Sure, let's solve each of the given products step by step.
### (i) [tex]\(\frac{5}{6} \times \frac{7}{11}\)[/tex]
To multiply fractions, you multiply the numerators together and the denominators together.
[tex]\[
\frac{5}{6} \times \frac{7}{11} = \frac{5 \times 7}{6 \times 11} = \frac{35}{66}
\][/tex]
Thus, [tex]\(\frac{5}{6} \times \frac{7}{11} \approx 0.5303\)[/tex]
### (ii) [tex]\(6 \times \frac{1}{5}\)[/tex]
Here, we are multiplying a whole number by a fraction. To do this, you can multiply the whole number by the numerator of the fraction and keep the denominator the same.
[tex]\[
6 \times \frac{1}{5} = \frac{6 \times 1}{5} = \frac{6}{5} = 1.2
\][/tex]
Thus, [tex]\(6 \times \frac{1}{5} = 1.2\)[/tex]
### (iii) [tex]\(2 \frac{1}{3} \times 3 \frac{1}{5}\)[/tex]
First, we need to convert the mixed numbers into improper fractions.
For [tex]\(2 \frac{1}{3}\)[/tex]:
[tex]\[
2 \frac{1}{3} = 2 + \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3}
\][/tex]
For [tex]\(3 \frac{1}{5}\)[/tex]:
[tex]\[
3 \frac{1}{5} = 3 + \frac{1}{5} = \frac{15}{5} + \frac{1}{5} = \frac{16}{5}
\][/tex]
Now, we can multiply the improper fractions:
[tex]\[
\frac{7}{3} \times \frac{16}{5} = \frac{7 \times 16}{3 \times 5} = \frac{112}{15}
\][/tex]
This improper fraction can be converted back into a mixed number if needed, but in decimal form it is approximately:
[tex]\(\frac{112}{15} \approx 7.4667\)[/tex]
Thus, [tex]\(2 \frac{1}{3} \times 3 \frac{1}{5} = 7.4667\)[/tex]
In summary:
1. [tex]\( \frac{5}{6} \times \frac{7}{11} \approx 0.5303 \)[/tex]
2. [tex]\( 6 \times \frac{1}{5} = 1.2 \)[/tex]
3. [tex]\( 2 \frac{1}{3} \times 3 \frac{1}{5} \approx 7.4667 \)[/tex]
