To determine the product of the mixed number [tex]\(3 \frac{2}{3}\)[/tex] and the fraction [tex]\( \frac{142}{5} \)[/tex], follow these steps:
1. Convert the mixed number to an improper fraction:
- [tex]\(3 \frac{2}{3}\)[/tex] equals [tex]\(3 + \frac{2}{3}\)[/tex].
- Rewrite [tex]\(3\)[/tex] as a fraction: [tex]\(3 = \frac{9}{3}\)[/tex].
- Now add the fractions: [tex]\(\frac{9}{3} + \frac{2}{3} = \frac{11}{3}\)[/tex].
2. Multiply the improper fractions:
- Multiply [tex]\(\frac{11}{3}\)[/tex] by [tex]\(\frac{142}{5}\)[/tex].
- This is done by multiplying the numerators together and the denominators together:
[tex]\[\frac{11 \times 142}{3 \times 5} = \frac{1562}{15}.\][/tex]
Therefore, the product of [tex]\(3 \frac{2}{3}\)[/tex] and [tex]\(\frac{142}{5}\)[/tex] is [tex]\(\frac{1562}{15}\)[/tex].
Now, compare this result with the given options:
- A. [tex]\( \frac{524}{15} \)[/tex]
- B. [tex]\( \frac{524}{5} \)[/tex]
- C. [tex]\( \frac{424}{5} \)[/tex]
- D. [tex]\( 54 \)[/tex]
Since [tex]\(\frac{1562}{15}\)[/tex] matches none of the options exactly, we must check for any simple errors or compare, but it appears there might have been a confusion here. The correct answer should be [tex]\(\frac{1562}{15}\)[/tex], which isn't explicitly listed as one of the given options.
However, among the provided choices, it does seem there might have been a mistake in the options provided. If the correct option had been [tex]\(\frac{1562}{15}\)[/tex], it would have matched perfectly without any ambiguity.
