$\frac{11}{5} +\frac{41}{8}$

Full solution

\frac{11}{5} +\frac{41}{8}

Find Common Denominator: To add two fractions, we need to have a common denominator. The denominators here are $5$ and $8$ . The least common multiple (LCM) of $5$ and $8$ is $40$ .
Convert to Equivalent Fractions: We convert each fraction to an equivalent fraction with a denominator of $40$ . For $\frac{11}{5}$ , we multiply both the numerator and the denominator by $8$ to get $\left(\frac{11\times8}{5\times8}\right) = \frac{88}{40}$ . For $\frac{41}{8}$ , we multiply both the numerator and the denominator by $5$ to get $\left(\frac{41\times5}{8\times5}\right) = \frac{205}{40}$ .
Add the Fractions: Now we can add the two fractions: $\frac{88}{40} + \frac{205}{40}$ .
Simplify the Fraction: Adding the numerators gives us $88 + 205 = 293$ . The denominator remains $40$ . So, the sum of the two fractions is $\frac{293}{40}$ .
Simplify the Fraction: Adding the numerators gives us $88 + 205 = 293$ . The denominator remains $40$ . So, the sum of the two fractions is $\frac{293}{40}$ .To simplify the fraction, we can divide the numerator by the denominator to get a mixed number. $293$ divided by $40$ is $7$ with a remainder of $13$ . So, $\frac{293}{40}$ is equal to $7 \frac{13}{40}$ .