Questions: Find the quotient. (-3/7) ÷ (-7/14) a. 6/49 b. -6/7 c. 6/7 d. -2/7 e. 2/7 Write the answer alphabet key (a, b, c, d, or e) in the blank, not including the punctuation.

Solution Steps

To find the quotient of two fractions, we can multiply the first fraction by the reciprocal of the second fraction. Simplify the resulting fraction to get the final answer.

1. Identify the two fractions: \(-\frac{3}{7}\) and \(-\frac{7}{14}\).
2. Find the reciprocal of the second fraction: \(-\frac{14}{7}\).
3. Multiply the first fraction by the reciprocal of the second fraction.
4. Simplify the resulting fraction to its lowest terms.
5. Compare the simplified fraction to the given options to find the correct answer.

We start with the two fractions: \[ \text{Fraction 1: } -\frac{3}{7}, \quad \text{Fraction 2: } -\frac{7}{14} \]

The reciprocal of \(-\frac{7}{14}\) is: \[ \text{Reciprocal of Fraction 2: } -\frac{14}{7} = -2 \]

Now, we multiply the first fraction by the reciprocal of the second fraction: \[ -\frac{3}{7} \cdot -2 = \frac{6}{7} \]

The result \(\frac{6}{7}\) is already in its simplest form.

We compare \(\frac{6}{7}\) with the provided options:

• a. \(\frac{6}{49}\)
• b. \(-\frac{6}{7}\)
• c. \(\frac{6}{7}\)
• d. \(-\frac{2}{7}\)
• e. \(\frac{2}{7}\)

The correct option that matches our result is option c.

Final Answer