Here, you will practice simplifying fractions involving zero.
Any fraction with zero in the numerator
and a nonzero number in the denominator
equals zero.
For example:
$\displaystyle\,
\cssId{s10}{\frac{0}{5}}
\cssId{s11}{= \frac{0}{-3}}
\cssId{s12}{= \frac{0}{1.4}}
\cssId{s13}{= 0}\,$
Why is this?
Here are two different ways you can think about it:
Division by zero is not allowed,
and we say that such a fraction is not defined.
For example:
$\displaystyle\,\frac{5}{0}\,$ is not defined;
$\displaystyle\,\frac{0}{0}\,$ is not defined
Why is this?
Consider, for example, the fraction $\frac50\,$.
You have $\,5\,$ objects.
You want to divide them into piles of size $\,0\,$.
How many piles?
Serious problem.
With piles of size zero, you're going to have trouble getting rid of your five objects.
You can't just snap your finger and have matter disappear!
A more precise argument also covers the case $\,\frac00\,$, but uses material from later in this course.
Interested?
Read the text.
Type in nd (uppercase or lowercase) if the fraction is not defined.