Fraction Calculator

Understanding Fractions: A Complete Guide

A fraction represents a part of a whole. It consists of two numbers separated by a line: the numerator (top number) tells you how many parts you have, and the denominator (bottom number) tells you how many equal parts the whole is divided into. For example, in the fraction 3/4, the whole is divided into 4 equal parts and you have 3 of them.

Fractions are everywhere in daily life — cooking recipes call for 2/3 cup of flour, lumber is sold in lengths like 5/8 of an inch, and probability is expressed as a fraction of possible outcomes. Understanding how to work with fractions is one of the most practical math skills you can develop.

Types of Fractions

How to Add Fractions

Adding fractions requires that both fractions share the same denominator (called a common denominator). If the denominators are already the same (like fractions), you simply add the numerators. If they differ, you need to find the Least Common Multiple (LCM) of the two denominators first.

Adding Fractions with the Same Denominator

Adding Fractions with Different Denominators (LCM Method)

When denominators differ, find the LCM of both denominators. This becomes your common denominator. Convert each fraction by multiplying numerator and denominator so both have the LCM as their denominator. Then add the new numerators.

Adding Mixed Numbers

To add mixed numbers, convert each to an improper fraction first: multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. Then add normally and convert back if needed.

How to Subtract Fractions

Subtracting fractions follows the same rules as addition. If denominators are the same, subtract the numerators. If different, find the LCM, convert both fractions, then subtract.

When subtracting mixed numbers and the fraction part of the first number is smaller than the fraction part of the second, you need to "borrow" 1 from the whole number, convert it to a fraction, and add it to the fraction part before subtracting.

How to Multiply Fractions

Multiplying fractions is the most straightforward operation — no common denominator is needed. Simply multiply the numerators together and the denominators together, then simplify the result.

Real-world example: A recipe calls for 2/3 cup of sugar, but you want to make 3/4 of the recipe. You need 2/3 × 3/4 = 6/12 = 1/2 cup of sugar.

How to Divide Fractions

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is simply the fraction flipped upside down — numerator and denominator swap positions. This is often remembered as "keep, change, flip."

Real-world example: You have 3/4 of a pizza and want to divide it equally into portions of 1/8 each. How many portions? 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6 portions.

How to Simplify Fractions

A fraction is in its simplest form (also called lowest terms or reduced form) when the numerator and denominator share no common factor other than 1. To simplify, find the Greatest Common Divisor (GCD) — the largest number that divides evenly into both the numerator and denominator — then divide both by it.

Converting Fractions to Decimals and Percentages

Converting between fractions, decimals, and percentages is a fundamental skill used constantly in finance, science, and everyday life.

Fraction to Decimal

Divide the numerator by the denominator. For example: 3/8 = 3 ÷ 8 = 0.375. Some fractions produce terminating decimals (like 1/4 = 0.25), while others produce repeating decimals (like 1/3 = 0.333...).

Decimal to Fraction

Count the decimal places. Write the decimal digits over the appropriate power of 10 (10, 100, 1000, etc.), then simplify. For example: 0.625 = 625/1000. GCD(625, 1000) = 125, so 625÷125 = 5 and 1000÷125 = 8, giving 5/8.

Fraction to Percentage

Convert to a decimal first, then multiply by 100. For example: 7/20 = 0.35 × 100 = 35%. Alternatively, create an equivalent fraction with denominator 100: 7/20 = 35/100 = 35%.

Real-World Applications of Fractions

• Cooking and baking: Most recipes use fractions — 3/4 cup, 1/2 teaspoon. Scaling recipes up or down requires multiplying or dividing fractions.
• Construction and measurements: Wood, pipe, and fabric are commonly sold in fractional inches or feet. A board cut to 5 3/8 inches requires precise fraction arithmetic.
• Finance: Interest rates, stock prices, and budget allocations often involve fractions. Understanding that a 1/4% rate difference on a mortgage makes a significant long-term difference is important.
• Probability: The chance of rolling a 3 on a die is 1/6. The chance of rolling an even number is 3/6 = 1/2. Combining probabilities uses fraction arithmetic.
• Science: Chemical concentrations, ratios in solutions, and scale models all rely on fractions. A 1:50 scale model has dimensions that are 1/50 of the original.
• Time management: Breaking a project into fractions of a day or week helps allocate effort. Spending 3/8 of your day on deep work and 1/4 on meetings leaves 3/8 for other tasks.