1. a) Write 15 minutes as a fraction of \( 1 \frac{1}{2} \) hours. (2) b) Write 35 metres as a fraction of 105 metres. (2) 2. Find the number that lies halfway between these fractions. (2) a) \( \frac{1}{3} \) and \( \frac{5}{9} \) (2) b) \( \frac{7}{15} \) and \( \frac{1}{3} \) 3. Calculate. (2) a) \( \frac{1}{2}-\frac{9}{4} \times \frac{7}{6}+2 \) (2) b) \( \left(-\frac{1}{2}\right)^{2} \times\left(-\frac{3}{4}\right)^{2} \) c) \( \sqrt[3]{-\frac{8}{216}}+\frac{1}{2} \) (2) d) \( \sqrt{\frac{16}{25}} \) (2) 4. Find three fractions between \( \frac{4}{10} \) and \( \frac{4}{5} \). (2) 5. What is the difforence between \( \frac{3}{5} \) and \( \frac{2}{3} \) ? (2) 6. What must be subtracted from \( \frac{8}{9} \) to give \( \frac{7}{8} \) ? (2) 7. A golf club has 144 members, of whom 63 are women (2) a) What fraction of the members are men? b) Two members of the club are standing for election to be president. Mandisa (4) gets \( \frac{3}{4} \) of the vote. If \( \frac{1}{3} \) of the members voted, how many votes did Mandisa get? (3) 8. A fuel tank is two-thirds full. Adding 60 more litres will fill the tank. What is the capacity of the tank? 9. Lungile pays \( \frac{2}{5} \) of her salary in income tax. She spends \( \frac{2}{3} \) of what is left on rent, food and transport. If she earns R 6400 per month, how much of her salary does she have left? Total marks: 35

Let's solve the problems step by step. ### 1. a) Write 15 minutes as a fraction of \( 1 \frac{1}{2} \) hours. **Known conditions:** - 15 minutes = \( \frac{15}{60} \) hours = \( \frac{1}{4} \) hours. - \( 1 \frac{1}{2} \) hours = \( \frac{3}{2} \) hours. **Fraction calculation:** \[ \text{Fraction} = \frac{\frac{1}{4}}{\frac{3}{2}} = \frac{1}{4} \times \frac{2}{3} = \frac{2}{12} = \frac{1}{6} \] ### 1. b) Write 35 metres as a fraction of 105 metres. **Known conditions:** - 35 metres and 105 metres. **Fraction calculation:** \[ \text{Fraction} = \frac{35}{105} = \frac{1}{3} \] ### 2. Find the number that lies halfway between these fractions. #### a) \( \frac{1}{3} \) and \( \frac{5}{9} \) **Finding the average:** \[ \text{Average} = \frac{\frac{1}{3} + \frac{5}{9}}{2} \] **Finding a common denominator (9):** \[ \frac{1}{3} = \frac{3}{9} \] \[ \text{Average} = \frac{\frac{3}{9} + \frac{5}{9}}{2} = \frac{\frac{8}{9}}{2} = \frac{8}{18} = \frac{4}{9} \] #### b) \( \frac{7}{15} \) and \( \frac{1}{3} \) **Finding the average:** \[ \text{Average} = \frac{\frac{7}{15} + \frac{1}{3}}{2} \] **Finding a common denominator (15):** \[ \frac{1}{3} = \frac{5}{15} \] \[ \text{Average} = \frac{\frac{7}{15} + \frac{5}{15}}{2} = \frac{\frac{12}{15}}{2} = \frac{12}{30} = \frac{2}{5} \] ### 3. Calculate. #### a) \( \frac{1}{2}-\frac{9}{4} \times \frac{7}{6}+2 \) **Calculating step by step:** 1. Calculate \( \frac{9}{4} \times \frac{7}{6} = \frac{63}{24} = \frac{21}{8} \). 2. Now calculate \( \frac{1}{2} - \frac{21}{8} + 2 \). 3. Convert \( \frac{1}{2} \) to eighths: \( \frac{1}{2} = \frac{4}{8} \). 4. Convert 2 to eighths: \( 2 = \frac{16}{8} \). 5. Now calculate: \( \frac{4}{8} - \frac{21}{8} + \frac{16}{8} = \frac{4 - 21 + 16}{8} = \frac{-1}{8} \). #### b) \( \left(-\frac{1}{2}\right)^{2} \times\left(-\frac{3}{4}\right)^{2} \) **Calculating:** 1. \( \left(-\frac{1}{2}\right)^{2} = \frac{1}{4} \). 2. \( \left(-\frac{3}{4}\right)^{2} = \frac{9}{16} \). 3. Now calculate \( \frac{1}{4} \times \frac{9}{16} = \frac{9}{64} \). #### c) \( \sqrt[3]{-\frac{8}{216}}+\frac{1}{2} \) **Calculating:** 1. \( -\frac{8}{216} = -\frac{1}{27} \). 2. \( \sqrt[3]{-\frac{1}{27}} = -\frac{1}{3} \). 3. Now calculate \( -\frac{1}{3} + \frac{1}{2} = -\frac{2}{6} + \frac{3}{6} = \frac{1}{6} \). #### d) \( \sqrt{\frac{16}{25}} \) **Calculating:** \[ \sqrt{\frac{16}{25}} = \frac{\sqrt{16}}{\sqrt{25}} = \frac{4}{5} \] ### 4. Find three fractions between \( \frac{4}{10} \) and \( \frac{4}{5} \). **Converting to a common denominator (10):** - \( \frac{4}{5} = \frac{8}{10} \). **Fractions between \( \frac{4}{10} \) and \( \frac{8}{10} \):** 1. \( \frac{5}{10} \) 2. \( \frac{6}{10} \) 3. \( \frac{7}{10} \) ### 5. What is the difference between \( \frac{3}{5} \) and \( \frac{2}{3} \)? **Finding a common denominator (15):** 1. \( \frac{3}{5} = \frac{9}{15} \) 2. \( \frac{2}{3} = \frac{10}{15} \) **Calculating the difference:** \[ \frac{9}{15} - \frac{10}{15} = -\frac{1}{15} \] ### 6. What must be subtracted from \( \frac{8}{9} \) to give \( \frac{7}{8} \)? **Setting up the equation:** \[ \frac{8}{9} - x = \frac{7}{8} \] \[ x = \frac{8}{9} - \frac{7}{8} \] **Finding a common denominator (72):** 1. \( \frac{8}{9} = \frac{64}{72} \) 2. \( \frac{7}{8} = \frac{63}{72} \) **Calculating:** \[ x = \frac{64}{72} - \frac{63}{72} = \frac{1}{72} \] ### 7. A golf club has 144 members, of whom 63 are women. #### a) What fraction of the members are men? **Calculating the number of men:** \[ \