Fraction Calculators
Perform arithmetic on fractions with like or unlike denominators, simplify down to simplest form using prime factor trees, and compare fractions effortlessly.
Free Fraction, Decimal & Percentage Calculators
Calculate, convert, simplify, and compare fractions, decimals, percentages, and ratios with free step-by-step math tools. Whether you are solving elementary math homework, preparing classroom resources, or verifying conversion rates, our calculators provide exact rational answers and step-by-step solutions.
Universal Real-Time Math Converter
Our flagship converter allows you to instantly switch between proper fractions, improper fractions, mixed numbers, terminating decimals, repeating decimals, percentages, and ratios. Enter any numerical value, and our mathematical engine simultaneously computes all equivalent representations alongside the greatest common factor (GCF), prime factorizations, and fully worked reduction steps.
Fraction Form
3 / 8
Numerator over Denominator
Decimal Form
0.375
Terminating Decimal
Percentage Form
37.5%
Parts per Hundred
Ratio Form
3 : 8
Antecedent to Consequent
Explore Our Math Calculators & Solvers
Choose a specialized tool below for detailed step-by-step arithmetic and full formulas.
Decimal Calculators
Seamlessly translate between decimals and simplified fractional notation, master place value concepts, and execute precision mathematical rounding.
Percentage Calculators
Calculate percentage increase, percentage decrease, sales discounts, test score conversions, and relative percentage differences with clear formulas.
Understanding Conversions: Fractions, Decimals, and Percentages
Fractions, decimals, and percentages are three distinct mathematical languages used to express parts of a whole. In arithmetic and daily problem solving, knowing how to transition seamlessly between these representations is a foundational skill.
How to Convert a Fraction to a Decimal
To turn any fraction into a decimal, divide the numerator (top number) by the denominator (bottom number) using standard long division. For example, to convert 3/4 into a decimal, perform 3 ÷ 4 = 0.75. When the denominator factors purely into powers of 2 and 5, the decimal terminates (such as 1/8 = 0.125). When other prime factors exist (like 3 or 7), the decimal forms an infinite repeating pattern (such as 1/3 = 0.3333...).
How to Convert a Decimal to a Fraction
To convert a terminating decimal into a fraction, identify the place value of the final digit. For one decimal place (tenths), place the digits over 10; for two places (hundredths), place over 100; for three places (thousandths), place over 1000. Finally, divide both the numerator and denominator by their greatest common factor (GCF) to express the fraction in simplest form. For instance, 0.375 becomes 375/1000, which reduces by 125 to 3/8.
How to Convert Fractions to Percentages
"Percent" literally translates to "per one hundred." To express a fraction as a percentage, first convert the fraction into a decimal by dividing the numerator by the denominator, and then multiply the decimal by 100%. For example, 5/8 = 0.625, and multiplying by 100 yields 62.5%.
How to Convert Percentages to Fractions
Remove the percent sign (%) and write the number over a denominator of 100. Then simplify the fraction to lowest terms. If the percentage includes a decimal (such as 12.5%), multiply both numerator and denominator by 10 to clear the decimal (125/1000) and then simplify (1/8).
Quick Reference: Common Fractions, Decimals, and Percentages
Use this verified reference table for rapid calculation and verification during homework and testing:
| Fraction | Decimal Form | Percentage | Type | Detailed Solution |
|---|---|---|---|---|
| 1/2 | 0.5 | 50% | Terminating | 1/2 as a decimal |
| 1/3 | 0.3333... | 33.33% | Repeating (0.3̄) | Calculate 1/3 |
| 1/4 | 0.25 | 25% | Terminating | 0.25 as a fraction |
| 3/4 | 0.75 | 75% | Terminating | 3/4 as a decimal |
| 1/8 | 0.125 | 12.5% | Terminating | Calculate 1/8 |
| 3/8 | 0.375 | 37.5% | Terminating | 3/8 as a decimal |
| 5/8 | 0.625 | 62.5% | Terminating | 5/8 as a decimal |
| 7/8 | 0.875 | 87.5% | Terminating | 0.875 as a fraction |
Interactive Math Practice Center
Test your arithmetic agility with our free interactive quiz platform. Practice reducing fractions to lowest terms, multiplying mixed numbers, and converting recurring decimals into fractions. Receive instant verification and detailed answer rationales on every question.
Start Free Math Practice →Printable Worksheets & Answer Keys
Ideal for homeschool parents and classroom math teachers. Download printable PDF worksheets covering fraction addition with unlike denominators, decimal conversions, percentage discount word problems, and proportion solving. Every worksheet includes a full teacher answer key.
Browse Free Printable Worksheets →Frequently Asked Questions (FAQ)
Are all calculators on Decimal & Fraction 100% free?
Yes, every single calculator, conversion chart, practice quiz, and printable worksheet is completely free with no registration or subscriptions required.
How do you determine if a fraction will result in a repeating decimal?
When a fraction is reduced to its simplest form, inspect the prime factors of the denominator. If the prime factors contain only 2s and 5s (the factors of the base-10 number system), the decimal is terminating. If any other prime factor exists (such as 3, 7, 11, or 13), the decimal will repeat infinitely.
What is the difference between a proper fraction and an improper fraction?
A proper fraction has a numerator smaller than its denominator (e.g. 3/4), representing a value strictly less than 1. An improper fraction has a numerator greater than or equal to its denominator (e.g. 7/4), representing a value greater than or equal to 1, which can also be expressed as a mixed number (1 3/4).
How are calculations verified for accuracy?
Calculations use exact rational-number arithmetic where applicable to minimize floating-point rounding errors.