¾
⅝
⅔
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⅞

Fraction Calculator

Add, subtract, multiply, divide, simplify, convert & compare fractions — with step-by-step solutions and interactive visual diagrams.

1 1st Fraction
+
2 2nd Fraction
Visual Diagram

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💡 Quick Tips

  • • Press Enter to calculate quickly
  • • Switch between pie & bar diagrams
  • • Click "Show Steps" for full solution
  • • Use negative numbers for negative fractions
  • • Toggle between simple & mixed number forms
Definition

What Is a Fraction?

A fraction is a number that represents a part of a whole, written as one integer (the numerator) over another integer (the denominator), separated by a horizontal line called a vinculum. The numerator tells how many parts are taken, and the denominator tells how many equal parts the whole is divided into.

For example, the fraction 3/4 means 3 parts out of 4 equal parts. The number above the line (3) is the numerator, and the number below the line (4) is the denominator. Every fraction represents a division: 3/4 = 3 ÷ 4 = 0.75.

Fractions appear in cooking and recipes (½ cup of sugar), measuring and construction (⅜-inch drill bit), splitting bills and costs (each person pays ⅓), and grades and test scores (scored 17/20 on an exam). A Fraction Calculator handles all 4 fraction operations — adding fractions, subtracting fractions, multiplying fractions, and dividing fractions — and returns results in lowest terms.

Types of Fractions

There are 3 main types of fractions: proper fractions, improper fractions, and mixed numbers.

Proper Fraction

The numerator is smaller than the denominator. The value is between 0 and 1.

1/2, 3/4, 5/8, 7/16

Improper Fraction

The numerator is equal to or greater than the denominator. The value is 1 or more.

5/3, 9/4, 7/7, 11/2

Mixed Number

A whole number combined with a proper fraction. Represents a value greater than 1.

1½, 2¾, 3⅝, 5⅓
How It Works

How to Use the Fraction Calculator

To use the fraction calculator, follow 4 steps to get an accurate answer with a full step-by-step breakdown.

1
①
Enter the First Fraction
Type the numerator and denominator of the first fraction. Add a whole number for mixed numbers.
2
②
Pick an Operation
Select addition (+), subtraction (−), multiplication (×), or division (÷) from the operator menu.
3
③
Enter the Second Fraction
Type the numerator and denominator of the second fraction. The calculator accepts proper fractions, improper fractions, and mixed numbers.
4
④
Get the Answer
Press Calculate to see the result in simplified form, as a decimal, as a percentage, and with a visual pie diagram.
Solution Process

Step-by-Step Solution

The fraction calculator shows a complete step-by-step solution for every calculation. Each step shows the mathematical operation performed, the intermediate result, and the reasoning behind each transformation — from finding the Least Common Denominator (LCD) to reducing the final answer to lowest terms.

Step-by-step solutions help students verify their work, identify mistakes, and learn fraction arithmetic through practice. Teachers and tutors use step-by-step fraction solutions to explain methods during lessons.

Addition

How to Add Fractions

To add fractions, the denominators must be the same. Find a common denominator, convert each fraction, add the numerators, and simplify the result to lowest terms.

Adding Fractions with the Same Denominator

Add the numerators and keep the denominator. The formula is: a/c + b/c = (a + b)/c.

2/7 + 3/7 = (2 + 3)/7 = 5/7

Adding Fractions with Different Denominators

Find the Least Common Denominator (LCD), convert each fraction to an equivalent fraction with the LCD, add the numerators, and simplify.

1/3 + 1/4 → LCD = 12 → 4/12 + 3/12 = 7/12

Adding Mixed Numbers

Convert each mixed number to an improper fraction, find the LCD, add the numerators, and convert back to a mixed number.

1½ + 2¼ → 3/2 + 9/4 → 6/4 + 9/4 = 15/4 = 3¾
Subtraction

How to Subtract Fractions

To subtract fractions, use the same approach as addition: find a common denominator, convert, subtract the numerators, and simplify.

