1\,$
$\displaystyle 3\bigl(-\frac13\bigr)$	Answer: not $\,0\,$, and not $\,1$

Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Writing Fractions in Simplest Form

(an even number, please)