Question

Find each sum or difference. Write in the simplest form.

$-\frac{3}{5}+\left(-\frac{1}{5}\right)$

Short answer

The simplest form is $-\frac{4}{5}$.

Step-by-step solution

Step 1. Concept of like and unlike signs.

Two like signs$+\left(+\right)$ and$-\left(-\right)$ always are positive.

Two unlike signs$+\left(-\right)$ and$-\left(+\right)$ always are negative.

Step 2. Take L.C.M of the denominators of each fraction.

The least common multiple (LCM) is the smallest number divisible by all the denominators.

$\text{L.C.Mof5and5is}=5$

Step 3. Evaluate the sum.

In order to add or subtract the fractions, first, make both the denominators equal to LCM and then add or subtract the numerators directly over the common denominator as shown below:

$$\begin{gathered} -\frac{3}{5}+\left(-\frac{1}{5}\right)=-\frac{3}{5}-\frac{1}{5} \\ =\frac{-3-1}{5} \\ =-\frac{4}{5} \end{gathered}$$

There is no factor that can divide both the numerator and denominator.

Therefore, the simplest form is $-\frac{4}{5}$.