Question

(fractions)
-1/4 x (3 1/2 - 5) ÷ -4 =

Answer 1

To solve the expression \(-\frac{1}{4} \times (3 \frac{1}{2} - 5) \div -4\), we will follow the order of operations.

1. Convert the mixed number \(3 \frac{1}{2}\) into an improper fraction:
\[
3 \frac{1}{2} = \frac{7}{2}
\]

2. Substitute this into the expression:
\[
-\frac{1}{4} \times \left(\frac{7}{2} - 5\right) \div -4
\]

3. Convert \(5\) to a fraction with a denominator of \(2\):
\[
5 = \frac{10}{2}
\]

4. Now subtract:
\[
\frac{7}{2} - \frac{10}{2} = \frac{7 - 10}{2} = \frac{-3}{2}
\]

5. Substitute this result back into the expression:
\[
-\frac{1}{4} \times \left(-\frac{3}{2}\right) \div -4
\]

6. Simplifying the multiplication:
\[
-\frac{1}{4} \times -\frac{3}{2} = \frac{3}{8}
\]

7. Now, divide by \(-4\) (which we can express as \(-\frac{4}{1}\)):
\[
\frac{3}{8} \div -4 = \frac{3}{8} \times -\frac{1}{4} = -\frac{3}{32}
\]

So, the final result is:
\[
-\frac{3}{32}
\]