# How do you solve 2j/7 - 1/7 = 3/14?

Jul 14, 2015

Rewrite with a common denominator or multiply through to remove the denominators then solve using standard arithmetic manipulations.

#### Explanation:

Note that there are two possible answers depending upon the interpretation of $2 \frac{j}{7}$

Interpretation 1 : $2 \frac{j}{7}$ is intended to be a multiplication: $2 \left(\frac{j}{7}\right)$
$2 \left(\frac{j}{7}\right) - \frac{1}{7} = \frac{3}{14}$
If we multiply all terms on both sides by $14$ we get
$\textcolor{w h i t e}{\text{XXXX}}$$4 j - 2 = 3$
$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow j = \frac{5}{4}$

Interpretation 2: $2 \frac{j}{7}$ is intended to be a mixed fraction$2 + \left(\frac{j}{7}\right)$
(It is unusual, but not impossible, that a variable is part of a mixed fraction).

$2 + \left(\frac{j}{7}\right) - \frac{1}{7} = \frac{3}{14}$
Again, if we multiply all terms on both sides by $14$ we get
$\textcolor{w h i t e}{\text{XXXX}}$$28 + 2 j - 2 = 3$
$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow 2 j + 26 = 3$
$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow 2 j = - 23$
$\textcolor{w h i t e}{\text{XXXX}}$$\rightarrow j = - \frac{23}{2}$