Add, subtract, multiply or divide fractions and mixed numbers — then simplify any fraction to lowest terms, with step-by-step working and decimal equivalents.
Enter two fractions (whole number part is optional for mixed numbers):
Result
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What is a fraction?
A fraction represents a part of a whole, written as numerator/denominator — for example 3/4 means 3 parts out of 4 equal parts. Fractions can be proper (numerator smaller than denominator, like 3/4), improper (numerator larger, like 7/4), or written as a mixed number combining a whole number and a proper fraction, like 1 3/4.
The calculator above handles all three forms: enter a whole number, a numerator and a denominator for each fraction, choose an operation, and get an exact simplified answer instantly.
Understanding Fraction Types and Concepts
Fractions come in several forms, each with its own use cases and properties. Mastering the differences will help you solve problems faster and recognize when to simplify or convert.
Proper fractions: The numerator is smaller than the denominator (e.g., 2/5, 7/9). These fractions are always less than 1. They're the most common type you'll encounter in basic arithmetic.
Improper fractions: The numerator is equal to or larger than the denominator (e.g., 7/4, 9/9). These fractions equal 1 or more. Although they look unusual, they're mathematically valid and often used in calculations before converting to mixed numbers for readability.
Mixed numbers: A whole number plus a proper fraction (e.g., 2 3/4, which equals 11/4). Mixed numbers are popular in everyday contexts like recipes ("add 2 1/2 cups of flour") but improper fractions are easier for multiplication and division.
Equivalent fractions: Different fractions representing the same value. For example, 1/2 = 2/4 = 3/6 = 4/8. To create an equivalent fraction, multiply or divide both numerator and denominator by the same number. Recognizing equivalent fractions is key to finding common denominators.
Unit fractions: Fractions with a numerator of 1, like 1/2, 1/3, 1/8. These are useful building blocks; any fraction can be expressed as a sum of unit fractions.
Fraction formulas
Addition: a/b + c/d = (a×d + c×b) / (b×d)
Subtraction: a/b − c/d = (a×d − c×b) / (b×d)
Multiplication: a/b × c/d = (a×c) / (b×d)
Division: a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)
Worked examples
Example 1 — Adding fractions with different denominators (1/4 + 1/3)
Imagine one circle divided into 4 equal slices and another divided into 3 equal slices. To compare them, we need a common denominator. Multiply 4 × 3 = 12 as the common base.
1/4 + 1/3 = (1×3 + 1×4) / (4×3) = (3 + 4) / 12 = 7/12
Result: 7/12 = 0.583333 (just over half a circle)
Example 2 — Multiplying fractions (2/3 × 3/5)
When multiplying fractions, find 2/3 of 3/5. Think of a rectangle: if you shade 3/5 horizontally and 2/3 vertically, the overlapping area is your answer.
2/3 × 3/5 = (2×3) / (3×5) = 6/15
Simplified by dividing both by their greatest common divisor (GCD = 3): 2/5 = 0.4 (a smaller piece than either original fraction)
Example 3 — Dividing mixed numbers (1 1/2 ÷ 3/4)
Convert the mixed number 1 1/2 to an improper fraction: 1 1/2 = 3/2. Division by a fraction means multiply by its reciprocal (flip it).
3/2 ÷ 3/4 = 3/2 × 4/3 = (3×4) / (2×3) = 12/6
Simplified (GCD = 6): 2 = 2.0 (you can fit exactly 2 portions of size 3/4 into 1 1/2)
Simplify a fraction
To reduce any fraction to its lowest terms, divide the numerator and denominator by their greatest common divisor (GCD). Use the quick tool below — it's the same math the main calculator uses to simplify every result automatically.
Common fraction-to-decimal conversions
Fraction
Decimal
1/2
0.5
1/3
0.333333
1/4
0.25
1/5
0.2
1/8
0.125
3/4
0.75
2/3
0.666667
5/8
0.625
Fractions in Real Life
Fractions aren't just abstract math concepts—they're embedded in everyday tasks, from cooking to building to science. Understanding fraction operations makes these real-world applications easier to handle.
Cooking and baking: Most recipes list ingredients in fractions: "Add 3/4 cup of sugar and 1/2 teaspoon of salt." If you're doubling a recipe, you multiply each fraction by 2. If you're halving it, you divide by 2. The calculator helps quickly convert 1 3/4 cups into the improper fraction 7/4, making scaling recipes simple.
Carpentry and construction: Building materials like lumber and fasteners are sized in fractions of inches. A piece of wood might be 2 5/8 inches thick. Cutting and joining pieces requires adding and subtracting these fractional measurements to avoid costly mistakes. Contractors often need to add lengths like 3/8" + 1/2" to find total thickness or clearance needed.
Medicine and science: Concentrations of chemicals, drug dosages, and lab recipes often use fractions or ratios. A chemist might mix 1/10 of a compound with 4/5 of a solvent. Scientists use fractions to express dilutions and proportions, and accurate calculation prevents safety issues and wasted materials.
Finance and budgeting: Financial ratios are fractions: your debt-to-income ratio, savings rate, or the fraction of your income allocated to rent. Dividing your budget into categories uses fractions (e.g., 1/3 for housing, 1/4 for food, 1/6 for transportation).
Time and scheduling: Dividing work shifts or time intervals uses fractions. If a project takes 2 1/4 hours and you have two people working, each person's share is roughly 1 1/8 hours. Fractions help distribute work and estimate timelines accurately.
How to use this calculator
Add / Subtract / Multiply / Divide: enter the numerator and denominator of each fraction (plus an optional whole number for mixed numbers), pick the operation, and press Calculate.
Simplify a Fraction: enter any numerator and denominator in the second tool to reduce it to lowest terms and see its decimal equivalent.
Results always show the simplified fraction, the mixed-number form (when applicable), and the exact decimal value.
Frequently asked questions
How do you add fractions?
Convert both fractions to a common denominator, then add the numerators and keep the denominator. Example: 1/4 + 1/3 = 3/12 + 4/12 = 7/12. If the fractions are mixed numbers, convert them to improper fractions first.
How do you subtract fractions?
Find a common denominator, then subtract the numerators. Example: 3/4 − 1/6 = 9/12 − 2/12 = 7/12. Simplify the result to lowest terms if possible.
How do you multiply fractions?
Multiply the numerators together and the denominators together, then simplify. Example: 2/3 × 3/5 = 6/15 = 2/5. No common denominator is needed for multiplication.
How do you divide fractions?
Multiply the first fraction by the reciprocal (flip) of the second fraction. Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3.
How do you simplify a fraction?
Divide both the numerator and denominator by their greatest common divisor (GCD). Example: 12/18 has a GCD of 6, so 12/18 = 2/3. The calculator above does this automatically in the “Simplify a Fraction” tool.
How do you convert a fraction to a decimal?
Divide the numerator by the denominator. Example: 3/8 = 3 ÷ 8 = 0.375. Every result on this calculator shows the decimal equivalent automatically.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, like 2 1/3 (two and one third). It equals the improper fraction 7/3. Enter the whole-number part in the “Whole” field to work with mixed numbers.
How do you find a common denominator?
The simplest method is to multiply the two denominators together, then scale each numerator to match. For example, for 1/4 and 1/3 the common denominator is 4 × 3 = 12. A smaller, more efficient option is the least common multiple (LCM) of both denominators.
Is this fraction calculator free?
Yes. BreezeCalc is completely free with no sign-up or account needed. All calculations happen instantly in your browser.
