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Percent to Fraction: Definition and Example | EDU.COM

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Percent to Fraction: Definition and Example | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">Percent to FractionPercent to Fraction: Definition and ExampleTable of ContentsDefinition of Percent-to-Fraction Conversion

Percent to fraction conversion refers to transforming a percentage value into fraction form. The word "percent" means "per 100," indicating that a percentage is essentially a fraction whose denominator is always 100. For instance, when we say 50% of a pizza, we mean 50100\frac{50}{100}10050​ or 12\frac{1}{2}21​ of the pizza. Converting percentages to fractions involves removing the percent sign, dividing by 100, and simplifying the resulting fraction.

There are three main types of percent-to-fraction conversions based on the nature of the percentage. First, whole number percent conversions (like 20% to 15\frac{1}{5}51​) involve straightforward division by 100. Second, mixed number percent conversions (such as 2.62.6%2.6) require first converting the mixed fraction to an improper fraction before dividing by 100. Third, decimal percent conversions (like 44.75%) involve removing the decimal point by multiplying both numerator and denominator appropriately after dividing by 100.

Examples of Percent-to-Fraction Conversion Example 1: Converting a Simple Percentage to a Fraction Problem:

Convert 12% to a fraction

Step-by-step solution:

Step 1, remove the percent sign and set up the division by 100: 12% = 12100\frac{12}{100}10012​

Step 2, look for common factors to simplify the fraction. Both 12 and 100 are divisible by 4: 12100=12÷4100÷4=325\frac{12}{100} = \frac{12 \div 4}{100 \div 4} = \frac{3}{25}10012​=100÷412÷4​=253​

Therefore, 12% expressed as a fraction in simplest form is 325\frac{3}{25}253​

Example 2: Converting a Mixed Number Percentage to a Fraction Problem:

Convert 645\frac{4}{5}54​% into a fraction

Step-by-step solution:

Step 1, we need to convert the mixed number 645\frac{4}{5}54​ to an improper fraction: 645=(5×6)+45=30+45=345\frac{4}{5} = \frac{(5 \times 6) + 4}{5} = \frac{30 + 4}{5} = \frac{34}{5}54​=5(5×6)+4​=530+4​=534​

Step 2, remove the percent sign and divide by 100:

645\frac{4}{5}54​% = 345100=345×1100=34500\frac{\frac{34}{5}}{100} = \frac{34}{5} \times \frac{1}{100} = \frac{34}{500}100534​​=534​×1001​=50034​

Step 3, simplify this fraction by finding the greatest common divisor of 34 and 500:

34500\frac{34}{500}50034​ = 34500\frac{34}{500}50034​ ÷ 2 = 17250\frac{17}{250}25017​

Therefore, 645\frac{4}{5}54​% expressed as a fraction is 17250\frac{17}{250}25017​

Example 3: Converting a Decimal Percentage to a Fraction Problem:

Convert 15.5% into a fraction

Step-by-step solution:

Step 1, remove the percent sign and set up the division by 100:

15.5% = 15.5100\frac{15.5}{100}10015.5​

Step 2, we need to eliminate the decimal. Since there's one digit after the decimal point, multiply both numerator and denominator by 10:

15.5100×1010=1551,000\frac{15.5}{100} \times \frac{10}{10} = \frac{155}{1,000}10015.5​×1010​=1,000155​

Step 3, simplify this fraction by finding common factors. Both 155 and 1,000 are divisible by 5:

1551,000=155÷51,000÷5=31200\frac{155}{1,000} = \frac{155 \div 5}{1,000 \div 5} = \frac{31}{200}1,000155​=1,000÷5155÷5​=20031​

Therefore, 15.5% expressed as a fraction in simplest form is 31200\frac{31}{200}20031​

Comments(6)NNatureLover21September 17, 2025I’ve been helping my kid with math, and this page made converting percentages to fractions so simple! The examples were super clear, and it’s great how it covered decimals too. Highly recommend it for parents or teachers!

NNatureLover89September 10, 2025I’ve been using the Percent to Fraction page to help my kids with their math homework, and it’s been a game-changer! The examples are super clear, and they finally get how to simplify fractions now.

MMsBrightIdeasAugust 27, 2025I used the Percent to Fraction examples from this site to help my kids with their homework, and it made things so much clearer! The step-by-step explanations are super helpful.

MCMs. CarterAugust 20, 2025This page was a lifesaver for my kids' homework! The step-by-step examples made converting percentages to fractions so clear. I've bookmarked it for future math nights!

MMathMom2025August 6, 2025This guide was so helpful for my 6th grader! The step-by-step examples made it easy to grasp, and now math homework’s way less stressful. Thanks for breaking it down!

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