Division by Zero & Fraction Bar Practice Problems

When we study the order of mathematical operations we come across the terms division bar and fraction bar, but what do they mean and why are they so special?

First of all, we must remember that the fraction bar—or vinculum—is exactly the same as a division. $10:2$ is the same as ${\ {10 \over 2}}$ and ${\ {10/ 2}}$.

Two things to remember:

• You cannot divide by $0$. To prove this, let's look at the following example: ${\ {3:0=}}$.
  To solve this, we must be able to do the following: ${\ {0 \cdot ?=3}}$. However, since there is no number that can be multiplied by $0$ to give the result $3$, there is also therefore no number that can be divided by $0$.
• When we have a fraction bar, it is as if there are parentheses in the numerator. We solve the numerator first and then continue with the exercise. For example:

${\ {{10-2 \over 2}= {8 \over 2} = 4}}$