EXERCISE 6.8 \( \begin{array}{l}\text { 1. Convert the following percentages into common fractions: } \\ \begin{array}{lll}\text { a) } \\ \text { 2. Convert the following fractions into percentages: } & \text { b) } 12 \% & \text { c) } 55 \%\end{array} \\ \begin{array}{lll}\text { a a) } \frac{33}{100} & \text { b) } \frac{24}{75} & \text { c) } \frac{15}{30}\end{array} \\ \begin{array}{l}\text { 3. Which is a better achievement: winning } 12 \text { out of the last } 20 \text { soccer } \\ \text { matches or } 22 \text { out of } 40 \text { soccer matches? }\end{array} \\ \text { 4. Calculate: } \\ \begin{array}{ll}\text { a) } 75 \% \text { of } 40 & \text { b) } 30 \% \text { of } 90\end{array} \\ \text { 5. John invested R1 } 000 \text { and by the end of a year he earned R50 interest. } \\ \text { By what percentage did his investment grow? } \\ \text { 6. In a bag of } 35 \text { marbles } 28 \text { are blue and the rest are red. Calculate the } \\ \text { percentage of the blue marbles. }\end{array} \) 7. In the Grade 7 class, 16 of the 40 students are boys. What percentage of the class are girls?

Let's solve the problems step by step. ### 1. Convert the following percentages into common fractions: **a)** \( 12\% \) To convert a percentage to a fraction, we divide by 100: \[ 12\% = \frac{12}{100} = \frac{3}{25} \] **b)** \( 55\% \) \[ 55\% = \frac{55}{100} = \frac{11}{20} \] ### 2. Convert the following fractions into percentages: **a)** \( \frac{33}{100} \) To convert a fraction to a percentage, we multiply by 100: \[ \frac{33}{100} \times 100 = 33\% \] **b)** \( \frac{24}{75} \) \[ \frac{24}{75} \times 100 = \frac{24 \times 100}{75} = 32\% \] **c)** \( \frac{15}{30} \) \[ \frac{15}{30} \times 100 = \frac{15 \times 100}{30} = 50\% \] ### 3. Which is a better achievement: winning 12 out of the last 20 soccer matches or 22 out of 40 soccer matches? To compare the achievements, we can convert both to percentages. **Achievement 1:** \( \frac{12}{20} \) \[ \frac{12}{20} \times 100 = 60\% \] **Achievement 2:** \( \frac{22}{40} \) \[ \frac{22}{40} \times 100 = 55\% \] **Conclusion:** Winning 12 out of 20 matches (60%) is a better achievement than winning 22 out of 40 matches (55%). ### 4. Calculate: **a)** \( 75\% \) of \( 40 \) \[ 75\% \text{ of } 40 = \frac{75}{100} \times 40 = 30 \] **b)** \( 30\% \) of \( 90 \) \[ 30\% \text{ of } 90 = \frac{30}{100} \times 90 = 27 \] ### 5. John invested R1,000 and by the end of a year he earned R50 interest. By what percentage did his investment grow? To find the percentage growth, we use the formula: \[ \text{Percentage Growth} = \left( \frac{\text{Interest}}{\text{Principal}} \right) \times 100 \] \[ \text{Percentage Growth} = \left( \frac{50}{1000} \right) \times 100 = 5\% \] ### 6. In a bag of 35 marbles, 28 are blue and the rest are red. Calculate the percentage of the blue marbles. To find the percentage of blue marbles: \[ \text{Percentage of Blue Marbles} = \left( \frac{\text{Number of Blue Marbles}}{\text{Total Number of Marbles}} \right) \times 100 \] \[ \text{Percentage of Blue Marbles} = \left( \frac{28}{35} \right) \times 100 = 80\% \] ### 7. In the Grade 7 class, 16 of the 40 students are boys. What percentage of the class are girls? First, we find the number of girls: \[ \text{Number of Girls} = \text{Total Students} - \text{Number of Boys} = 40 - 16 = 24 \] Now, we calculate the percentage of girls: \[ \text{Percentage of Girls} = \left( \frac{\text{Number of Girls}}{\text{Total Students}} \right) \times 100 \] \[ \text{Percentage of Girls} = \left( \frac{24}{40} \right) \times 100 = 60\% \] ### Summary of Answers: 1. \( 12\% = \frac{3}{25} \), \( 55\% = \frac{11}{20} \) 2. \( \frac{33}{100} = 33\% \), \( \frac{24}{75} = 32\% \), \( \frac{15}{30} = 50\% \) 3. Winning 12 out of 20 matches is better (60%). 4. \( 75\% \) of \( 40 = 30 \), \( 30\% \) of \( 90 = 27 \) 5. Investment grew by \( 5\% \). 6. Percentage of blue marbles = \( 80\% \). 7. Percentage of girls = \( 60\% \).