To evaluate the expression \((- 4 \frac{1}{4} - 5 \frac{1}{2}) / -3.75\), we will break it down into steps.
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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 \( -5 \frac{1}{2} \): \[ -5 \frac{1}{2} = -\left(5 \times 2 + 1\right)/2 = -\frac{11}{2} \]
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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: \[ -\frac{11}{2} = -\frac{11 \times 2}{2 \times 2} = -\frac{22}{4} \]
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Combine the fractions: \[ -\frac{17}{4} - \frac{22}{4} = -\frac{39}{4} \]
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Divide by -3.75. First, convert -3.75 into a fraction. Since \(3.75 = \frac{375}{100} = \frac{15}{4}\), we have: \[ -3.75 = -\frac{15}{4} \]
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Now calculate: \[ \frac{-\frac{39}{4}}{-\frac{15}{4}} = \frac{39}{15} \]
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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: \[ \boxed{\frac{13}{5}} \quad \text{or as a mixed number} \quad 2 \frac{3}{5} \]
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