Answer :
Percent means per hundred, which means, when you are using a percent, you are actually using a ratio to compare the number of your percent to one hundred.
For example, suppose we have 5%. The percent symbol (%) indicates that we are using a ratio to compare 5 to 100, and remember that we use fractions to express ratios, so we can express 5% as the ratio [tex] \frac{5}{100} [/tex]. Notice that we can simplify our ratio, both numerator and denominator are divisible by 5, so lets simplify it: [tex] \frac{5}{100} = \frac{1}{20} [/tex]. We can conclude that we can express 5% as the ratio [tex] \frac{1}{20} [/tex].
Now that we know we can express a percent as ratio, lets show how the percent is related to a proportion:
Suppose that in a class of 30 students are 12 girls, and you want to find how many percent of girls are in your class using a proportion:
Let [tex]x[/tex]% be the percent girls. Since we know that percents can be expressed as ratios, [tex]x[/tex]%=[tex] \frac{x}{100} [/tex]: Now we can use the fact that the students are in a ratio 12 to 30 to establish our proportion:
[tex] \frac{12}{30} = \frac{x}{100} [/tex]
[tex]x= \frac{(12)(100)}{30} [/tex]
[tex]x=40[/tex]
We just prove that 40% of the students are girls.
The proportion that we used in this problem is called a percent proportion, and its formula: [tex] \frac{a}{b} = \frac{x}{100} [/tex] can be use to relate a percent with a proportion.
For example, suppose we have 5%. The percent symbol (%) indicates that we are using a ratio to compare 5 to 100, and remember that we use fractions to express ratios, so we can express 5% as the ratio [tex] \frac{5}{100} [/tex]. Notice that we can simplify our ratio, both numerator and denominator are divisible by 5, so lets simplify it: [tex] \frac{5}{100} = \frac{1}{20} [/tex]. We can conclude that we can express 5% as the ratio [tex] \frac{1}{20} [/tex].
Now that we know we can express a percent as ratio, lets show how the percent is related to a proportion:
Suppose that in a class of 30 students are 12 girls, and you want to find how many percent of girls are in your class using a proportion:
Let [tex]x[/tex]% be the percent girls. Since we know that percents can be expressed as ratios, [tex]x[/tex]%=[tex] \frac{x}{100} [/tex]: Now we can use the fact that the students are in a ratio 12 to 30 to establish our proportion:
[tex] \frac{12}{30} = \frac{x}{100} [/tex]
[tex]x= \frac{(12)(100)}{30} [/tex]
[tex]x=40[/tex]
We just prove that 40% of the students are girls.
The proportion that we used in this problem is called a percent proportion, and its formula: [tex] \frac{a}{b} = \frac{x}{100} [/tex] can be use to relate a percent with a proportion.