Fraction Converter

What Is a Fraction Converter?

A fraction converter is a tool that moves values between fractional and decimal notation, and reduces fractions to their simplest form. Fractions express a part of a whole using a numerator (top number) and a denominator (bottom number). Decimals express the same value using the base-10 place value system. Being able to convert quickly between these formats is essential in mathematics, cooking, construction, finance, and everyday measurement.

This converter handles three operations: converting a fraction to a decimal, converting a decimal to a fraction, and simplifying a fraction to its lowest terms. Each mode uses established mathematical methods and produces an instant result without needing AI. You can also send any conversion to the AI for a detailed step-by-step explanation. For other math help, see the free AI math solver or the percentage calculator.

How to Convert a Fraction to a Decimal

Division Method

Converting a fraction to a decimal requires one operation: divide the numerator by the denominator. The result is the decimal equivalent of the fraction.

For example, to convert 3/4 to a decimal: 3 ÷ 4 = 0.75. To convert 1/3 to a decimal: 1 ÷ 3 = 0.3333... (repeating). Some fractions produce terminating decimals that end after a finite number of digits. Others produce repeating decimals where one or more digits repeat indefinitely.

Common Fractions to Decimals Table

How to Convert a Decimal to a Fraction

Place Value Method

To convert a terminating decimal to a fraction, count the number of digits after the decimal point and use that count to determine the denominator. A decimal with one place uses 10 as the denominator, two places uses 100, three places uses 1000, and so on.

Repeating Decimals

Repeating decimals such as 0.3333... or 0.142857... require a different method. For a single repeating digit, set x equal to the decimal, multiply both sides by 10, then subtract the original equation. For 0.3333...: let x = 0.3333..., then 10x = 3.3333..., so 10x - x = 3, giving 9x = 3, and x = 3/9 = 1/3. The built-in converter handles terminating decimals. Use the AI option for repeating decimals and the AI will work through the algebra. For broader math support, try the AI math solvers collection.

How to Simplify a Fraction

Finding the GCD

Simplifying a fraction means reducing it to its lowest terms by dividing both the numerator and denominator by their Greatest Common Divisor (GCD). The GCD is the largest number that divides evenly into both values. The Euclidean algorithm is the standard method for finding the GCD efficiently.

A fraction is in its simplest form when the GCD of the numerator and denominator is 1, meaning no number other than 1 divides evenly into both. This is also called an irreducible fraction.

Common Fraction Decimal Equivalents

These equivalents appear frequently in construction, cooking, finance, and academic work. Memorizing the most common ones speeds up everyday calculations.

Mixed Numbers and Improper Fractions

A mixed number combines a whole number and a fraction, such as 2 3/4. An improper fraction has a numerator larger than its denominator, such as 11/4. These two forms represent the same value and can be converted between each other.

To convert a mixed number to an improper fraction: multiply the whole number by the denominator, then add the numerator. For 2 3/4: (2 × 4) + 3 = 11, so the improper fraction is 11/4.

To convert an improper fraction to a mixed number: divide the numerator by the denominator. The quotient is the whole number, and the remainder becomes the new numerator over the original denominator. For 11/4: 11 ÷ 4 = 2 remainder 3, so the mixed number is 2 3/4.

To convert a mixed number to a decimal, first convert to an improper fraction, then divide the numerator by the denominator. For 2 3/4: 11 ÷ 4 = 2.75. Use the AI math solvers for complex mixed number problems, or the degrees converter for angle-related fraction calculations.

Frequently Asked Questions