Let's solve each division problem step by step.
### Part i) \( 12 \div \frac{3}{4} \)
1. To divide by a fraction, you multiply by its reciprocal.
[tex]\[
12 \div \frac{3}{4} = 12 \times \frac{4}{3}
\][/tex]
2. Perform the multiplication.
[tex]\[
12 \times \frac{4}{3} = \frac{12 \times 4}{3} = \frac{48}{3} = 16
\][/tex]
So,
[tex]\[
12 \div \frac{3}{4} = 16
\][/tex]
### Part ii) \( \frac{2}{5} \div \frac{1}{2} \)
1. To divide by a fraction, multiply by its reciprocal.
[tex]\[
\frac{2}{5} \div \frac{1}{2} = \frac{2}{5} \times \frac{2}{1}
\][/tex]
2. Perform the multiplication.
[tex]\[
\frac{2}{5} \times \frac{2}{1} = \frac{2 \times 2}{5 \times 1} = \frac{4}{5} = 0.8
\][/tex]
So,
[tex]\[
\frac{2}{5} \div \frac{1}{2} = 0.8
\][/tex]
### Part iii) \( 4 \frac{3}{7} \div 1 \frac{1}{5} \)
1. Convert the mixed numbers to improper fractions.
[tex]\[
4 \frac{3}{7} = \frac{4 \times 7 + 3}{7} = \frac{28 + 3}{7} = \frac{31}{7}
\][/tex]
[tex]\[
1 \frac{1}{5} = \frac{1 \times 5 + 1}{5} = \frac{5 + 1}{5} = \frac{6}{5}
\][/tex]
2. To divide by a fraction, multiply by its reciprocal.
[tex]\[
\frac{31}{7} \div \frac{6}{5} = \frac{31}{7} \times \frac{5}{6}
\][/tex]
3. Perform the multiplication.
[tex]\[
\frac{31}{7} \times \frac{5}{6} = \frac{31 \times 5}{7 \times 6} = \frac{155}{42} = 3.6904761904761907
\][/tex]
So,
[tex]\[
4 \frac{3}{7} \div 1 \frac{1}{5} = 3.6904761904761907
\][/tex]
### Summary:
i) \( 12 \div \frac{3}{4} = 16 \)
ii) \( \frac{2}{5} \div \frac{1}{2} = 0.8 \)
iii) [tex]\( 4 \frac{3}{7} \div 1 \frac{1}{5} = 3.6904761904761907 \)[/tex]
