Question

Multiply −1.7 by 2 1/2 . Write the answer as a mixed number in simplest form.(1 point)

Answer 1

To multiply \(-1.7\) by \(2 \frac{1}{2}\), we first convert \(2 \frac{1}{2}\) into an improper fraction.

1. Convert \(2 \frac{1}{2}\) to an improper fraction:
\[
2 \frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}
\]

2. Now we multiply:
\[
-1.7 \times \frac{5}{2}
\]
To make the multiplication easier, we convert \(-1.7\) to a fraction:
\[
-1.7 = -\frac{17}{10}
\]

3. Now perform the multiplication of the two fractions:
\[
-\frac{17}{10} \times \frac{5}{2} = -\frac{17 \times 5}{10 \times 2} = -\frac{85}{20}
\]

4. Now we simplify \(-\frac{85}{20}\):
- The greatest common divisor (GCD) of \(85\) and \(20\) is \(5\).
- Divide both the numerator and the denominator by \(5\):
\[
-\frac{85 \div 5}{20 \div 5} = -\frac{17}{4}
\]

5. Convert \(-\frac{17}{4}\) to a mixed number:
\(-\frac{17}{4}\) can be expressed as:
\[
-4 \frac{1}{4} \quad \text{(since \(17 \div 4\) gives \(4\) remainder \(1\))}
\]

Therefore, \(-1.7\) multiplied by \(2 \frac{1}{2}\) gives:

\[
\boxed{-4 \frac{1}{4}}
\]