Answer :
Sure, let's work through both parts of the question step by step.
### Converting Percentages to Fractions in Simplest Form
To convert a percentage to a fraction, we place the percentage over 100 and simplify it.
a) [tex]\(29 \%\)[/tex]
[tex]\[ 29\% = \frac{29}{100} \][/tex]
[tex]\[ \text{This fraction is already in its simplest form.} \][/tex]
b) [tex]\(34 \%\)[/tex]
[tex]\[ 34\% = \frac{34}{100} \][/tex]
[tex]\[ \frac{34 \div 2}{100 \div 2} = \frac{17}{50} \][/tex]
c) [tex]\(30 \%\)[/tex]
[tex]\[ 30\% = \frac{30}{100} \][/tex]
[tex]\[ \frac{30 \div 10}{100 \div 10} = \frac{3}{10} \][/tex]
d) [tex]\(82 \%\)[/tex]
[tex]\[ 82\% = \frac{82}{100} \][/tex]
[tex]\[ \frac{82 \div 2}{100 \div 2} = \frac{41}{50} \][/tex]
e) [tex]\(100 \%\)[/tex]
[tex]\[ 100\% = \frac{100}{100} \][/tex]
[tex]\[ \text{This fraction simplifies to } 1 \][/tex]
f) [tex]\(50 \%\)[/tex]
[tex]\[ 50\% = \frac{50}{100} \][/tex]
[tex]\[ \frac{50 \div 50}{100 \div 50} = \frac{1}{2} \][/tex]
g) [tex]\(90 \%\)[/tex]
[tex]\[ 90\% = \frac{90}{100} \][/tex]
[tex]\[ \frac{90 \div 10}{100 \div 10} = \frac{9}{10} \][/tex]
h) [tex]\(81 \%\)[/tex]
[tex]\[ 81\% = \frac{81}{100} \][/tex]
[tex]\[ \text{This fraction is already in its simplest form.} \][/tex]
i) [tex]\(45 \%\)[/tex]
[tex]\[ 45\% = \frac{45}{100} \][/tex]
[tex]\[ \frac{45 \div 5}{100 \div 5} = \frac{9}{20} \][/tex]
j) [tex]\(16 \%\)[/tex]
[tex]\[ 16\% = \frac{16}{100} \][/tex]
[tex]\[ \frac{16 \div 4}{100 \div 4} = \frac{4}{25} \][/tex]
So, the fractions in simplest form are:
[tex]\[ \frac{29}{100}, \frac{17}{50}, \frac{3}{10}, \frac{41}{50}, 1, \frac{1}{2}, \frac{9}{10}, \frac{81}{100}, \frac{9}{20}, \frac{4}{25} \][/tex]
### Writing Fractions as Percentages
To convert a fraction to a percentage, we first convert it to a fraction with a denominator of 100, if it isn't already, and then multiply the numerator by 100.
a) [tex]\(\frac{3}{10}\)[/tex]
[tex]\[ \frac{3}{10} = \frac{3 \times 10}{10 \times 10} = \frac{30}{100} \][/tex]
[tex]\[ = 30\% \][/tex]
b) [tex]\(\frac{9}{10}\)[/tex]
[tex]\[ \frac{9}{10} = \frac{9 \times 10}{10 \times 10} = \frac{90}{100} \][/tex]
[tex]\[ = 90\% \][/tex]
c) [tex]\(\frac{14}{100}\)[/tex]
[tex]\[ \text{This fraction is already over 100.} \][/tex]
[tex]\[ = 14\% \][/tex]
d) [tex]\(\frac{7}{10}\)[/tex]
[tex]\[ \frac{7}{10} = \frac{7 \times 10}{10 \times 10} = \frac{70}{100} \][/tex]
[tex]\[ = 70\% \][/tex]
e) [tex]\(\frac{77}{100}\)[/tex]
[tex]\[ \text{This fraction is already over 100.} \][/tex]
[tex]\[ = 77\% \][/tex]
f) [tex]\(\frac{66}{100}\)[/tex]
[tex]\[ \text{This fraction is already over 100.} \][/tex]
[tex]\[ = 66\% \][/tex]
g) [tex]\(\frac{9}{20}\)[/tex]
[tex]\[ \frac{9}{20} = \frac{9 \times 5}{20 \times 5} = \frac{45}{100} \][/tex]
[tex]\[ = 45\% \][/tex]
h) [tex]\(\frac{2}{50}\)[/tex]
[tex]\[ \frac{2}{50} = \frac{2 \times 2}{50 \times 2} = \frac{4}{100} \][/tex]
[tex]\[ = 4\% \][/tex]
i) [tex]\(\frac{1}{25}\)[/tex]
[tex]\[ \frac{1}{25} = \frac{1 \times 4}{25 \times 4} = \frac{4}{100} \][/tex]
[tex]\[ = 4\% \][/tex]
j) [tex]\(\frac{1}{4}\)[/tex]
[tex]\[ \frac{1}{4} = \frac{1 \times 25}{4 \times 25} = \frac{25}{100} \][/tex]
[tex]\[ = 25\% \][/tex]
k) [tex]\(\frac{3}{4}\)[/tex]
[tex]\[ \frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100} \][/tex]
[tex]\[ = 75\% \][/tex]
l) [tex]\(\frac{5}{5}\)[/tex]
[tex]\[ \text{This fraction is equivalent to } 1\text{, which equals } 100\%. \][/tex]
So, the fractions converted to percentages are:
[tex]\[ 30\%, 90\%, 14\%, 70\%, 77\%, 66\%, 45\%, 4\%, 4\%, 25\%, 75\%, 100\% \][/tex]
### Converting Percentages to Fractions in Simplest Form
To convert a percentage to a fraction, we place the percentage over 100 and simplify it.
