Divide. Write your answer in simplest form.
StartFraction 7 Over 39 EndFraction
divided by1 and six thirteenths
Question content area bottom
Part 1
Select the correct choice below and fill in any answer boxes in your choice.
A.
StartFraction 7 Over 39 EndFraction
divided by1 and six thirteenths
equals
  
enter your response here
​(Simplify your answer. Type a whole​ number, fraction, or mixed​ number.)
B.
The quotient is undefined.

To solve \( \frac{7}{39} \div 1 \frac{6}{13} \), we first convert the mixed number \( 1 \frac{6}{13} \) into an improper fraction.

### Step 1: Convert the mixed number into an improper fraction
The mixed number \( 1 \frac{6}{13} \) is equivalent to:
\[
1 \frac{6}{13} = \frac{13 \times 1 + 6}{13} = \frac{19}{13}
\]

### Step 2: Perform the division by multiplying by the reciprocal
Now, rewrite the division as multiplication by the reciprocal of \( \frac{19}{13} \):
\[
\frac{7}{39} \div \frac{19}{13} = \frac{7}{39} \times \frac{13}{19}
\]

### Step 3: Multiply the fractions
Multiply the numerators and the denominators:
\[
\frac{7 \times 13}{39 \times 19} = \frac{91}{741}
\]

### Step 4: Simplify the fraction
Now simplify \( \frac{91}{741} \). The greatest common divisor (GCD) of 91 and 741 is 7, so divide both the numerator and the denominator by 7:
\[
\frac{91 \div 7}{741 \div 7} = \frac{13}{106}
\]

### Final Answer:
The simplified form of the quotient is:
\[
\frac{13}{106}
\]

So the correct choice is **A**: \( \frac{13}{106} \).

---

Would you like any further details or clarification on the steps? Here are some related questions to consider:

1. How do you convert mixed numbers into improper fractions?
2. What is the reciprocal of a fraction, and why is it used in division?
3. How do you find the greatest common divisor (GCD) of two numbers?
4. Can any fraction be simplified further, and how do you determine that?
5. What are the common mistakes made when dividing fractions?

**Tip:** Always remember to check if both the numerator and denominator have common factors when simplifying fractions.

Divide. Write your answer in simplest form. StartFraction 7 Over 39 EndFraction divided by 1 and six thirteenths.

Learn how to solve the fraction division problem 7/39 ÷ 1 6/13 by converting mixed numbers into improper fractions, multiplying by the reciprocal, and simplifying the result. This guide covers key concepts such as division of fractions and finding the greatest common divisor, suitable for Grades 5-7.

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