Q18. - Algebra 1

Question

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

$\frac{1}{6}+\left(-\frac{1}{2}\right)$

Step-by-Step Solution

Answer

The simplest form is $-\frac{1}{3}$.

Step 1. Concept of like and unlike signs.

If there is sign like $+\left(+\right)$ or $-\left(-\right)$ then the resulting sign will be positive and if there is unlike $+\left(-\right)$ sign $-\left(+\right)$ or then the resulting will be negative

Thus the simple form of given expression by nature of sign is

$\frac{1}{6}-\frac{1}{2}$

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

Since, 6 is completely divided by 2,

Thus

$\text{L.C.M of 6 and 2 is}=6$

Step 2. Evaluate the difference.

First, make the denominators of all fractions equal to LCM by multiplying the numerator and denominator with an integer. Then add/subtract the numerators directly over the common denominator.

$$\begin{gathered} \frac{1}{6}-\frac{1}{2}=\frac{1}{6}-\frac{1\cdot 3}{2\cdot 3} \\ =\frac{1}{6}-\frac{3}{6} \\ =\frac{1-3}{6} \\ =\frac{-2}{6} \end{gathered}$$

Step 3. Simplify the result.

Write the fraction with factor form and then simplify it.

$\begin{array}{l}=\frac{-2}{2\times 3}\\ =-\frac{1}{3}\end{array}$

Therefore, the simplest form is $-\frac{1}{3}$.