Question

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

−4520
negative 4 Start Fraction 5 over 20 End Fraction

−234100
negative 2 Start Fraction 34 over 100 End Fraction

−414
negative 4 Start Fraction 1 over 4 End Fraction

−174

Answer 1

To multiply \(-1.7\) by \(2 \frac{1}{2}\), we first convert both numbers into a more manageable form.

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

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

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

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

5. Finally, convert \(-\frac{17}{4}\) to a mixed number:
\(-\frac{17}{4} = -4 \frac{1}{4}\) (since \(17 \div 4 = 4\) remainder \(1\)).

So the answer is:
\[
\text{negative } 4 \frac{1}{4}
\]

Thus, the correct answer is: **−4 Start Fraction 1 over 4 End Fraction**.