3  Fractions, decimals, percents

3.1 Proportion and percent

Another interpretation of fractions is as a proportion.

For example, the statement “3/4 of the people in Taos County like dogs” means that in a typical group of 4 people, three of them will like dogs.

We can also represent proportion as a percent, which tells us how many compared to a group size of 100.

  • Since \(\frac{3}{4} = \frac{75}{100}\), the proportion 3/4 is equivalent to 75%.

Finally, we can represent fraction as a decimal number.

  • We have \(\frac{3}{4} = \frac{75}{100} = 0.75\).

In summary, we have \(\frac{3}{4} = 75\% = 0.75\)

Example 3.1 (Practice: converting fractions to decimals and percents)  

  1. \(\dfrac{1}{4} =\)

  2. \(\dfrac{3}{5} =\)

  3. \(\dfrac{7}{8} =\)

  4. \(\dfrac{2}{3} =\)

  5. \(\dfrac{5}{6} =\)

  6. \(\dfrac{3}{10} =\)

  7. \(\dfrac{5}{4} =\)

  8. \(\dfrac{7}{5} =\)

  1. \(\dfrac{1}{4} = 0.25 = 25\%\)

  2. \(\dfrac{3}{5} = 0.6 = 60\%\)

  3. \(\dfrac{7}{8} = 0.875 = 87.5\%\)

  4. \(\dfrac{2}{3} = 0.\overline{6} = 66.\overline{6}\%\)

  5. \(\dfrac{5}{6} = 0.8\overline{3} = 83.\overline{3}\%\)

  6. \(\dfrac{3}{10} = 0.3 = 30\%\)

  7. \(\dfrac{5}{4} = 1.25 = 125\%\)

  8. \(\dfrac{7}{5} = 1.4 = 140\%\)

Example 3.2 (Practice: converting percents to fractions)  

  1. \(25\% =\)

  2. \(40\% =\)

  3. \(75\% =\)

  4. \(60\% =\)

  5. \(3.5\% =\)

  6. \(8.25\% =\)

  1. \(25\% = \dfrac{25}{100} = \dfrac{1}{4}\)

  2. \(40\% = \dfrac{40}{100} = \dfrac{2}{5}\)

  3. \(75\% = \dfrac{75}{100} = \dfrac{3}{4}\)

  4. \(60\% = \dfrac{60}{100} = \dfrac{3}{5}\)

  5. \(3.5\% = \dfrac{3.5}{100}= \dfrac{35}{1000} = \dfrac{7}{200}\)

  6. \(8.25\% = \dfrac{8.25}{100} =\dfrac{825}{10000} = \dfrac{1}{125}\)

Example 3.3 (Practice: converting decimals to percents and fractions)  

  1. \(0.4 =\)

  2. \(0.7 =\)

  3. \(0.125 =\)

  4. \(0.625 =\)

  5. \(1.09 =\)

  6. \(0.375 =\)

  1. \(0.4 = 40\% = \dfrac{4}{10}\)

  2. \(0.7 = 70\% = \dfrac{7}{10}\)

  3. \(0.125 = 12.5\% = \dfrac{125}{1000}\)

  4. \(0.625 = 62.5\% = \dfrac{625}{1000}\)

  5. \(1.09 = 109\% = \dfrac{109}{100}\)

  6. \(0.375 = 37.5\% = \dfrac{375}{1000}\)

3.2 Computing percents from amounts

The UNM-Taos Institutional Research Office gathers and computes various data about students attending UNM-Taos. The following problems use data from the Spring 2026 Census Snapshot.

In Spring 2026, UNM-Taos had 1321 students. Of these students, 717 were continuing students (who had attended a previous semester). The percent of continuing students was \[ \frac{\text{number of continuing students}}{\text{number of total students}} = \frac{717}{1321} \approx 0.54 = 54\%. \]

Example 3.4 (Practice: computing percents from amounts)  

  1. There were 50 transfer students. What percent is this?

  2. There were 57 first-year students. What percent is this?

  3. There were 933 who consider UNM-Taos as their “home campus” (as opposed to dual-enrollment students or students from other UNM campuses who are taking classes here). What percent is this?

