To solve the problem of finding the product of [tex]\(-\frac{3}{5}\)[/tex] and [tex]\(-1 \frac{1}{3}\)[/tex], we need to follow a few detailed steps:
1. Convert the mixed number to an improper fraction:
The mixed number given is [tex]\(-1 \frac{1}{3}\)[/tex].
- First, recall that a mixed number can be converted to an improper fraction by multiplying the integer part by the denominator of the fractional part, then adding the numerator, and placing the result over the original denominator.
- For [tex]\(-1 \frac{1}{3}\)[/tex], we have:
[tex]\[
-1 \frac{1}{3} = -1 - \frac{1}{3}
\][/tex]
- Convert the integer part [tex]\(-1\)[/tex] to a fraction with the same denominator as the fractional part:
[tex]\[
-1 = -\frac{3}{3}
\][/tex]
- Combine with [tex]\(\frac{1}{3}\)[/tex]:
[tex]\[
-\frac{3}{3} - \frac{1}{3} = -\frac{4}{3}
\][/tex]
2. Multiply the fractions:
Now, we need to multiply the improper fraction [tex]\(-\frac{4}{3}\)[/tex] by [tex]\(-\frac{3}{5}\)[/tex]:
[tex]\[
\left(-\frac{3}{5}\right) \left(-\frac{4}{3}\right)
\][/tex]
3. Carry out the multiplication:
- Multiply the numerators together:
[tex]\[
-3 \times -4 = 12
\][/tex]
- Multiply the denominators together:
[tex]\[
5 \times 3 = 15
\][/tex]
- Combine the results into a single fraction:
[tex]\[
\frac{12}{15}
\][/tex]
4. Simplify the fraction if possible:
- The fraction [tex]\(\frac{12}{15}\)[/tex] can be simplified, as both the numerator and the denominator have a common factor of 3.
[tex]\[
\frac{12 \div 3}{15 \div 3} = \frac{4}{5}
\][/tex]
Therefore, the product of [tex]\(-\frac{3}{5}\)[/tex] and [tex]\(-1 \frac{1}{3}\)[/tex] is:
[tex]\(\boxed{\frac{4}{5}}\)[/tex]
In decimal form, this answer is approximately [tex]\(0.8\)[/tex].
