Evaluate the expression.

6÷ (–4 – –1 1/2+3 3/4)
Write your answer as a fraction or as a whole or mixed number.

1 answer

To evaluate the expression \(6 \div (-4 - -1 \frac{1}{2} + 3 \frac{3}{4})\), we will first simplify the expression inside the parentheses step-by-step.

  1. Convert the mixed numbers to improper fractions:
    • \(-1 \frac{1}{2} = -\frac{3}{2}\)
    • \(3 \frac{3}{4} = \frac{15}{4}\)

Now the expression inside the parentheses becomes: \[ -4 - -\frac{3}{2} + \frac{15}{4} \]

  1. Rewrite \(-4\) as a fraction: \(-4 = -\frac{16}{4}\).

Now we have: \[ -\frac{16}{4} + \frac{3}{2} + \frac{15}{4} \]

  1. To add and subtract the fractions, we will need a common denominator. The least common denominator of \(4\) and \(2\) is \(4\). Convert \(\frac{3}{2}\) to have this denominator: \(\frac{3}{2} = \frac{6}{4}\).

  2. Now substitute that back into the expression: \[ -\frac{16}{4} + \frac{6}{4} + \frac{15}{4} \]

  3. Combine the fractions: \[ (-16 + 6 + 15) / 4 = (-16 + 21) / 4 = 5 / 4 \]

Now we have simplified the expression inside the parentheses to \(\frac{5}{4}\).

  1. Now evaluate the initial expression: \[ 6 \div \frac{5}{4} \]

  2. Dividing by a fraction is the same as multiplying by its reciprocal: \[ 6 \times \frac{4}{5} = \frac{6 \times 4}{5} = \frac{24}{5} \]

So, the final result is: \[ \frac{24}{5} \]

This can also be expressed as a mixed number: \[ 4 \frac{4}{5} \]

Thus, the answer is \(\frac{24}{5}\) or \(4 \frac{4}{5}\).