Question

perform the indicated operation. if possible, reduce the answer to its lowest terms.

( 2\frac{2}{3} + 1\frac{3}{4} = )

(type an integer or a simplified fraction.)

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(2\frac{2}{3}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(2\frac{2}{3}\), we have \(a = 2\), \(b = 2\), \(c = 3\). Then \(\frac{2\times3 + 2}{3}=\frac{6 + 2}{3}=\frac{8}{3}\).

Next, convert \(1\frac{3}{4}\) to an improper fraction. Here, \(a = 1\), \(b = 3\), \(c = 4\). So \(\frac{1\times4 + 3}{4}=\frac{4 + 3}{4}=\frac{7}{4}\).

Step2: Find a common denominator and add the fractions

The denominators are 3 and 4, so the least common denominator (LCD) is \(3\times4 = 12\).

Rewrite \(\frac{8}{3}\) with denominator 12: \(\frac{8\times4}{3\times4}=\frac{32}{12}\).

Rewrite \(\frac{7}{4}\) with denominator 12: \(\frac{7\times3}{4\times3}=\frac{21}{12}\).

Now add the two fractions: \(\frac{32}{12}+\frac{21}{12}=\frac{32 + 21}{12}=\frac{53}{12}\).

We can also convert this back to a mixed number if needed, but since the problem allows a simplified fraction, \(\frac{53}{12}\) is already in simplest form (53 is a prime number and does not divide 12).

Answer:

\(\frac{53}{12}\)