What is the quotient of 3 7/9÷1 1/5 ? Simplify the answer, if possible.(1 point) Responses 27/85 Start Fraction 27 over 85 End Fraction 4 8/15 4 Start Fraction 8 over 15 End Fraction 15/68 Start Fraction 15 over 68 End Fraction 3 4/27

Answer 1

To find the quotient of \( 3 \frac{7}{9} \div 1 \frac{1}{5} \), we first convert the mixed numbers into improper fractions.

1. Convert \( 3 \frac{7}{9} \) into an improper fraction: \[ 3 \frac{7}{9} = \frac{3 \times 9 + 7}{9} = \frac{27 + 7}{9} = \frac{34}{9} \]

2. Convert \( 1 \frac{1}{5} \) into an improper fraction: \[ 1 \frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{5 + 1}{5} = \frac{6}{5} \]

Now, we can perform the division: \[ \frac{34}{9} \div \frac{6}{5} = \frac{34}{9} \times \frac{5}{6} \]

Multiply the fractions: \[ \frac{34 \times 5}{9 \times 6} = \frac{170}{54} \]

Next, we simplify the fraction \( \frac{170}{54} \). Find the greatest common divisor (GCD) of 170 and 54, which is 2.

Now divide the numerator and the denominator by their GCD: \[ \frac{170 \div 2}{54 \div 2} = \frac{85}{27} \]

Since \( \frac{85}{27} \) is in its simplest form, the answer is: \[ \frac{85}{27} \]

Looking at the provided responses, this is not listed. If we were to convert \( \frac{85}{27} \) to a mixed number: \[ 85 ÷ 27 = 3 \quad \text{(Remainder 4)} \] So: \[ \frac{85}{27} = 3 \frac{4}{27} \]

Thus, the final answer in mixed number form is: \[ 3 \frac{4}{27} \]

The answer is \( 3 \frac{4}{27} \).