How to Solve Word Problems Involving Comparing Percent and Fractions?
Should you compare a percent to a fraction directly? Not until they are in the same form. The easiest strategy is to convert both values to decimals, then compare. This lesson shows you exactly how to handle GED word problems that ask you to compare, order, or decide between a percentage and a fraction.
What Does It Mean to Compare Percent and Fractions?
Comparing a percent and a fraction means determining which is larger, smaller, or whether they are equal. Because percent and fraction express the same kind of “part of a whole,” you can convert them to a common form — decimals work best — and compare the decimal values directly.
Key equivalences to remember:
- \(\color{blue}{\frac{1}{2} = 50\%}\)
- \(\color{blue}{\frac{1}{4} = 25\%}\)
- \(\color{blue}{\frac{3}{4} = 75\%}\)
- \(\color{blue}{\frac{1}{5} = 20\%}\)
- \(\color{blue}{\frac{2}{5} = 40\%}\)
How to Compare Percent and Fractions in Word Problems
Step 1 — Convert to decimals
Change the percent to a decimal (divide by 100). Divide the fraction’s numerator by its denominator to get its decimal.
Step 2 — Compare the decimals
Use <, >, \(\color{blue}{\text{ or } = \text{ to }}\) compare. The larger decimal corresponds to the larger percent/fraction.
Step 3 — Interpret in context
Apply the comparison to the real-world situation in the word problem (e.g., which score is higher, which discount is better).
Step-by-Step Summary
- Write both values (percent and fraction) in decimal form.
- Align decimal points and compare digit by digit, starting from the left.
- Use the comparison to answer the word problem.
- State your answer in words: “X is greater than Y” or “they are equal.”
Watch: Fractions to Percents (Video Lesson)
Math with Mr. J demonstrates converting fractions to percents — the key skill for comparing them:
Worked Examples
Example 1: Is 60% greater than, less than, or equal to \(\color{blue}{\frac{3}{5}}\)?
\(\color{blue}{60\% = 0.60}\). \(\color{blue}{\frac{3}{5} = 3 &\text{ div }; 5 = 0.60}\). Both equal 0.60.
Answer: 60% = \(\color{blue}{\frac{3}{5}}\) (they are equal)
Example 2: Which is greater: 45% or \(\color{blue}{\frac{7}{16}}\)?
\(\color{blue}{45\% = 0.45}\). \(\color{blue}{\frac{7}{16} = 7 &\text{ div }; 16 = 0.4375}\). Since \(\color{blue}{0.45 > 0.4375}\):
Answer: 45% is greater
Example 3: Sarah scored \(\color{blue}{\frac{18}{25}}\) on Test A and 72% on Test B. Which score is higher?
\(\color{blue}{\frac{18}{25} = 18 &\text{ div }; 25 = 0.72 = 72\%}\). Both scores are equal.
Answer: The scores are equal (both 72%)
Example 4: Store A offers a \(\color{blue}{\frac{3}{8}}\) discount; Store B offers a 40% discount. Which store offers the better deal?
\(\color{blue}{\frac{3}{8} = 0.375 = 37.5\%}\). \(\color{blue}{40\% = 0.40}\). Since \(\color{blue}{40\% > 37.5\%}\):
Answer: Store B offers the better discount
More Practice: Percents and Equivalent Fractions
Math Antics reinforces the connection between percents and fractions, making comparisons clear:
Exercises
- Is \(\color{blue}{\frac{5}{8}}\) greater than, less than, or equal to 62%?
- A student got \(\color{blue}{\frac{14}{20}}\) on Quiz 1 and 68% on Quiz 2. Which is the higher score?
- Compare \(\color{blue}{\frac{1}{3}}\) and 34%.
- A recipe uses \(\color{blue}{\frac{3}{5}}\) cup of sugar, and another uses 58% of a cup. Which uses more sugar?
- Order from least to greatest: 0.7, \(\color{blue}{\frac{3}{4}}\), 68%.
Answers
- \(\color{blue}{\frac{5}{8} = 0.625 = 62.5\% > 62\%}\), so \(\color{blue}{\frac{5}{8}}\) is greater
- \(\color{blue}{\frac{14}{20} = 70\% > 68\%}\), so Quiz 1 is higher
- \(\color{blue}{\frac{1}{3} \approx 33.3\% < 34\%}\), so 34% is greater
- \(\color{blue}{\frac{3}{5} = 60\% > 58\%}\), so the first recipe uses more sugar
- \(\color{blue}{68\% = 0.68 < 0.70 < \frac{3}{4} = 0.75}\), so: 68%, 0.7, \(\color{blue}{\frac{3}{4}}\)
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Frequently Asked Questions
What is the fastest way to compare a fraction and a percent?
Convert the fraction to a percent by dividing the numerator by the denominator and multiplying by 100. Then compare two percents directly.
Do I have to use decimals, or can I use fractions?
You can convert the percent to a fraction over 100 and find a common denominator. Most students find decimals quicker, but both methods give the same result.
What if the fraction is a mixed number?
Convert the mixed number to an improper fraction first (or to a decimal by dividing), then compare as usual.
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