Find: b. `20 (5)/(6) div 15`

Answer

To solve the problem \( 20 \frac{5}{6} \div 15 \), we will follow these steps:

### Step 1: Convert the mixed number to an improper fraction
First, we need to convert \( 20 \frac{5}{6} \) into an improper fraction.

To do this, we multiply the whole number (20) by the denominator (6) and then add the numerator (5):

\[ 20 \frac{5}{6} = \frac{20 \times 6 + 5}{6} = \frac{120 + 5}{6} = \frac{125}{6} \]

### Step 2: Set up the division
Now we need to divide \( \frac{125}{6} \) by 15. Division by a number can be converted to multiplication by its reciprocal. Therefore, we can rewrite the division as follows:

\[ \frac{125}{6} \div 15 = \frac{125}{6} \times \frac{1}{15} \]

### Step 3: Multiply the fractions
Now we multiply the two fractions:

\[ \frac{125 \times 1}{6 \times 15} = \frac{125}{90} \]

### Step 4: Simplify the fraction
Next, we need to simplify \( \frac{125}{90} \). We can find the greatest common divisor (GCD) of 125 and 90, which is 5.

Now, we divide both the numerator and the denominator by 5:

\[ \frac{125 \div 5}{90 \div 5} = \frac{25}{18} \]

### Step 5: Convert to a mixed number (if necessary)
Finally, we can convert \( \frac{25}{18} \) into a mixed number. Since 25 is greater than 18, we divide 25 by 18:

\[ 25 \div 18 = 1 \quad \text{(whole number)} \]
\[ 25 - 18 = 7 \quad \text{(remainder)} \]

So, we can express \( \frac{25}{18} \) as:

\[ 1 \frac{7}{18} \]

### Final Answer
Thus, the solution to \( 20 \frac{5}{6} \div 15 \) is:

\[ 1 \frac{7}{18} \]

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