Question

Simplify $\frac{3}{4}+\frac{5}{6}$.

Answer 1

Simplify the given expression.

Step 1: Convert the given fractions into like fractions and add.

Like fractions.

Fractions with the same denominators are called like fractions.

The given fractions are $\frac{3}{4}$ and $\frac{5}{6}$.

The LCM of $4$ and $6$ is $12$. Therefore,

$\frac{3}{4}=\frac{3\times 3}{4\times 3}=\frac{9}{12}$

$\frac{5}{6}=\frac{5\times 2}{6\times 2}=\frac{10}{12}$

Substitute the obtained like fractions into the given expression:

$\begin{array}{rcl}\frac{3}{4}+\frac{5}{6}& =& \frac{9}{12}+\frac{10}{12}\\ & =& \frac{9+10}{12}\\ & =& \frac{19}{12}\end{array}$

Step 2: Convert the improper fraction $\frac{19}{12}$ into a mixed fraction:

Mixed fraction.

A mixed fraction has a combination of a whole and a part. For example, $7\frac{2}{3}$ is a mixed fraction.

Convert an improper fraction into a mixed fraction.

We can express an improper fraction as a mixed fraction by dividing the numerator by the denominator to obtain the quotient and the remainder. Then the mixed fraction will be written as $\mathrm{Quotient}\frac{\mathrm{Remainder}}{\mathrm{Divisor}}$.

Therefore, the mixed fraction of the improper fraction $\frac{19}{12}$ will be $1\frac{7}{12}$.

Hence, $\frac{3}{4}+\frac{5}{6}=1\frac{7}{12}$.