To find the solutions for Exercise 2.3, we will work through each part step-by-step, showing the calculation involved.
### Part 1: Finding the fractions
#### (i) [tex]\(\frac{1}{4}\)[/tex] of
1. (a) [tex]\(\frac{1}{4} \times \frac{1}{4}\)[/tex]
[tex]\[ \frac{1}{4} \times \frac{1}{4} = \frac{1 \times 1}{4 \times 4} = \frac{1}{16} = 0.0625 \][/tex]
2. (b) [tex]\(\frac{1}{4} \times \frac{3}{5}\)[/tex]
[tex]\[ \frac{1}{4} \times \frac{3}{5} = \frac{1 \times 3}{4 \times 5} = \frac{3}{20} = 0.15 \][/tex]
3. (c) [tex]\(\frac{1}{4} \times \frac{4}{3}\)[/tex]
[tex]\[ \frac{1}{4} \times \frac{4}{3} = \frac{1 \times 4}{4 \times 3} = \frac{4}{12} = \frac{1}{3} \approx 0.3333 \][/tex]
#### (ii) [tex]\(\frac{1}{7}\)[/tex] of
1. (a) [tex]\(\frac{1}{7} \times \frac{2}{9}\)[/tex]
[tex]\[ \frac{1}{7} \times \frac{2}{9} = \frac{1 \times 2}{7 \times 9} = \frac{2}{63} \approx 0.0317 \][/tex]
2. (b) [tex]\(\frac{1}{7} \times \frac{6}{5}\)[/tex]
[tex]\[ \frac{1}{7} \times \frac{6}{5} = \frac{1 \times 6}{7 \times 5} = \frac{6}{35} \approx 0.1714 \][/tex]
3. (c) [tex]\(\frac{1}{7} \times \frac{3}{10}\)[/tex]
[tex]\[ \frac{1}{7} \times \frac{3}{10} = \frac{1 \times 3}{7 \times 10} = \frac{3}{70} \approx 0.0429 \][/tex]
#### (iii) [tex]\(\frac{1}{3}\)[/tex] of
1. (a) [tex]\(\frac{1}{3} \times \frac{3}{7}\)[/tex]
[tex]\[ \frac{1}{3} \times \frac{3}{7} = \frac{1 \times 3}{3 \times 7} = \frac{3}{21} = \frac{1}{7} \approx 0.1429 \][/tex]
2. (b) [tex]\(\frac{1}{3} \times \frac{1}{3}\)[/tex]
[tex]\[ \frac{1}{3} \times \frac{1}{3} = \frac{1 \times 1}{3 \times 3} = \frac{1}{9} \approx 0.1111 \][/tex]
3. (c) [tex]\(\frac{1}{3} \times \frac{12}{13}\)[/tex]
[tex]\[ \frac{1}{3} \times \frac{12}{13} = \frac{1 \times 12}{3 \times 13} = \frac{12}{39} = \frac{4}{13} \approx 0.3077 \][/tex]
### Summary of Results
- (i)
- (a) [tex]\(0.0625\)[/tex]
- (b) [tex]\(0.15\)[/tex]
- (c) [tex]\(0.3333\)[/tex]
- (ii)
- (a) [tex]\(0.0317\)[/tex]
- (b) [tex]\(0.1714\)[/tex]
- (c) [tex]\(0.0429\)[/tex]
- (iii)
- (a) [tex]\(0.1429\)[/tex]
- (b) [tex]\(0.1111\)[/tex]
- (c) [tex]\(0.3077\)[/tex]
These values are the solutions to the fractions presented in the exercise.
