Sure, let's go through each of the problems step by step.
### Part 1: Multiplying Fractions
We need to multiply the fractions [tex]\(\frac{6}{11}\)[/tex] and [tex]\(\frac{33}{40}\)[/tex].
1. Multiplying the Numerators and Denominators:
[tex]\[
\frac{6}{11} \times \frac{33}{40} = \frac{6 \times 33}{11 \times 40}
\][/tex]
2. Calculate the Numerator:
[tex]\[
6 \times 33 = 198
\][/tex]
3. Calculate the Denominator:
[tex]\[
11 \times 40 = 440
\][/tex]
4. Forming the New Fraction:
[tex]\[
\frac{198}{440} = 0.45
\][/tex]
So, the product of [tex]\(\frac{6}{11}\)[/tex] and [tex]\(\frac{33}{40}\)[/tex] is approximately [tex]\(0.45\)[/tex].
### Part 2: Multiplying a Whole Number with a Mixed Number
We need to multiply [tex]\(12\)[/tex] by the mixed number [tex]\(2 \frac{2}{3}\)[/tex].
1. Convert the Mixed Number to an Improper Fraction:
[tex]\[
2 \frac{2}{3} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3}
\][/tex]
Or alternatively,
[tex]\[
2 \frac{2}{3} = 2 + \frac{2}{3} = 2.6666666666666665
\][/tex]
2. Multiply the Whole Number by the Improper Fraction:
[tex]\[
12 \times \frac{8}{3} = 12 \times 2.6666666666666665 = 32
\][/tex]
So, the product of [tex]\(12\)[/tex] and [tex]\(2 \frac{2}{3}\)[/tex] is [tex]\(32\)[/tex].
### Summary of the Results:
1. The product of [tex]\(\frac{6}{11}\)[/tex] and [tex]\(\frac{33}{40}\)[/tex] is approximately [tex]\(0.45\)[/tex].
2. The product of [tex]\(12\)[/tex] and [tex]\(2 \frac{2}{3}\)[/tex] is [tex]\(32\)[/tex].
Therefore, the final answers are:
[tex]\[
\boxed{0.45 \text{ and } 32}
\][/tex]
