Question

write each percent as a fraction or a mixed number in lowest terms.

1. 19%
2. $2\frac{1}{2}\\%$
3. 72%
4. 130%
5. 40%
6. $87\frac{1}{2}\\%$
7. 50%
8. $18\frac{3}{4}\\%$

compare by using >, <, or = for each.

Explanation:

Step1: Recall the definition of percentage to fraction conversion

To convert a percentage to a fraction, we use the rule: \( x\%=\frac{x}{100} \). For mixed number percentages, first convert the mixed number to an improper fraction, then divide by 100.

Step2: Solve problem 22 (19%)

Using the rule \( x\% = \frac{x}{100} \), for \( 19\% \), we have \( 19\%=\frac{19}{100} \). Since 19 and 100 have no common factors other than 1, this is in lowest terms.

Step3: Solve problem 23 (130%)

For \( 130\% \), using the rule, we get \( 130\%=\frac{130}{100} \). Simplify by dividing numerator and denominator by 10: \( \frac{130\div10}{100\div10}=\frac{13}{10} \), which can be written as the mixed number \( 1\frac{3}{10} \).

Step4: Solve problem 24 (50%)

For \( 50\% \), using the rule, \( 50\% = \frac{50}{100} \). Simplify by dividing numerator and denominator by 50: \( \frac{50\div50}{100\div50}=\frac{1}{2} \).

Step5: Solve problem 25 (\( 2\frac{1}{2}\% \))

First, convert the mixed number \( 2\frac{1}{2} \) to an improper fraction. \( 2\frac{1}{2}=\frac{2\times2 + 1}{2}=\frac{5}{2} \). Then, using the percentage to fraction rule, \( 2\frac{1}{2}\%=\frac{\frac{5}{2}}{100}=\frac{5}{2}\times\frac{1}{100}=\frac{5}{200} \). Simplify by dividing numerator and denominator by 5: \( \frac{5\div5}{200\div5}=\frac{1}{40} \).

Step6: Solve problem 26 (40%)

For \( 40\% \), using the rule, \( 40\%=\frac{40}{100} \). Simplify by dividing numerator and denominator by 20: \( \frac{40\div20}{100\div20}=\frac{2}{5} \).

Step7: Solve problem 27 (\( 18\frac{3}{4}\% \))

First, convert \( 18\frac{3}{4} \) to an improper fraction. \( 18\frac{3}{4}=\frac{18\times4+3}{4}=\frac{75}{4} \). Then, \( 18\frac{3}{4}\%=\frac{\frac{75}{4}}{100}=\frac{75}{4}\times\frac{1}{100}=\frac{75}{400} \). Simplify by dividing numerator and denominator by 25: \( \frac{75\div25}{400\div25}=\frac{3}{16} \).

Step8: Solve problem 28 (72%)

For \( 72\% \), using the rule, \( 72\%=\frac{72}{100} \). Simplify by dividing numerator and denominator by 4: \( \frac{72\div4}{100\div4}=\frac{18}{25} \).

Step9: Solve problem 29 (\( 87\frac{1}{2}\% \))

First, convert \( 87\frac{1}{2} \) to an improper fraction. \( 87\frac{1}{2}=\frac{87\times2 + 1}{2}=\frac{175}{2} \). Then, \( 87\frac{1}{2}\%=\frac{\frac{175}{2}}{100}=\frac{175}{2}\times\frac{1}{100}=\frac{175}{200} \). Simplify by dividing numerator and denominator by 25: \( \frac{175\div25}{200\div25}=\frac{7}{8} \).

Answer:

s (for each sub - problem):

1. \( \boldsymbol{\frac{19}{100}} \)
2. \( \boldsymbol{1\frac{3}{10}} \) (or \( \boldsymbol{\frac{13}{10}} \))
3. \( \boldsymbol{\frac{1}{2}} \)
4. \( \boldsymbol{\frac{1}{40}} \)
5. \( \boldsymbol{\frac{2}{5}} \)
6. \( \boldsymbol{\frac{3}{16}} \)
7. \( \boldsymbol{\frac{18}{25}} \)
8. \( \boldsymbol{\frac{7}{8}} \)