Sure, let's handle the given expressions step-by-step.
### Part (i)
[tex]\[
\frac{3}{5} \div \frac{1}{2}
\][/tex]
To divide by a fraction, you multiply by its reciprocal:
[tex]\[
\frac{3}{5} \div \frac{1}{2} = \frac{3}{5} \times \frac{2}{1} = \frac{3 \times 2}{5 \times 1} = \frac{6}{5} = 1.2
\][/tex]
So,
[tex]\[
\frac{3}{5} \div \frac{1}{2} = 1.2
\][/tex]
### Part (ii)
[tex]\[
\frac{1}{2} \div \frac{3}{5}
\][/tex]
Again, to divide by a fraction, you multiply by its reciprocal:
[tex]\[
\frac{1}{2} \div \frac{3}{5} = \frac{1}{2} \times \frac{5}{3} = \frac{1 \times 5}{2 \times 3} = \frac{5}{6} \approx 0.8333333333
\][/tex]
So,
[tex]\[
\frac{1}{2} \div \frac{3}{5} \approx 0.8333333333
\][/tex]
### Part (iii)
[tex]\[
2 \frac{1}{2} \div \frac{3}{5}
\][/tex]
First, convert the mixed number [tex]\(2 \frac{1}{2}\)[/tex] to an improper fraction:
[tex]\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}
\][/tex]
Now, divide by [tex]\(\frac{3}{5}\)[/tex] by multiplying with its reciprocal:
[tex]\[
\frac{5}{2} \div \frac{3}{5} = \frac{5}{2} \times \frac{5}{3} = \frac{5 \times 5}{2 \times 3} = \frac{25}{6} \approx 4.1666666667
\][/tex]
So,
[tex]\[
2 \frac{1}{2} \div \frac{3}{5} \approx 4.1666666667
\][/tex]
### Part (iv)
[tex]\[
5 \frac{1}{6} \div \frac{9}{2}
\][/tex]
First, convert the mixed number [tex]\(5 \frac{1}{6}\)[/tex] to an improper fraction:
[tex]\[
5 \frac{1}{6} = 5 + \frac{1}{6} = \frac{30}{6} + \frac{1}{6} = \frac{31}{6}
\][/tex]
Now, divide by [tex]\(\frac{9}{2}\)[/tex] by multiplying with its reciprocal:
[tex]\[
\frac{31}{6} \div \frac{9}{2} = \frac{31}{6} \times \frac{2}{9} = \frac{31 \times 2}{6 \times 9} = \frac{62}{54} = \frac{31}{27} \approx 1.1481481481
\][/tex]
So,
[tex]\[
5 \frac{1}{6} \div \frac{9}{2} \approx 1.1481481481
\][/tex]
These are the step-by-step solutions to the given problems.
