Question

6\frac{3}{7}+1\frac{2}{5}=

Explanation:

Step1: Convert mixed numbers to improper fractions

For \(6\frac{3}{7}\), the improper fraction is \(\frac{6\times7 + 3}{7}=\frac{45}{7}\). For \(1\frac{2}{5}\), the improper fraction is \(\frac{1\times5+2}{5}=\frac{7}{5}\).

Step2: Find a common denominator

The least common denominator of 7 and 5 is \(7\times5 = 35\).

Step3: Rewrite fractions with the common denominator

\(\frac{45}{7}=\frac{45\times5}{7\times5}=\frac{225}{35}\) and \(\frac{7}{5}=\frac{7\times7}{5\times7}=\frac{49}{35}\).

Step4: Add the fractions

\(\frac{225}{35}+\frac{49}{35}=\frac{225 + 49}{35}=\frac{274}{35}\).

Step5: Convert back to a mixed number (optional)

\(\frac{274}{35}=7\frac{29}{35}\) (since \(35\times7 = 245\) and \(274-245 = 29\)).

Answer:

\(7\frac{29}{35}\) (or \(\frac{274}{35}\))