Changing percents to fractions
Converting a percent to a fraction means writing the percent's value over a denominator of 100 and then simplifying. 45% becomes 45/100, which simplifies to 9/20 by dividing both by 5. For fractional percents like 33 and 1/3%, write as (100/3) divided by 100 = 100/300 = 1/3. This Grade 7 math skill from Saxon Math, Course 2 reinforces the definition of percent as 'per hundred' and is needed when percent problems are more efficiently solved using fraction arithmetic than decimal arithmetic.
Key Concepts
Property To convert a percent to a fraction, write the percent's value as the numerator over a denominator of 100. Then, simplify the fraction to its lowest terms. So, $P\% = \frac{P}{100}$.
Examples To convert 80 percent: $80\% = \frac{80}{100} = \frac{4 \cdot 20}{5 \cdot 20} = \frac{4}{5}$. To convert 25 percent: $25\% = \frac{25}{100} = \frac{1 \cdot 25}{4 \cdot 25} = \frac{1}{4}$. To convert 60 percent: $60\% = \frac{60}{100} = \frac{3 \cdot 20}{5 \cdot 20} = \frac{3}{5}$.
Explanation Percentages are just fractions wearing a fancy costume! The word 'percent' is Latin for 'per hundred.' So, to reveal a percent's true identity, you just place it over 100 and simplify. It's a quick change act for numbers, turning something like 80% into a simpler form like $\frac{4}{5}$.
Common Questions
How do I convert a percent to a fraction?
Write the percent as a fraction over 100, then simplify by dividing numerator and denominator by their GCF. For example, 60% = 60/100 = 3/5.
What is 75% as a fraction?
75% = 75/100 = 3/4 (divide by 25).
What is 33 and 1/3% as a fraction?
33 and 1/3% = (100/3)% over 100 = (100/3) divided by 100 = (100/3) times (1/100) = 1/3.
Why is a percent defined as a fraction over 100?
The word 'percent' literally means 'per hundred.' So 45% means 45 per 100, or 45/100. The definition makes the conversion straightforward.
When do students learn to convert percents to fractions?
Percent-to-fraction conversion is a Grade 6-7 skill. Saxon Math, Course 2 covers it in Chapter 2 as part of the fraction-decimal-percent number system.
What percents should students know as fractions?
Benchmark conversions: 25% = 1/4, 50% = 1/2, 75% = 3/4, 20% = 1/5, 10% = 1/10, 33 and 1/3% = 1/3, 66 and 2/3% = 2/3. Memorizing these speeds up many calculations.
When is it more useful to convert a percent to a fraction rather than a decimal?
When the resulting fraction is a simple one-digit fraction (like 1/4 or 1/3), fraction arithmetic may be easier than decimal arithmetic. For example, finding 1/3 of 99 is easier than 0.333... times 99.