Questions: 3 1/10 +5 1/10 F 8 1/20 G 8 1/10 H 8 1/5 J 8 2/5 K None of these

Transcript text: \[ \begin{array}{r} 3 \frac{1}{10} \\ +5 \frac{1}{10} \\ \hline \end{array} \] F $8 \frac{1}{20}$ G $8 \frac{1}{10}$ H $\quad 8 \frac{1}{5}$ J $8 \frac{2}{5}$ K None of these

Solution

Solution Steps

To solve the problem of adding the mixed numbers $3 \frac{1}{10}$ and $5 \frac{1}{10}$, we first convert the mixed numbers to improper fractions. Then, we add the fractions together. Finally, we convert the result back to a mixed number to find the correct answer.

Step 1: Convert Mixed Numbers to Improper Fractions

We start by converting the mixed numbers $3 \frac{1}{10}$ and $5 \frac{1}{10}$ into improper fractions: \[ 3 \frac{1}{10} = \frac{31}{10}, \quad 5 \frac{1}{10} = \frac{51}{10} \]

Step 2: Add the Improper Fractions

Next, we add the two improper fractions: \[ \frac{31}{10} + \frac{51}{10} = \frac{31 + 51}{10} = \frac{82}{10} = \frac{41}{5} \]

Step 3: Convert the Result Back to a Mixed Number

Now, we convert the improper fraction $\frac{41}{5}$ back to a mixed number: \[ \frac{41}{5} = 8 \frac{1}{5} \]