Subtracting Fractions with the Same Denominator

Subtract the numerators and keep the denominator. The formula is: a/c − b/c = (a − b)/c.

5/8 − 3/8 = (5 − 3)/8 = 2/8 = 1/4

Subtracting Fractions with Different Denominators

Find the LCD, convert each fraction, subtract the numerators, and simplify to lowest terms.

3/4 − 1/3 → LCD = 12 → 9/12 − 4/12 = 5/12

Common Mistakes When Subtracting Fractions

The 3 most common mistakes when subtracting fractions are: (1) subtracting denominators instead of keeping them the same, (2) forgetting to find the LCD, and (3) not simplifying the result. For example, 5/8 − 3/8 ≠ 2/0 — the denominator stays 8.

Multiplication

How to Multiply Fractions

Multiplying fractions is the simplest fraction operation. Multiply the numerators together, multiply the denominators together, and simplify. No common denominator is needed.

Multiplying Fractions Rule

The formula is: a/b × c/d = (a × c) / (b × d). Cross-cancel common factors before multiplying to keep numbers small.

2/3 × 4/5 = (2 × 4) / (3 × 5) = 8/15

Multiplying Mixed Numbers

Convert each mixed number to an improper fraction first, then multiply numerators and denominators.

1½ × 2⅓ → 3/2 × 7/3 = 21/6 = 7/2 = 3½

Multiplying a Fraction by a Whole Number

Write the whole number as a fraction over 1, then multiply normally.

3/4 × 6 = 3/4 × 6/1 = 18/4 = 9/2 = 4½

What Does "of" Mean in Fraction Problems?

In fraction math, the word "of" means multiplication. "½ of 20" means ½ × 20 = 10. "⅓ of 90" means ⅓ × 90 = 30.

Division

How to Divide Fractions

To divide fractions, use the Keep-Change-Flip method: keep the first fraction, change division to multiplication, and flip (find the reciprocal of) the second fraction.

Dividing Fractions Rule (Keep-Change-Flip)

The formula is: a/b ÷ c/d = a/b × d/c = (a × d) / (b × c). This method works because dividing by a fraction is the same as multiplying by the reciprocal of that fraction.

3/4 ÷ 2/5 → 3/4 × 5/2 = 15/8 = 1⅞
Interactive: Keep-Change-Flip
3/4
÷ → ×
2/5 → 5/2
= 15/8

What Is a Reciprocal?

A reciprocal is a fraction flipped upside down. The reciprocal of 2/3 is 3/2. The reciprocal of 5 (which is 5/1) is 1/5. The reciprocal of 1/4 is 4/1 = 4. Multiplying any number by the reciprocal of that number always equals 1.

Dividing Mixed Numbers

Convert mixed numbers to improper fractions, then apply Keep-Change-Flip.

2½ ÷ 1¼ → 5/2 ÷ 5/4 → 5/2 × 4/5 = 20/10 = 2
Simplification

How to Simplify Fractions (Reduce to Lowest Terms)

To simplify a fraction, divide both the numerator and the denominator by their Greatest Common Factor (GCF). A fraction is in lowest terms when the GCF of the numerator and denominator is 1 — no number other than 1 divides both evenly.

Steps to Simplify a Fraction

  1. Find all factors of the numerator.
  2. Find all factors of the denominator.
  3. Identify the Greatest Common Factor (GCF).
  4. Divide both numerator and denominator by the GCF.
Simplify 12/18: Factors of 12 = {1, 2, 3, 4, 6, 12}. Factors of 18 = {1, 2, 3, 6, 9, 18}. GCF = 6. Result: 12 ÷ 6 / 18 ÷ 6 = 2/3.
Interactive Fraction Simplifier
Conversion

Converting Between Improper Fractions and Mixed Numbers

An improper fraction has a numerator greater than or equal to the denominator (like 7/4). A mixed number has a whole-number part and a fractional part (like 1¾). Both represent the same value.

