Question

Simplify the following complex fraction. 3/7 - 1/3/ 2/3 -1/7


A. 2/9


B. -2


C. 2/11


D. 3/2

Answer 1

To simplify the given complex fraction \( \frac{\frac{3}{7} - \frac{1}{3}}{\frac{2}{3} - \frac{1}{7}} \), we will first simplify both the numerator and the denominator separately.

**Numerator: \( \frac{3}{7} - \frac{1}{3} \)**

To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 7 and 3 is 21.

- Convert \( \frac{3}{7} \):
\[
\frac{3}{7} = \frac{3 \times 3}{7 \times 3} = \frac{9}{21}
\]

- Convert \( \frac{1}{3} \):
\[
\frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21}
\]

Now, perform the subtraction:
\[
\frac{3}{7} - \frac{1}{3} = \frac{9}{21} - \frac{7}{21} = \frac{2}{21}
\]

**Denominator: \( \frac{2}{3} - \frac{1}{7} \)**

Again, we will find a common denominator. The LCM of 3 and 7 is 21.

- Convert \( \frac{2}{3} \):
\[
\frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21}
\]

- Convert \( \frac{1}{7} \):
\[
\frac{1}{7} = \frac{1 \times 3}{7 \times 3} = \frac{3}{21}
\]

Now, perform the subtraction:
\[
\frac{2}{3} - \frac{1}{7} = \frac{14}{21} - \frac{3}{21} = \frac{11}{21}
\]

**Now we can combine the results:**
\[
\frac{\frac{2}{21}}{\frac{11}{21}} = \frac{2}{21} \div \frac{11}{21}
\]

When dividing by a fraction, we multiply by its reciprocal:
\[
= \frac{2}{21} \times \frac{21}{11} = \frac{2 \times 21}{21 \times 11} = \frac{2}{11}
\]

Thus, the simplified form of the given complex fraction is \( \frac{2}{11} \).

The answer is:
**C. \( \frac{2}{11} \)**