# Algebra Expressions with Fraction Bars

## Key Questions

• The fraction bar represents the operation of division.
To write the fraction $\frac{21}{7}$ is the same as 21÷7.
In a way it is a compact and immediate way of writing rational numbers. For example:
$0.25$ can be written as $\frac{1}{4}$
In some cases it is easier to understand a fraction than a decimal; in a car, for example, it is used to represent the content of the fuel tank. (Picture source: www.shutterstock.com)

• That depends on how much the fraction bar expands throughout the expression.
If it is the entire expression:

$\frac{\left(6 + 2\right) - 2 \cdot \left(3 - 7\right)}{3 \left(6 - 5\right)} = \frac{16}{3}$

Naturally, the way to go about this is to solve the numerator first, then the denominator. Eventually, when you get the final result, you divide.

But if the division only goes through only individual elements:

$\left(\frac{6 + 2 \cdot 3}{10 - 4}\right) \cdot {\left(3 - 1\right)}^{2} + 3 - 4 = 7$

You would follow PEMDAS normally, left to right, check parenthesis and exponents, multiply and divide, then add and subtract. When experiencing a fraction bar, you have to go through numerator first, then denominator before moving on to the next element.

• It depends on the expression:

$\frac{x}{4} + 2 = \frac{x}{4} + \frac{8}{4} = \frac{x + 8}{4}$

$\frac{2 x}{x + 1} + \frac{5}{x + 1} = \frac{2 x + 5}{x + 1}$

$\frac{3 x - 2}{5} + \frac{x - 7}{x} = \frac{\left(3 x - 2\right) x}{5 x} + \frac{\left(x - 7\right) 5}{5 x} = \frac{\left(3 {x}^{2} - 2 x\right) + \left(5 x - 35\right)}{5 x} = \frac{3 {x}^{2} + 3 x - 35}{5 x}$

$\frac{3 x}{\sqrt{2}} = \frac{3 x}{\sqrt{2}} \frac{\sqrt{2}}{\sqrt{2}} = \frac{3 x \sqrt{2}}{2}$

$\frac{{x}^{2} - 1}{{x}^{2} - 4 x - 5} = \frac{\left(x + 1\right) \left(x - 1\right)}{\left(x + 1\right) \left(x - 5\right)} = \frac{x + 1}{x - 5}$

Post a particular problem.