Question

Evaluate the expression shown below and write your answer as either a mixed number or fraction in simplest form, or a decimal.
(- 4 1/4 - 5 1/2) / -3.75

Answer 1

To evaluate the expression \((- 4 \frac{1}{4} - 5 \frac{1}{2}) / -3.75\), we will break it down into steps.

1. **Convert the mixed numbers to improper fractions**:
- For \( -4 \frac{1}{4} \):
\[
-4 \frac{1}{4} = -\left(4 \times 4 + 1\right)/4 = -\frac{17}{4}
\]
- For \( -5 \frac{1}{2} \):
\[
-5 \frac{1}{2} = -\left(5 \times 2 + 1\right)/2 = -\frac{11}{2}
\]

2. **Find a common denominator** for \(-\frac{17}{4}\) and \(-\frac{11}{2}\). The least common multiple of 4 and 2 is 4. Rewrite \(-\frac{11}{2}\) with a denominator of 4:
\[
-\frac{11}{2} = -\frac{11 \times 2}{2 \times 2} = -\frac{22}{4}
\]

3. **Combine the fractions**:
\[
-\frac{17}{4} - \frac{22}{4} = -\frac{39}{4}
\]

4. **Divide by -3.75**. First, convert -3.75 into a fraction. Since \(3.75 = \frac{375}{100} = \frac{15}{4}\), we have:
\[
-3.75 = -\frac{15}{4}
\]

5. **Now calculate**:
\[
\frac{-\frac{39}{4}}{-\frac{15}{4}} = \frac{39}{15}
\]

6. **Simplify \(\frac{39}{15}\)**. The greatest common divisor (GCD) of 39 and 15 is 3:
\[
\frac{39 \div 3}{15 \div 3} = \frac{13}{5}
\]

Thus, the value of the expression \((- 4 \frac{1}{4} - 5 \frac{1}{2}) / -3.75\) is:
\[
\boxed{\frac{13}{5}} \quad \text{or as a mixed number} \quad 2 \frac{3}{5}
\]