a) [tex]\(29 \%\)[/tex]
[tex]\[ 29\% = \frac{29}{100} \][/tex]
[tex]\[ \text{This fraction is already in its simplest form.} \][/tex]
b) [tex]\(34 \%\)[/tex]
[tex]\[ 34\% = \frac{34}{100} \][/tex]
[tex]\[ \frac{34 \div 2}{100 \div 2} = \frac{17}{50} \][/tex]
c) [tex]\(30 \%\)[/tex]
[tex]\[ 30\% = \frac{30}{100} \][/tex]
[tex]\[ \frac{30 \div 10}{100 \div 10} = \frac{3}{10} \][/tex]
d) [tex]\(82 \%\)[/tex]
[tex]\[ 82\% = \frac{82}{100} \][/tex]
[tex]\[ \frac{82 \div 2}{100 \div 2} = \frac{41}{50} \][/tex]
e) [tex]\(100 \%\)[/tex]
[tex]\[ 100\% = \frac{100}{100} \][/tex]
[tex]\[ \text{This fraction simplifies to } 1 \][/tex]
f) [tex]\(50 \%\)[/tex]
[tex]\[ 50\% = \frac{50}{100} \][/tex]
[tex]\[ \frac{50 \div 50}{100 \div 50} = \frac{1}{2} \][/tex]
g) [tex]\(90 \%\)[/tex]
[tex]\[ 90\% = \frac{90}{100} \][/tex]
[tex]\[ \frac{90 \div 10}{100 \div 10} = \frac{9}{10} \][/tex]
h) [tex]\(81 \%\)[/tex]
[tex]\[ 81\% = \frac{81}{100} \][/tex]
[tex]\[ \text{This fraction is already in its simplest form.} \][/tex]
i) [tex]\(45 \%\)[/tex]
[tex]\[ 45\% = \frac{45}{100} \][/tex]
[tex]\[ \frac{45 \div 5}{100 \div 5} = \frac{9}{20} \][/tex]
j) [tex]\(16 \%\)[/tex]
[tex]\[ 16\% = \frac{16}{100} \][/tex]
[tex]\[ \frac{16 \div 4}{100 \div 4} = \frac{4}{25} \][/tex]
So, the fractions in simplest form are:
[tex]\[ \frac{29}{100}, \frac{17}{50}, \frac{3}{10}, \frac{41}{50}, 1, \frac{1}{2}, \frac{9}{10}, \frac{81}{100}, \frac{9}{20}, \frac{4}{25} \][/tex]
### Writing Fractions as Percentages
To convert a fraction to a percentage, we first convert it to a fraction with a denominator of 100, if it isn't already, and then multiply the numerator by 100.
a) [tex]\(\frac{3}{10}\)[/tex]
[tex]\[ \frac{3}{10} = \frac{3 \times 10}{10 \times 10} = \frac{30}{100} \][/tex]
[tex]\[ = 30\% \][/tex]
b) [tex]\(\frac{9}{10}\)[/tex]
[tex]\[ \frac{9}{10} = \frac{9 \times 10}{10 \times 10} = \frac{90}{100} \][/tex]
[tex]\[ = 90\% \][/tex]
c) [tex]\(\frac{14}{100}\)[/tex]
[tex]\[ \text{This fraction is already over 100.} \][/tex]
[tex]\[ = 14\% \][/tex]
d) [tex]\(\frac{7}{10}\)[/tex]
[tex]\[ \frac{7}{10} = \frac{7 \times 10}{10 \times 10} = \frac{70}{100} \][/tex]
[tex]\[ = 70\% \][/tex]
e) [tex]\(\frac{77}{100}\)[/tex]
[tex]\[ \text{This fraction is already over 100.} \][/tex]
[tex]\[ = 77\% \][/tex]
f) [tex]\(\frac{66}{100}\)[/tex]
[tex]\[ \text{This fraction is already over 100.} \][/tex]
[tex]\[ = 66\% \][/tex]
g) [tex]\(\frac{9}{20}\)[/tex]
[tex]\[ \frac{9}{20} = \frac{9 \times 5}{20 \times 5} = \frac{45}{100} \][/tex]
[tex]\[ = 45\% \][/tex]
h) [tex]\(\frac{2}{50}\)[/tex]
[tex]\[ \frac{2}{50} = \frac{2 \times 2}{50 \times 2} = \frac{4}{100} \][/tex]
[tex]\[ = 4\% \][/tex]
i) [tex]\(\frac{1}{25}\)[/tex]
[tex]\[ \frac{1}{25} = \frac{1 \times 4}{25 \times 4} = \frac{4}{100} \][/tex]
[tex]\[ = 4\% \][/tex]
j) [tex]\(\frac{1}{4}\)[/tex]
[tex]\[ \frac{1}{4} = \frac{1 \times 25}{4 \times 25} = \frac{25}{100} \][/tex]
[tex]\[ = 25\% \][/tex]
k) [tex]\(\frac{3}{4}\)[/tex]
[tex]\[ \frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100} \][/tex]
[tex]\[ = 75\% \][/tex]
l) [tex]\(\frac{5}{5}\)[/tex]
[tex]\[ \text{This fraction is equivalent to } 1\text{, which equals } 100\%. \][/tex]
So, the fractions converted to percentages are:
[tex]\[ 30\%, 90\%, 14\%, 70\%, 77\%, 66\%, 45\%, 4\%, 4\%, 25\%, 75\%, 100\% \][/tex]
