Question

Evaluate the expression. Simplify if possible.
-4 1/3 - (-7/12) = [__] [__]/[__]

Answer 1

To evaluate the expression \(-4 \frac{1}{3} - \left(-\frac{7}{12}\right)\), we can first convert \(-4 \frac{1}{3}\) into an improper fraction.

1. Convert \(-4 \frac{1}{3}\):
\[
-4 \frac{1}{3} = -\left(4 \times 3 + 1\right)/3 = -\frac{13}{3}
\]

So the expression now looks like:
\[
-\frac{13}{3} - \left(-\frac{7}{12}\right) = -\frac{13}{3} + \frac{7}{12}
\]

2. Now, we need a common denominator to add these fractions. The least common multiple of 3 and 12 is 12.

Convert \(-\frac{13}{3}\) to have a denominator of 12:
\[
-\frac{13}{3} = -\frac{13 \times 4}{3 \times 4} = -\frac{52}{12}
\]

Now we can add the two fractions:
\[
-\frac{52}{12} + \frac{7}{12} = \frac{-52 + 7}{12} = \frac{-45}{12}
\]

3. Now simplify \(\frac{-45}{12}\):
The greatest common divisor (GCD) of 45 and 12 is 3. We can simplify:
\[
\frac{-45 \div 3}{12 \div 3} = \frac{-15}{4}
\]

So, the final result is:
\[
\frac{-15}{4}
\]

To put this in the requested format \([__] [__]/[__]\), we have:
- The whole part is \(-15\).
- The numerator is \(15\), and the denominator is \(4\).

The final result is:
\[
-15 \frac{3}{4}
\]

In the specified format: \([-15]\ [15]/[4]\). However, note that in your format it would represent:
\[-15 \quad [15]/[4]\]
which means:
\(
\boxed{-15} \quad \boxed{15}/\boxed{4}
\)