Question

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

$\frac{11}{12}-\frac{3}{4}$

Short answer

The difference is$\frac{1}{6}$.

Step-by-step solution

Step 1. Take L.C.M of the denominators of each fraction.

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

$\text{L.C.Mof12and4is}=12$

Step 2. 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:

$$\begin{gathered} \frac{11}{12}-\frac{3}{4}=\frac{11}{12}-\frac{3\times 3}{4\times 3} \\ =\frac{11}{12}-\frac{9}{12} \\ =\frac{11-9}{12} \\ =\frac{2}{12} \end{gathered}$$

Step 3. simplify the result.

To simplify it further, rewrite the numerator and denominator in factored form and cancel out the common factors to get

$$\begin{gathered} \frac{2}{12}=\frac{2}{6\times 2} \\ =\frac{1}{6} \end{gathered}$$

Therefore, the simplest form is$\frac{1}{6}$.