Percents With Fractions
Percents with fractions involves converting percent values that contain fractions, like 83 1/3% or 16 2/3%, into simplified fractions. The process starts by writing the percent as a fraction over 100, creating a complex fraction, then simplifying. For instance, 16 2/3% = (50/3)/100 = 50/300 = 1/6. This skill is covered in Chapter 8 of Saxon Math Course 2 for 7th grade math and is important for working with common fractional percents that appear frequently in discounts, probability, and standardized tests.
Key Concepts
Property A percent is just a fraction with a denominator of 100. To convert a percent that contains a fraction, simply write it over 100, like this: $$ 83\frac{1}{3}\% = \frac{83\frac{1}{3}}{100} $$.
Examples Convert the percent to a complex fraction, then simplify: $ 16\frac{2}{3}\% = \frac{16\frac{2}{3}}{100} = \frac{\frac{50}{3}}{\frac{100}{1}} = \frac{50}{3} \cdot \frac{1}{100} = \frac{50}{300} = \frac{1}{6} $ A percent is a fraction over 100: $ 66\frac{2}{3}\% = \frac{\frac{200}{3}}{100} = \frac{200}{3} \cdot \frac{1}{100} = \frac{200}{300} = \frac{2}{3} $ Write as a fraction, then multiply by the reciprocal of the denominator: $ 8\frac{1}{3}\% = \frac{\frac{25}{3}}{100} = \frac{25}{3} \cdot \frac{1}{100} = \frac{25}{300} = \frac{1}{12} $.
Explanation Don't let fractional percents scare you! Just remember that 'percent' means 'out of 100.' Put that funky fraction over 100 to create a complex fraction. Then, use your simplification superpowers to turn both the top and bottom into simple fractions and solve. It’s a two step takedown: first make the complex fraction, then simplify it!
Common Questions
How do you convert a percent with a fraction to a regular fraction?
Write the percent over 100 to create a complex fraction, then simplify. For 16 2/3%, write 16 2/3 over 100, convert to 50/3 divided by 100, which equals 50/300 = 1/6. The key step is converting the mixed number in the numerator to an improper fraction first.
What is 33 1/3% as a fraction?
33 1/3% equals 1/3. Write 33 1/3 over 100: that is 100/3 divided by 100, which simplifies to 100/300 = 1/3. This is one of the most common fractional percents students should memorize.
What is 83 1/3% as a fraction?
83 1/3% equals 5/6. Write 83 1/3 over 100: that is 250/3 divided by 100 = 250/300 = 5/6. Recognizing that 83 1/3% is the complement of 16 2/3% (which equals 1/6) can help verify the answer.
Why do some percents have fractions in them?
Some ratios do not convert to neat whole-number percents. For example, 1/3 of 100 is 33.333..., so it is written as 33 1/3%. These fractional percents arise naturally when dividing quantities that are not factors of 100.
What are the most common fractional percents to memorize?
The most important ones are 33 1/3% = 1/3, 66 2/3% = 2/3, 16 2/3% = 1/6, 83 1/3% = 5/6, and 12 1/2% = 1/8. Memorizing these saves time on tests and in real-world calculations.
When do students learn percents with fractions?
This topic appears in 7th grade math. Saxon Math Course 2 covers it in Chapter 8, where students build on earlier percent and fraction skills to handle more complex conversions involving fractional percents.