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

1. Write both values (percent and fraction) in decimal form.
2. Align decimal points and compare digit by digit, starting from the left.
3. Use the comparison to answer the word problem.
4. 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

1. Is \(\color{blue}{\frac{5}{8}}\) greater than, less than, or equal to 62%?
2. A student got \(\color{blue}{\frac{14}{20}}\) on Quiz 1 and 68% on Quiz 2. Which is the higher score?
3. Compare \(\color{blue}{\frac{1}{3}}\) and 34%.
4. A recipe uses \(\color{blue}{\frac{3}{5}}\) cup of sugar, and another uses 58% of a cup. Which uses more sugar?
5. Order from least to greatest: 0.7, \(\color{blue}{\frac{3}{4}}\), 68%.

Answers

1. \(\color{blue}{\frac{5}{8} = 0.625 = 62.5\% > 62\%}\), so \(\color{blue}{\frac{5}{8}}\) is greater
2. \(\color{blue}{\frac{14}{20} = 70\% > 68\%}\), so Quiz 1 is higher
3. \(\color{blue}{\frac{1}{3} \approx 33.3\% < 34\%}\), so 34% is greater
4. \(\color{blue}{\frac{3}{5} = 60\% > 58\%}\), so the first recipe uses more sugar
5. \(\color{blue}{68\% = 0.68 < 0.70 < \frac{3}{4} = 0.75}\), so: 68%, 0.7, \(\color{blue}{\frac{3}{4}}\)

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Frequently Asked Questions

How do you compare fractions and percents?

Put both values in the same form before comparing. The quickest way is to change each to a decimal: divide the percent by 100, and divide the fraction’s numerator by its denominator. To compare 3/8 and 35%, find 3 ÷ 8 = 0.375 and 35% = 0.35. Since 0.375 > 0.35, 3/8 is the larger amount.

How do you compare fractions, decimals and percents?

Convert every value to a decimal, line them up by place value, then order them. For example, to order 0.6, 5/8 and 58%, write 5/8 = 0.625 and 58% = 0.58. From least to greatest, that gives 58%, 0.6, 5/8. In a word problem, finish by explaining what the order means, such as which test score is highest.

What are some ways to compare fractions and percentages?

You can change everything to decimals, change the fraction to a percent by multiplying its decimal by 100, or use known benchmarks. Remembering that 1/4 = 25%, 1/2 = 50% and 3/4 = 75% helps you see quickly that 4/5, which is 80%, beats a 70% discount, for example. Pick whichever method makes the numbers easiest.

Can you use a calculator to compare fractions and percents?

Yes. Type the fraction as a division, such as 7 ÷ 20 = 0.35, and turn the percent into a decimal by dividing by 100. Then compare the two decimals. It still pays to know common equivalents like 2/5 = 40% and 1/5 = 20%, so you can catch a mistyped entry and work faster on word problems.

Related Topics

• Representing Percentage
• Fractional and Decimal Percentages
• Word Problems of Percent Fractions Decimals
• Solving Percentage Word Problems
• Convert Between Fractions and Decimals