Question

Preview Percent means "out of 100 ." You can think of a percent as the numerator of a fraction with a denominator of \(100 .\) For example, \(25 \%\) means \(\frac{25}{100} .\) You can change a fraction to a percent by first finding an equivalent fraction with a denominator of 100 a. Change the following fractions to percents: \(\frac{3}{4}, \frac{1}{5}, \frac{20}{50}, \frac{8}{25}\) b. In Althea's homeroom, 14 of the 20 students ride the bus to school. What percent of the students take the bus? c. Of the 500 people in the audience at the school play, 350 bought their tickets in advance. What percent of the audience bought tickets in advance?

Short answer

a) \(75\%\), \(20\%\), \(40\%\), \(32\%\) b) 70% c) 70%

Step-by-step solution

Understanding Fractions to Percents

To convert a fraction to a percent, find an equivalent fraction with a denominator of 100, then read the numerator directly as the percent. Percent means 'out of 100.'

Convert \(\frac{3}{4}\) to a Percent

Multiply both the numerator and the denominator by 25 to get a fraction with a denominator of 100: \(\frac{3}{4} = \frac{3 \cdot 25}{4 \cdot 25} = \frac{75}{100}\). So, \(\frac{3}{4}\) is 75%.

Convert \(\frac{1}{5}\) to a Percent

Multiply both the numerator and the denominator by 20: \(\frac{1}{5} = \frac{1 \cdot 20}{5 \cdot 20} = \frac{20}{100}\). So, \(\frac{1}{5}\) is 20%.

Convert \(\frac{20}{50}\) to a Percent

Multiply both the numerator and the denominator by 2: \(\frac{20}{50} = \frac{20 \cdot 2}{50 \cdot 2} = \frac{40}{100}\). So, \(\frac{20}{50}\) is 40%.

Convert \(\frac{8}{25}\) to a Percent

Multiply both the numerator and the denominator by 4: \(\frac{8}{25} = \frac{8 \cdot 4}{25 \cdot 4} = \frac{32}{100}\). So, \(\frac{8}{25}\) is 32%.

Convert 14 out of 20 students to a Percent

First, write the fraction: \(\frac{14}{20}\). Next, find an equivalent fraction with a denominator of 100. Multiply both the numerator and denominator by 5: \(\frac{14 \cdot 5}{20 \cdot 5} = \frac{70}{100}\). This means 70% of the students take the bus.

Convert 350 out of 500 ticket buyers to a Percent

First, write the fraction: \(\frac{350}{500}\). Simplify the fraction by dividing both the numerator and the denominator by 5: \(\frac{350 \div 5}{500 \div 5} = \frac{70}{100}\). This means 70% of the audience bought tickets in advance.

Key concepts

Fractions to Percent

Converting fractions to percents is a crucial skill in mathematics. To do this, you need to convert a fraction into an equivalent fraction with a denominator of 100. This is because a percent is essentially a fraction that describes a number out of 100. For example, if you have the fraction \(\frac{3}{4}\), you want to find an equivalent fraction that has 100 as the denominator. You do this by multiplying both the numerator and the denominator by the same number. Here, you would multiply by 25 to get \(\frac{75}{100}\), which translates to 75%. Similarly, \(\frac{1}{5}\) becomes \(\frac{20}{100}\), so it's 20%.

Equivalent Fractions

Equivalent fractions are fractions that have different numerators and denominators but represent the same value. For example, \(\frac{1}{2}\) and \(\frac{2}{4}\) are equivalent because when simplified, they both equal \(\frac{1}{2}\). To convert a fraction to a percent, you look for an equivalent fraction with a denominator of 100. Let's take \(\frac{8}{25}\) as an example. Multiply both the numerator and the denominator by 4 to get \(\frac{32}{100}\), which tells you that \(\frac{8}{25}\) is equivalent to 32%.

Percent Calculation

Once you have an equivalent fraction with a denominator of 100, calculating the percent is straightforward. The numerator of the fraction becomes the percent. For instance, \(\frac{20}{50}\) can be converted to a fraction with a denominator of 100 by multiplying both the numerator and the denominator by 2 to get \(\frac{40}{100}\). This means that \(\frac{20}{50}\) is equivalent to 40%.
Similarly, another example is converting 14 out of 20 students to a percent. First, write the fraction as \(\frac{14}{20}\). Multiply both the numerator and denominator by 5 to get \(\frac{70}{100}\). Thus, 70% of the students take the bus.

Numerator and Denominator

Understanding the roles of the numerator and denominator in fractions is essential for converting them to percents. The numerator is the top number and tells you how many parts you have. The denominator is the bottom number and shows the total number of equal parts the whole is divided into. In the fraction \(\frac{3}{4}\), 3 is the numerator and 4 is the denominator.
When converting such a fraction to a percent, you adjust both the numerator and the denominator to form an equivalent fraction with a denominator of 100. For example, \(\frac{350}{500}\) can be simplified by dividing both the numerator and the denominator by 5 to get \(\frac{70}{100}\), showing that 70% of the audience bought tickets in advance.