Answer :
Sure! Let's express each percentage as a fraction and simplify it to its simplest form. Here's how you can do that for each part:
a. [tex]$5 \%$[/tex]
To express 5% as a fraction, you write it as 5 over 100, because "percent" means "per hundred."
So, [tex]\( \frac{5}{100} \)[/tex].
Now, simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 5 in this case:
[tex]\( \frac{5 \div 5}{100 \div 5} = \frac{1}{20} \)[/tex].
b. [tex]$10 \%$[/tex]
Write 10% as a fraction: [tex]\( \frac{10}{100} \)[/tex].
Simplify by dividing the numerator and the denominator by 10:
[tex]\( \frac{10 \div 10}{100 \div 10} = \frac{1}{10} \)[/tex].
c. [tex]$50 \%$[/tex]
Write 50% as a fraction: [tex]\( \frac{50}{100} \)[/tex].
Simplify by dividing by 50:
[tex]\( \frac{50 \div 50}{100 \div 50} = \frac{1}{2} \)[/tex].
d. [tex]$33 \frac{1}{3} \%$[/tex]
First, convert the mixed number to an improper fraction: [tex]\( 33 \frac{1}{3} = \frac{100}{3} \)[/tex].
Write as a fraction of 100: [tex]\( \frac{\frac{100}{3}}{100} \)[/tex].
Which simplifies to:
[tex]\[
\frac{100}{3} \times \frac{1}{100} = \frac{100}{300} = \frac{1}{3}
\][/tex]
So the simplified fraction is [tex]\( \frac{1}{3} \)[/tex].
e. [tex]$66 \frac{2}{3} \%$[/tex]
Convert the mixed number to an improper fraction: [tex]\( 66 \frac{2}{3} = \frac{200}{3} \)[/tex].
Write as a fraction of 100: [tex]\( \frac{\frac{200}{3}}{100} \)[/tex].
This simplifies to:
[tex]\[
\frac{200}{3} \times \frac{1}{100} = \frac{200}{300} = \frac{2}{3}
\][/tex]
So the simplified fraction is [tex]\( \frac{2}{3} \)[/tex].
f. [tex]$12 \frac{1}{2} \%$[/tex]
Convert the mixed number to an improper fraction: [tex]\( 12 \frac{1}{2} = \frac{25}{2} \)[/tex].
Write as a fraction of 100: [tex]\( \frac{\frac{25}{2}}{100} \)[/tex].
This simplifies to:
[tex]\[
\frac{25}{2} \times \frac{1}{100} = \frac{25}{200} = \frac{1}{8}
\][/tex]
So the simplified fraction is [tex]\( \frac{1}{8} \)[/tex].
That's how you can express each percentage as a fraction in its simplest form!
a. [tex]$5 \%$[/tex]
To express 5% as a fraction, you write it as 5 over 100, because "percent" means "per hundred."
So, [tex]\( \frac{5}{100} \)[/tex].
Now, simplify the fraction by dividing the numerator and the denominator by their greatest common divisor, which is 5 in this case:
[tex]\( \frac{5 \div 5}{100 \div 5} = \frac{1}{20} \)[/tex].
b. [tex]$10 \%$[/tex]
Write 10% as a fraction: [tex]\( \frac{10}{100} \)[/tex].
Simplify by dividing the numerator and the denominator by 10:
[tex]\( \frac{10 \div 10}{100 \div 10} = \frac{1}{10} \)[/tex].
c. [tex]$50 \%$[/tex]
Write 50% as a fraction: [tex]\( \frac{50}{100} \)[/tex].
Simplify by dividing by 50:
[tex]\( \frac{50 \div 50}{100 \div 50} = \frac{1}{2} \)[/tex].
d. [tex]$33 \frac{1}{3} \%$[/tex]
First, convert the mixed number to an improper fraction: [tex]\( 33 \frac{1}{3} = \frac{100}{3} \)[/tex].
Write as a fraction of 100: [tex]\( \frac{\frac{100}{3}}{100} \)[/tex].
Which simplifies to:
[tex]\[
\frac{100}{3} \times \frac{1}{100} = \frac{100}{300} = \frac{1}{3}
\][/tex]
So the simplified fraction is [tex]\( \frac{1}{3} \)[/tex].
e. [tex]$66 \frac{2}{3} \%$[/tex]
Convert the mixed number to an improper fraction: [tex]\( 66 \frac{2}{3} = \frac{200}{3} \)[/tex].
Write as a fraction of 100: [tex]\( \frac{\frac{200}{3}}{100} \)[/tex].
This simplifies to:
[tex]\[
\frac{200}{3} \times \frac{1}{100} = \frac{200}{300} = \frac{2}{3}
\][/tex]
So the simplified fraction is [tex]\( \frac{2}{3} \)[/tex].
f. [tex]$12 \frac{1}{2} \%$[/tex]
Convert the mixed number to an improper fraction: [tex]\( 12 \frac{1}{2} = \frac{25}{2} \)[/tex].
Write as a fraction of 100: [tex]\( \frac{\frac{25}{2}}{100} \)[/tex].
This simplifies to:
[tex]\[
\frac{25}{2} \times \frac{1}{100} = \frac{25}{200} = \frac{1}{8}
\][/tex]
So the simplified fraction is [tex]\( \frac{1}{8} \)[/tex].
That's how you can express each percentage as a fraction in its simplest form!