Improper Fraction to Mixed Number

Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same.

7/4 → 7 ÷ 4 = 1 remainder 3 → 1¾

Mixed Number to Improper Fraction

Multiply the whole number by the denominator, add the numerator, and place the sum over the original denominator.

2⅗ → (2 × 5 + 3) / 5 = 13/5
Improper → Mixed Number
Mixed Number → Improper
Quick Reference

Fraction Operations: Quick-Reference Formula Table

Operation Formula Example
Addition (same denom.) a/c + b/c = (a+b)/c 2/5 + 1/5 = 3/5
Addition (diff. denom.) a/b + c/d = (ad+bc)/bd 1/3 + 1/4 = 7/12
Subtraction a/b − c/d = (ad−bc)/bd 3/4 − 1/3 = 5/12
Multiplication a/b × c/d = ac/bd 2/3 × 4/5 = 8/15
Division a/b ÷ c/d = ad/bc 3/4 ÷ 2/5 = 15/8
Simplify (a÷GCF)/(b÷GCF) 12/18 → 2/3
To Decimal a ÷ b 3/4 = 0.75
To Percent (a ÷ b) × 100 3/4 = 75%
Real-World Uses

Real-Life Examples of Fraction Calculations

🍳

Cooking and Recipes

A recipe calls for ¾ cup of flour, and you want to make 1½ batches. Multiply ¾ × 3/2 = 9/8 = 1⅛ cups of flour. Scaling recipes up or down requires multiplying fractions by the batch multiplier. A Fraction Calculator gives the exact amount without rounding errors.
💰

Splitting Bills and Costs

Three friends split a $45 dinner bill, but one person ate ½ of the food while the other two each ate ¼. Multiply each fraction by $45: ½ × 45 = $22.50, and ¼ × 45 = $11.25 for each of the other two. Fraction operations handle unequal splits accurately.
🛠️

Measuring and Construction

A carpenter cuts a board from 5¾ feet to 3⅜ feet. Subtract 3⅜ from 5¾: convert to improper fractions, find the LCD, and subtract. 23/4 − 27/8 = 46/8 − 27/8 = 19/8 = 2⅜ feet of material removed. Construction measurements in inches and feet use fractions (⅛", ¼", ⅜", ½").
🎓

Grades and Test Scores

A student scores 17/20 on quiz 1 and 22/25 on quiz 2. To compare, convert both to equivalent fractions with a common denominator or to percentages: 17/20 = 85% and 22/25 = 88%. Fraction to percentage conversion (divide numerator by denominator, multiply by 100) makes comparing test results straightforward.
Negative Values

Working with Negative Fractions

A negative fraction has one negative sign. The sign can appear in front of the fraction (−3/4), in the numerator (−3/4), or in the denominator (3/−4) — all 3 forms represent the same value. By convention, the negative sign is placed in front of the fraction or with the numerator.

Rules for Doing Math with Negative Fractions

(−) × (−) = (+)
Negative × Negative = Positive: (−1/2) × (−3/4) = 3/8
(−) × (+) = (−)
Negative × Positive = Negative: (−1/2) × (3/4) = −3/8
(−) + (−) = (−)
Negative + Negative = More Negative: (−1/3) + (−1/4) = −7/12
a − (−b) = a + b
Subtracting a negative is the same as adding: 1/2 − (−1/3) = 1/2 + 1/3 = 5/6

The fraction calculator handles negative fractions in all 4 operations. Enter a negative sign with the numerator.

Conversions

Converting Fractions to Decimals and Percentages

Fractions, decimals, and percentages are 3 ways to represent the same value. Converting between them is a core skill in algebra and everyday math.

Fraction to Decimal

Divide the numerator by the denominator. 3/4 = 3 ÷ 4 = 0.75. Some fractions produce repeating decimals: 1/3 = 0.333... and 1/6 = 0.1666...

