Question

3\frac{4}{5} + 4\frac{1}{3} =

Explanation:

Step1: Convert mixed numbers to improper fractions

To add mixed numbers \(3\frac{4}{5}\) and \(4\frac{1}{3}\), first convert them to improper fractions. For \(3\frac{4}{5}\), we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(3\frac{4}{5}=\frac{3\times5 + 4}{5}=\frac{15 + 4}{5}=\frac{19}{5}\). For \(4\frac{1}{3}\), we have \(4\frac{1}{3}=\frac{4\times3+1}{3}=\frac{12 + 1}{3}=\frac{13}{3}\).

Step2: Find a common denominator

The denominators are 5 and 3. The least common denominator (LCD) of 5 and 3 is \(5\times3 = 15\).

Step3: Rewrite fractions with the common denominator

Rewrite \(\frac{19}{5}\) and \(\frac{13}{3}\) with denominator 15. For \(\frac{19}{5}\), multiply numerator and denominator by 3: \(\frac{19\times3}{5\times3}=\frac{57}{15}\). For \(\frac{13}{3}\), multiply numerator and denominator by 5: \(\frac{13\times5}{3\times5}=\frac{65}{15}\).

Step4: Add the fractions

Now add the two fractions: \(\frac{57}{15}+\frac{65}{15}=\frac{57 + 65}{15}=\frac{122}{15}\).

Step5: Convert back to a mixed number (optional)

Convert \(\frac{122}{15}\) to a mixed number. Divide 122 by 15: \(15\times8 = 120\), so \(\frac{122}{15}=8\frac{2}{15}\). But if we just want the improper fraction or the mixed number, we can present it. Alternatively, if we add the whole numbers and the fractions separately: the whole numbers are 3 and 4, so \(3 + 4=7\). The fractions are \(\frac{4}{5}\) and \(\frac{1}{3}\). Find a common denominator for the fractions: \(\frac{4}{5}+\frac{1}{3}=\frac{12 + 5}{15}=\frac{17}{15}=1\frac{2}{15}\). Then add the whole number result and the fraction result: \(7+1\frac{2}{15}=8\frac{2}{15}\), which is the same as \(\frac{122}{15}\).

Answer:

\(8\frac{2}{15}\) (or \(\frac{122}{15}\))