Question

Add −12/7+(3/14) . Write your answer as a reduced improper fraction

Answer 1

To add the fractions \(-\frac{12}{7}\) and \(\frac{3}{14}\), we need to find a common denominator. The denominators are 7 and 14, and the least common denominator (LCD) is 14.

Next, we need to express \(-\frac{12}{7}\) with the denominator of 14:

\[
-\frac{12}{7} = -\frac{12 \times 2}{7 \times 2} = -\frac{24}{14}
\]

Now we can add the two fractions:

\[
-\frac{24}{14} + \frac{3}{14} = \frac{-24 + 3}{14} = \frac{-21}{14}
\]

Now, we simplify \(-\frac{21}{14}\). The greatest common divisor (GCD) of 21 and 14 is 7. Therefore, we divide the numerator and the denominator by 7:

\[
-\frac{21 \div 7}{14 \div 7} = -\frac{3}{2}
\]

Thus, the final answer as a reduced improper fraction is:

\[
\boxed{-\frac{3}{2}}
\]