  1. \(\dfrac{50}{1321} \approx 0.0378 = 3.78\%\)

  2. \(\dfrac{57}{1321} \approx 0.0432 = 4.32\%\)

  3. \(\dfrac{933}{1321} \approx 0.7063 = 70.63\%\)

3.3 Computing amounts from percents

In Spring 2026, 66% of students enrolled at UNM-Taos were classified as female. Given that there were 1321 total students, we can compute the number of female students as \[ 66\% \text{ of }1321 = 0.66\cdot 1321 = 871.86 \approx 872\text{ students}. \]

Example 3.5 (Practice: computing amounts from percents)  

  1. 57% of the students were degree-seeking students. How many students is this?

  2. 42% of the students were full-time students. How many students is this?

  3. 27% of the students taking classes at UNM-Taos were students from the Albuquerque campus. How many students is this?

  1. \(0.57 \cdot 1321 \approx 753.0\) students

  2. \(0.42 \cdot 1321 \approx 554.8 \approx 555\) students

  3. \(0.27 \cdot 1321 \approx 356.7 \approx 357\) students

3.4 Homework exercises

Exercise 3.1 Convert each fraction to a decimal and to a percent.

  1. \(\dfrac{1}{2}\)

  2. \(\dfrac{4}{5}\)

  3. \(\dfrac{3}{8}\)

  4. \(\dfrac{5}{9}\)

  5. \(\dfrac{7}{10}\)

  6. \(\dfrac{1}{3}\)

  7. \(\dfrac{2}{5}\)

  8. \(\dfrac{9}{4}\)

  9. \(\dfrac{11}{5}\)

  10. \(\dfrac{8}{3}\)

  1. \(\dfrac{1}{2} = 0.5 = 50\%\)

  2. \(\dfrac{4}{5} = 0.8 = 80\%\)

  3. \(\dfrac{3}{8} = 0.375 = 37.5\%\)

  4. \(\dfrac{5}{9} = 0.\overline{5} = 55.\overline{5}\%\)

  5. \(\dfrac{7}{10} = 0.7 = 70\%\)

  6. \(\dfrac{1}{3} = 0.\overline{3} = 33.\overline{3}\%\)

  7. \(\dfrac{2}{5} = 0.4 = 40\%\)

  8. \(\dfrac{9}{4} = 2.25 = 225\%\)

  9. \(\dfrac{11}{5} = 2.2 = 220\%\)

  10. \(\dfrac{8}{3} = 2.\overline{6} = 266.\overline{6}\%\)

Exercise 3.2 Convert each percent to a fraction. Simplify your answer.

  1. \(30\%\)

  2. \(50\%\)

  3. \(20\%\)

  4. \(65\%\)

  5. \(45\%\)

  6. \(70\%\)

  7. \(15\%\)

  8. \(90\%\)

  9. \(12.5\%\)

  10. \(37.5\%\)

  1. \(30\% = \dfrac{30}{100} = \dfrac{3}{10}\)

  2. \(50\% = \dfrac{50}{100} = \dfrac{1}{2}\)

  3. \(20\% = \dfrac{20}{100} = \dfrac{1}{5}\)

  4. \(65\% = \dfrac{65}{100} = \dfrac{13}{20}\)

  5. \(45\% = \dfrac{45}{100} = \dfrac{9}{20}\)

  6. \(70\% = \dfrac{70}{100} = \dfrac{7}{10}\)

  7. \(15\% = \dfrac{15}{100} = \dfrac{3}{20}\)

  8. \(90\% = \dfrac{90}{100} = \dfrac{9}{10}\)

  9. \(12.5\% = \dfrac{12.5}{100} = \dfrac{125}{1000} = \dfrac{1}{8}\)

  10. \(37.5\% = \dfrac{37.5}{100} = \dfrac{375}{1000} = \dfrac{3}{8}\)

Exercise 3.3 Convert each decimal to a percent and to a fraction. Do not simplify the fraction.

