Answer :
Sure! Let's go through each part of the question step-by-step.
### 1. Convert the following percentages into common fractions:
a) 80%
To convert a percentage to a fraction, divide by 100 and simplify if possible.
[tex]\( \frac{80}{100} = \frac{4}{5} \)[/tex].
b) 12%
Convert to a fraction by dividing by 100.
[tex]\( \frac{12}{100} = \frac{3}{25} \)[/tex].
c) 55%
Convert to a fraction.
[tex]\( \frac{55}{100} = \frac{11}{20} \)[/tex].
d) 94%
Convert to a fraction.
[tex]\( \frac{94}{100} = \frac{47}{50} \)[/tex].
### 2. Convert the following fractions into percentages:
a) [tex]\(\frac{33}{100}\)[/tex]
To convert a fraction to a percentage, multiply by 100.
[tex]\( 33\% \)[/tex].
b) [tex]\(\frac{24}{75}\)[/tex]
Convert to a percentage.
[tex]\[ \left(\frac{24}{75} \times 100\right)\% = 32\% \][/tex].
c) [tex]\(\frac{15}{30}\)[/tex]
Convert to a percentage.
[tex]\[ \left(\frac{15}{30} \times 100\right)\% = 50\% \][/tex].
d) [tex]\(\frac{16}{20}\)[/tex]
Convert to a percentage.
[tex]\[ \left(\frac{16}{20} \times 100\right)\% = 80\% \][/tex].
### 3. Which is a better achievement: winning 12 out of the last 20 soccer matches or 22 out of 40 soccer matches?
- Winning 12 out of 20 matches:
[tex]\(\frac{12}{20} = 0.6\)[/tex] or 60%.
- Winning 22 out of 40 matches:
[tex]\(\frac{22}{40} = 0.55\)[/tex] or 55%.
Thus, winning 12 out of 20 matches is a better achievement.
### 4. Calculate:
a) 75% of 40
[tex]\[ 0.75 \times 40 = 30 \][/tex].
b) 30% of 90
[tex]\[ 0.3 \times 90 = 27 \][/tex].
### 5. John invested R1,000 and by the end of a year he earned R50 interest. By what percentage did his investment grow?
The percentage growth is calculated by:
[tex]\[ \frac{50}{1000} \times 100 = 5\% \][/tex].
### 6. In a bag of 35 marbles, 28 are blue and the rest are red. Calculate the percentage of red marbles.
Number of red marbles = 35 - 28 = 7.
Calculate the percentage of red marbles:
[tex]\[ \frac{7}{35} \times 100 = 20\% \][/tex].
### 7. In the Grade 7 class, 16 out of the 40 students are boys. What percentage of the class are girls?
Number of girls = 40 - 16 = 24.
Calculate the percentage of girls:
[tex]\[ \frac{24}{40} \times 100 = 60\% \][/tex].
I hope this detailed explanation helps you understand the steps involved! If you have any more questions, feel free to ask!
### 1. Convert the following percentages into common fractions:
a) 80%
To convert a percentage to a fraction, divide by 100 and simplify if possible.
[tex]\( \frac{80}{100} = \frac{4}{5} \)[/tex].
b) 12%
Convert to a fraction by dividing by 100.
[tex]\( \frac{12}{100} = \frac{3}{25} \)[/tex].
c) 55%
Convert to a fraction.
[tex]\( \frac{55}{100} = \frac{11}{20} \)[/tex].
d) 94%
Convert to a fraction.
[tex]\( \frac{94}{100} = \frac{47}{50} \)[/tex].
### 2. Convert the following fractions into percentages:
a) [tex]\(\frac{33}{100}\)[/tex]
To convert a fraction to a percentage, multiply by 100.
[tex]\( 33\% \)[/tex].
b) [tex]\(\frac{24}{75}\)[/tex]
Convert to a percentage.
[tex]\[ \left(\frac{24}{75} \times 100\right)\% = 32\% \][/tex].
c) [tex]\(\frac{15}{30}\)[/tex]
Convert to a percentage.
[tex]\[ \left(\frac{15}{30} \times 100\right)\% = 50\% \][/tex].
d) [tex]\(\frac{16}{20}\)[/tex]
Convert to a percentage.
[tex]\[ \left(\frac{16}{20} \times 100\right)\% = 80\% \][/tex].
### 3. Which is a better achievement: winning 12 out of the last 20 soccer matches or 22 out of 40 soccer matches?
- Winning 12 out of 20 matches:
[tex]\(\frac{12}{20} = 0.6\)[/tex] or 60%.
- Winning 22 out of 40 matches:
[tex]\(\frac{22}{40} = 0.55\)[/tex] or 55%.
Thus, winning 12 out of 20 matches is a better achievement.
### 4. Calculate:
a) 75% of 40
[tex]\[ 0.75 \times 40 = 30 \][/tex].
b) 30% of 90
[tex]\[ 0.3 \times 90 = 27 \][/tex].
### 5. John invested R1,000 and by the end of a year he earned R50 interest. By what percentage did his investment grow?
The percentage growth is calculated by:
[tex]\[ \frac{50}{1000} \times 100 = 5\% \][/tex].
### 6. In a bag of 35 marbles, 28 are blue and the rest are red. Calculate the percentage of red marbles.
Number of red marbles = 35 - 28 = 7.
Calculate the percentage of red marbles:
[tex]\[ \frac{7}{35} \times 100 = 20\% \][/tex].
### 7. In the Grade 7 class, 16 out of the 40 students are boys. What percentage of the class are girls?
Number of girls = 40 - 16 = 24.
Calculate the percentage of girls:
[tex]\[ \frac{24}{40} \times 100 = 60\% \][/tex].
I hope this detailed explanation helps you understand the steps involved! If you have any more questions, feel free to ask!
