Question

Evaluate the expression. Simplify if possible.
-3 5/6 - (2 1/3) = [__] [__]/[__]

Answer 1

To evaluate the expression \(-3 \frac{5}{6} - (2 \frac{1}{3})\), we first need to convert the mixed numbers into improper fractions.

1. Convert \(-3 \frac{5}{6}\) into an improper fraction:
\[
-3 \frac{5}{6} = -\left(3 \cdot 6 + 5\right)/6 = -\frac{18 + 5}{6} = -\frac{23}{6}
\]

2. Convert \(2 \frac{1}{3}\) into an improper fraction:
\[
2 \frac{1}{3} = 2 \cdot 3 + 1/3 = \frac{6 + 1}{3} = \frac{7}{3}
\]

Now, the expression becomes:
\[
-\frac{23}{6} - \frac{7}{3}
\]

To perform the subtraction, we need a common denominator. The least common denominator between 6 and 3 is 6. We can convert \(\frac{7}{3}\) into sixths:
\[
\frac{7}{3} = \frac{7 \cdot 2}{3 \cdot 2} = \frac{14}{6}
\]

Now, substituting back into the expression:
\[
-\frac{23}{6} - \frac{14}{6} = -\frac{23 + 14}{6} = -\frac{37}{6}
\]

The fraction \(-\frac{37}{6}\) is already in simplest form. Finally, we can express this as a mixed number:
\[
-\frac{37}{6} = -6 \frac{1}{6}
\]

Therefore, the answer can be given as follows:
\[
-6 \quad 1 \quad 6
\]

Putting it in the format you provided:
- Answer: \([-6] [1]/[6]\)