Question

Find the product (multiply) and simplify your answer to a mixed number.

−2 1/4(−5 2/3)

Answer 1

To find the product of \(-2 \frac{1}{4}\) and \(-5 \frac{2}{3}\), we first convert these mixed numbers into improper fractions.

1. Convert \(-2 \frac{1}{4}\):

\[
-2 \frac{1}{4} = -\left(2 \times 4 + 1\right)/4 = -\frac{9}{4}
\]

2. Convert \(-5 \frac{2}{3}\):

\[
-5 \frac{2}{3} = -\left(5 \times 3 + 2\right)/3 = -\frac{17}{3}
\]

Now we will multiply these two improper fractions:

\[
-\frac{9}{4} \times -\frac{17}{3} = \frac{9 \times 17}{4 \times 3} = \frac{153}{12}
\]

Next, we simplify \(\frac{153}{12}\):

1. Find the greatest common divisor (GCD) of 153 and 12. The prime factors of 153 are \(3 \times 51\) and \(51 = 3 \times 17\), so \(153 = 3^2 \times 17\). The prime factors of 12 are \(2^2 \times 3\). Their GCD is \(3\).

2. Divide the numerator and the denominator by their GCD (3):

\[
\frac{153 \div 3}{12 \div 3} = \frac{51}{4}
\]

Now convert \(\frac{51}{4}\) to a mixed number:

1. Divide \(51\) by \(4\):
- \(51 \div 4 = 12\) remainder \(3\).

So, \(\frac{51}{4} = 12 \frac{3}{4}\).

Thus, the final answer is:

\[
\boxed{12 \frac{3}{4}}
\]