Solve the following expression :
`8 3/7 + 6 1/5`

Answer

To solve the expression \( 8 \frac{3}{7} + 6 \frac{1}{5} \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we convert the mixed numbers into improper fractions.

For \( 8 \frac{3}{7} \):
\[ 8 \frac{3}{7} = \frac{8 \times 7 + 3}{7} = \frac{56 + 3}{7} = \frac{59}{7} \]

For \( 6 \frac{1}{5} \):
\[ 6 \frac{1}{5} = \frac{6 \times 5 + 1}{5} = \frac{30 + 1}{5} = \frac{31}{5} \]

### Step 2: Add the Improper Fractions
Now we have:
\[ \frac{59}{7} + \frac{31}{5} \]

To add these fractions, we need a common denominator. The least common multiple (LCM) of 7 and 5 is 35.

### Step 3: Convert Fractions to Have a Common Denominator
Convert \( \frac{59}{7} \) to a fraction with a denominator of 35:
\[ \frac{59}{7} = \frac{59 \times 5}{7 \times 5} = \frac{295}{35} \]

Convert \( \frac{31}{5} \) to a fraction with a denominator of 35:
\[ \frac{31}{5} = \frac{31 \times 7}{5 \times 7} = \frac{217}{35} \]

### Step 4: Add the Converted Fractions
Now we can add the two fractions:
\[ \frac{295}{35} + \frac{217}{35} = \frac{295 + 217}{35} = \frac{512}{35} \]

### Step 5: Convert the Improper Fraction Back to a Mixed Number
To convert \( \frac{512}{35} \) back to a mixed number, we divide 512 by 35:
\[ 512 \div 35 = 14 \quad \text{(whole number part)} \]
The remainder is:
\[ 512 - (35 \times 14) = 512 - 490 = 22 \]
Thus, we can express it as:
\[ \frac{512}{35} = 14 \frac{22}{35} \]

### Final Answer
The final answer is:
\[ 8 \frac{3}{7} + 6 \frac{1}{5} = 14 \frac{22}{35} \]

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