Question

$4\frac{5}{6} + 5\frac{3}{5}$

Explanation:

Step1: Convert mixed numbers to improper fractions

For \( 4\frac{5}{6} \), multiply the whole number \( 4 \) by the denominator \( 6 \) and add the numerator \( 5 \): \( 4\times6 + 5 = 24 + 5 = 29 \), so \( 4\frac{5}{6}=\frac{29}{6} \).
For \( 5\frac{3}{5} \), multiply the whole number \( 5 \) by the denominator \( 5 \) and add the numerator \( 3 \): \( 5\times5 + 3 = 25 + 3 = 28 \), so \( 5\frac{3}{5}=\frac{28}{5} \).

Step2: Find a common denominator

The denominators are \( 6 \) and \( 5 \), and their least common multiple is \( 30 \).
Convert \( \frac{29}{6} \) to a fraction with denominator \( 30 \): \( \frac{29}{6}=\frac{29\times5}{6\times5}=\frac{145}{30} \).
Convert \( \frac{28}{5} \) to a fraction with denominator \( 30 \): \( \frac{28}{5}=\frac{28\times6}{5\times6}=\frac{168}{30} \).

Step3: Add the fractions

\( \frac{145}{30}+\frac{168}{30}=\frac{145 + 168}{30}=\frac{313}{30} \).

Step4: Convert back to a mixed number (optional)

Divide \( 313 \) by \( 30 \): \( 313\div30 = 10\) with a remainder of \( 13 \), so \( \frac{313}{30}=10\frac{13}{30} \).

Answer:

\( 10\frac{13}{30} \) (or \( \frac{313}{30} \))