Sure, let's solve each of the products step-by-step.
### (i) Calculate the product [tex]\(\frac{5}{6} \times \frac{7}{11}\)[/tex]:
To find the product of two fractions, simply multiply the numerators and multiply the denominators:
[tex]\[
\frac{5}{6} \times \frac{7}{11} = \frac{5 \times 7}{6 \times 11} = \frac{35}{66}
\][/tex]
Evaluating the fraction, we obtain:
[tex]\[
\frac{35}{66} \approx 0.5303030303030303
\][/tex]
### (ii) Calculate the product [tex]\(6 \times \frac{1}{5}\)[/tex]:
To multiply a whole number by a fraction, multiply the whole number by the numerator and keep the denominator the same:
[tex]\[
6 \times \frac{1}{5} = \frac{6 \times 1}{5} = \frac{6}{5}
\][/tex]
Evaluating the fraction, we get:
[tex]\[
\frac{6}{5} = 1.2
\][/tex]
### (iii) Calculate the product of the mixed numbers [tex]\(2 \frac{1}{3} \times 3 \frac{1}{5}\)[/tex]:
First, convert the mixed numbers to improper fractions:
[tex]\[
2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}
\][/tex]
[tex]\[
3 \frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{16}{5}
\][/tex]
Next, find the product of the two improper fractions:
[tex]\[
\frac{7}{3} \times \frac{16}{5} = \frac{7 \times 16}{3 \times 5} = \frac{112}{15}
\][/tex]
Evaluating the fraction, we obtain:
[tex]\[
\frac{112}{15} \approx 7.466666666666668
\][/tex]
Thus, the results of our calculations are:
- [tex]\(\frac{5}{6} \times \frac{7}{11} = 0.5303030303030303\)[/tex]
- [tex]\(6 \times \frac{1}{5} = 1.2\)[/tex]
- [tex]\(2 \frac{1}{3} \times 3 \frac{1}{5} = 7.466666666666668\)[/tex]
