Question

solve. \\(1 \dfrac{4}{5} + \dfrac{1}{3} = \underline{\quad\quad}\\)

Explanation:

Step1: Convert mixed number to improper fraction

To add \(1\frac{4}{5}\) and \(\frac{1}{3}\), first convert the mixed number \(1\frac{4}{5}\) 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 \(1\frac{4}{5}\), we have \(a = 1\), \(b = 4\), \(c = 5\). Then \(1\times5 + 4 = 9\), so \(1\frac{4}{5}=\frac{9}{5}\).

Step2: Find a common denominator

Now we need to add \(\frac{9}{5}\) and \(\frac{1}{3}\). The common denominator of 5 and 3 is \(5\times3 = 15\). Convert each fraction to have the denominator 15. For \(\frac{9}{5}\), multiply the numerator and denominator by 3: \(\frac{9\times3}{5\times3}=\frac{27}{15}\). For \(\frac{1}{3}\), multiply the numerator and denominator by 5: \(\frac{1\times5}{3\times5}=\frac{5}{15}\).

Step3: Add the fractions

Now add the two fractions with the common denominator: \(\frac{27}{15}+\frac{5}{15}=\frac{27 + 5}{15}=\frac{32}{15}\).

Step4: Convert back to mixed number (optional)

We can convert \(\frac{32}{15}\) back to a mixed number. Divide 32 by 15: \(15\times2 = 30\), so \(32 = 15\times2+2\). Thus, \(\frac{32}{15}=2\frac{2}{15}\).

Answer:

\(2\frac{2}{15}\) (or \(\frac{32}{15}\))