Add -12/7 + (3/-4). Write your answer as a reduced improper fraction.

1 answer

To add the fractions \(-\frac{12}{7}\) and \(\frac{3}{-4}\), we first rewrite \(\frac{3}{-4}\) as \(-\frac{3}{4}\).

Now, our expression becomes:

\[ -\frac{12}{7} - \frac{3}{4} \]

To add these two fractions, we need a common denominator. The denominators are 7 and 4. The least common multiple (LCM) of 7 and 4 is 28.

Next, we convert each fraction to have the common denominator of 28:

  1. For \(-\frac{12}{7}\):

\[ -\frac{12}{7} = -\frac{12 \times 4}{7 \times 4} = -\frac{48}{28} \]

  1. For \(-\frac{3}{4}\):

\[ -\frac{3}{4} = -\frac{3 \times 7}{4 \times 7} = -\frac{21}{28} \]

Now we can add the two fractions:

\[ -\frac{48}{28} - \frac{21}{28} = -\frac{48 + 21}{28} = -\frac{69}{28} \]

Now we have the improper fraction \(-\frac{69}{28}\). The fraction is already in its reduced form, because 69 and 28 have no common factors other than 1.

Therefore, the final answer is:

\[ \boxed{-\frac{69}{28}} \]