Find :
b. `7 (5)/(6) + 4 (2)/(5) - 6 (2)/(15)`

Answer

To solve the expression \( 7 \frac{5}{6} + 4 \frac{2}{5} - 6 \frac{2}{15} \), we will follow these steps:

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

1. For \( 7 \frac{5}{6} \):
\[ 7 \frac{5}{6} = \frac{(7 \times 6) + 5}{6} = \frac{42 + 5}{6} = \frac{47}{6} \]

2. For \( 4 \frac{2}{5} \):
\[ 4 \frac{2}{5} = \frac{(4 \times 5) + 2}{5} = \frac{20 + 2}{5} = \frac{22}{5} \]

3. For \( 6 \frac{2}{15} \):
\[ 6 \frac{2}{15} = \frac{(6 \times 15) + 2}{15} = \frac{90 + 2}{15} = \frac{92}{15} \]

### Step 2: Rewrite the Expression
Now we can rewrite the expression using the improper fractions:
\[ \frac{47}{6} + \frac{22}{5} - \frac{92}{15} \]

### Step 3: Find a Common Denominator
The denominators are 6, 5, and 15. The least common multiple (LCM) of these numbers is 30.

### Step 4: Convert Each Fraction to Have the Common Denominator
1. Convert \( \frac{47}{6} \) to have a denominator of 30:
\[ \frac{47}{6} = \frac{47 \times 5}{6 \times 5} = \frac{235}{30} \]

2. Convert \( \frac{22}{5} \) to have a denominator of 30:
\[ \frac{22}{5} = \frac{22 \times 6}{5 \times 6} = \frac{132}{30} \]

3. Convert \( \frac{92}{15} \) to have a denominator of 30:
\[ \frac{92}{15} = \frac{92 \times 2}{15 \times 2} = \frac{184}{30} \]

### Step 5: Rewrite the Expression with the Common Denominator
Now the expression becomes:
\[ \frac{235}{30} + \frac{132}{30} - \frac{184}{30} \]

### Step 6: Combine the Fractions
Since the denominators are the same, we can combine the numerators:
\[ \frac{235 + 132 - 184}{30} = \frac{183}{30} \]

### Step 7: Simplify the Result
Now we simplify \( \frac{183}{30} \):
1. Divide both the numerator and denominator by their greatest common divisor (GCD), which is 3:
\[ \frac{183 \div 3}{30 \div 3} = \frac{61}{10} \]

### Step 8: Convert Back to a Mixed Number
Convert \( \frac{61}{10} \) back to a mixed number:
\[ \frac{61}{10} = 6 \frac{1}{10} \]

### Final Answer
Thus, the final answer is:
\[ 6 \frac{1}{10} \]

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