  1. \(0.6\)

  2. \(0.3\)

  3. \(0.875\)

  4. \(0.225\)

  5. \(1.15\)

  6. \(0.625\)

  7. \(0.475\)

  8. \(2.25\)

  9. \(0.325\)

  10. \(1.85\)

  1. \(0.6 = 60\% = \dfrac{6}{10}\)

  2. \(0.3 = 30\% = \dfrac{3}{10}\)

  3. \(0.875 = 87.5\% = \dfrac{875}{1000}\)

  4. \(0.225 = 22.5\% = \dfrac{225}{1000}\)

  5. \(1.15 = 115\% = \dfrac{115}{100}\)

  6. \(0.625 = 62.5\% = \dfrac{625}{1000}\)

  7. \(0.475 = 47.5\% = \dfrac{475}{1000}\)

  8. \(2.25 = 225\% = \dfrac{225}{100}\)

  9. \(0.325 = 32.5\% = \dfrac{325}{1000}\)

  10. \(1.85 = 185\% = \dfrac{185}{100}\)

Exercise 3.4 According to the 2020 census, Taos County had a total population of 34,489 people. Use this information to answer the following questions. Round your answers to two decimal places.

  1. There were 17,430 people classified as Hispanic residents. What percent is this?

  2. There were 13,706 people classified as White (non-Hispanic) residents. What percent is this?

  3. There were 2,108 people classified as American Indian/Alaska Native residents. What percent is this?

  4. Of the 15,747 households, 3,514 had children under the age of 18 living with them. What percent of households is this?

  5. There were 20,904 housing units in the county, of which 5,157 were vacant. What percent of housing units were vacant?

  6. Of the 34,489 residents, 18,833 lived in rural areas. What percent lived in rural areas?

  1. \(\dfrac{17,430}{34,489} \approx 0.5053 = 50.53\%\)

  2. \(\dfrac{13,706}{34,489} \approx 0.3974 = 39.74\%\)

  3. \(\dfrac{2,108}{34,489} \approx 0.0611 = 6.11\%\)

  4. \(\dfrac{3,514}{15,747} \approx 0.2232 = 22.32\%\)

  5. \(\dfrac{5,157}{20,904} \approx 0.2467 = 24.67\%\)

  6. \(\dfrac{18,833}{34,489} \approx 0.5461 = 54.61\%\)

Exercise 3.5 According to the 2020 census, New Mexico had a total population of 2,117,522 people. Use this information to answer the following questions. Round your answers to the nearest whole number.

  1. 47.7% of the residents were classified as Hispanic. How many residents is this?

  2. 36.5% of the residents were classified as White (non-Hispanic). How many residents is this?

  3. 9.5% of the residents were classified as American Indian/Alaska Native. How many residents is this?

  4. 18.5% of the residents were ages 65 and older. How many residents is this?

  5. 76.1% of the residents were ages 18 and older. How many residents is this?

  6. 1.8% of the residents were classified as Black or African American. How many residents is this?

  7. 2.8% of the residents identified as two or more races. How many residents is this?

  1. \(0.477 \cdot 2,117,522 \approx 1,010,058\) residents

  2. \(0.365 \cdot 2,117,522 \approx 772,895\) residents

  3. \(0.095 \cdot 2,117,522 \approx 201,165\) residents

  4. \(0.185 \cdot 2,117,522 \approx 391,742\) residents

  5. \(0.761 \cdot 2,117,522 \approx 1,611,434\) residents

  6. \(0.018 \cdot 2,117,522 \approx 38,115\) residents

  7. \(0.028 \cdot 2,117,522 \approx 59,291\) residents