Question

Multiply -1.7 by 2 1/2 and write the answer as a mixed number in simplest form

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:
\[
2 \frac{1}{2} = 2 \times 2 + 1 = 4 + 1 = 5
\]
So, \(2 \frac{1}{2} = \frac{5}{2}\).

2. Now multiply \(-1.7\) by \(\frac{5}{2}\). First, we can convert \(-1.7\) into a fraction:
\[
-1.7 = -\frac{17}{10}
\]

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

4. Next, simplify \(-\frac{85}{20}\) by finding the greatest common divisor (GCD) of 85 and 20. The GCD is 5.
\[
-\frac{85 \div 5}{20 \div 5} = -\frac{17}{4}
\]

5. Now, convert \(-\frac{17}{4}\) into a mixed number:
\[
-\frac{17}{4} = -4 \frac{1}{4}
\]
(since \(17 \div 4 = 4\) remainder \(1\))

So, the final answer as a mixed number in simplest form is:
\[
\boxed{-4 \frac{1}{4}}
\]