Find `(13)/(15) div 8 (2)/(3)`

Answer

To solve the problem \( \frac{13}{15} \div 8 \frac{2}{3} \), we can follow these steps:

### Step 1: Convert the mixed number to an improper fraction
The mixed number \( 8 \frac{2}{3} \) can be converted to an improper fraction.

To do this, we multiply the whole number (8) by the denominator (3) and then add the numerator (2):
\[ 8 \frac{2}{3} = \frac{8 \times 3 + 2}{3} = \frac{24 + 2}{3} = \frac{26}{3} \]

### Step 2: Rewrite the division as multiplication
Now we need to rewrite the division of fractions. The rule for dividing fractions states that \( \frac{a}{b} \div \frac{c}{d} \) can be rewritten as \( \frac{a}{b} \times \frac{d}{c} \).

So, we can rewrite our expression:
\[ \frac{13}{15} \div \frac{26}{3} = \frac{13}{15} \times \frac{3}{26} \]

### Step 3: Multiply the fractions
Now we can multiply the fractions:
\[ \frac{13 \times 3}{15 \times 26} \]

### Step 4: Simplify the fractions
Before multiplying, we can simplify the fractions.

- The number 3 in the numerator can be simplified with the 15 in the denominator:
\[ 3 \div 3 = 1 \quad \text{and} \quad 15 \div 3 = 5 \]

- Next, we can simplify the number 13 in the numerator with the 26 in the denominator:
\[ 13 \div 13 = 1 \quad \text{and} \quad 26 \div 13 = 2 \]

Now our expression looks like this:
\[ \frac{1 \times 1}{5 \times 2} = \frac{1}{10} \]

### Final Answer
Thus, the answer to the question \( \frac{13}{15} \div 8 \frac{2}{3} \) is:
\[ \frac{1}{10} \]

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