Converting Percents to Fractions
Grade 8 math lesson on converting percents to fractions by removing the percent sign and dividing by 100. Students learn to simplify the resulting fractions and apply percent-to-fraction conversions in real-world contexts.
Key Concepts
Property To perform calculations with percents, we first convert the percent to a fraction. For example, $40\% = \frac{40}{100} = \frac{2}{5}$.
Examples A simple conversion: $70\% = \frac{70}{100} = \frac{7}{10}$. With a mixed number percent: $37\frac{1}{2}\% = \frac{37.5}{100} = \frac{375}{1000} = \frac{3}{8}$. For a small percentage: $4\% = \frac{4}{100} = \frac{1}{25}$.
Explanation To change a percent back into a familiar fraction, just take the number, drop the % symbol, and place it over 100. That’s it! The percent has revealed its true fractional form. Don’t forget to simplify the fraction to its most handsome, reduced self, because nobody likes a clunky, unsimplified fraction at the dinner table.
Common Questions
How do you convert a percent to a fraction?
To convert a percent to a fraction, remove the percent sign and write the number over 100, then simplify. For example, 75% = 75/100 = 3/4. For 33.3%, write 33.3/100 = 333/1000 = 1/3.
Why do we divide by 100 when converting percent to fraction?
The word percent means per hundred (from Latin per centum). So 75% means 75 per hundred, which is the same as the fraction 75/100.
How do you simplify a fraction after converting from a percent?
Find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. For example, 60/100: the GCF of 60 and 100 is 20, so 60/100 = 3/5.
What are common percent to fraction conversions to memorize?
Useful conversions: 25% = 1/4, 50% = 1/2, 75% = 3/4, 33.3% = 1/3, 66.7% = 2/3, 20% = 1/5, 10% = 1/10, 1% = 1/100.