Fraction to Percentage

Divide the numerator by the denominator, then multiply by 100. 3/4 = 0.75 × 100 = 75%. Alternatively, find an equivalent fraction with a denominator of 100: 3/4 = 75/100 = 75%.

Decimal to Fraction

Write the decimal as a fraction over 1, multiply numerator and denominator by 10 for each decimal place, and simplify. 0.6 = 6/10 = 3/5. For 0.125: 125/1000 = 1/8.

Fraction → Decimal → Percentage Converter
Watch Out

Common Fraction Mistakes and How to Fix Them

✗ 1/2 + 1/3 = 2/5
✓ 1/2 + 1/3 = 3/6 + 2/6 = 5/6
Adding numerators and denominators separately is wrong. Find the LCD first.
✗ 2/3 × 4/5 — finding a common denominator
✓ 2/3 × 4/5 = 8/15 — multiply straight across
Multiplication does not need a common denominator.
✗ 3/4 ÷ 2/5 = 3/4 × 2/5
✓ 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8
Division requires flipping the second fraction (reciprocal), not multiplying directly.
✗ Forgetting to simplify 8/12
✓ 8/12 = 2/3 (GCF = 4)
Always reduce the answer to lowest terms using the GCF.
✗ Converting 2⅗ → 7/5
✓ 2⅗ → (2 × 5 + 3)/5 = 13/5
Multiply the whole number by the denominator, then add the numerator.
Education

Fractions by Grade Level: What Students Learn and When

Grade 1–2
Introduction to halves and quarters using shapes and objects.
Grade 3
Understanding numerator and denominator. Comparing fractions with the same denominator. Placing fractions on a number line. Identifying equivalent fractions.
Grade 4
Adding and subtracting fractions with the same denominator. Comparing fractions with different denominators. Converting improper fractions to mixed numbers.
Grade 5
Adding and subtracting fractions with different denominators using the LCD. Multiplying fractions by whole numbers and by other fractions.
Grade 6
Dividing fractions using Keep-Change-Flip. Working with negative fractions. Converting between fractions, decimals, and percentages.
Grade 7+
Fraction operations in algebraic expressions. Complex fractions. Ratios and proportional reasoning with fractions.
Fractions Tools

All Fractions Calculators

Choose from our 22 specialized math tools with step-by-step explanations.

➕

Basic Operations

Add, subtract, multiply, divide, and calculate exponents of fractions.

➕ Fraction Addition a/b + c/d ➖ Fraction Subtraction a/b - c/d ✖️ Fraction Multiplication a/b × c/d ➗ Fraction Division a/b ÷ c/d ⚡ Fraction Exponent (a/b)ⁿ
📉

Simplifying & Equivalence

Reduce, convert mixed numbers, find equivalents, and simplify complex fractions.

📉 Fraction Simplifier Reduce GCF 🔄 Equivalent Fractions a/b = c/d 📦 Mixed Number Mixed Math ⇄ Improper Fraction a/b ⇄ w a/b 🪜 Complex Fractions Stack / Nested 🐘 Big Fractions Large Numbers
🔢

Conversions & Ratios

Convert fractions to and from decimal numbers, percentages, and ratios.

🔢 Fraction to Decimal Fraction → 0.5 🔀 Decimal to Fraction 0.5 → Fraction 📊 Fraction to Percent Fraction → 50% 📈 Percent to Fraction 50% → Fraction ⚖️ Ratio to Fraction Ratio → Fraction
❓

Compare & Visualize

Compare two fractions, sort lists, and visualize fractions on an interactive number line.

❓ Comparing Fractions a/b > c/d? 🗂️ Ordering Fractions Sort Lists 📏 Fraction Number Line Visual Plot
🔍

Advanced Math Tools

Find Least Common Denominators (LCD), Greatest Common Factors (GCF), and solve ratios.

🔍 LCD Calculator Common Denom 🔑 GCF Calculator Greatest Factor ❌ Cross Multiplication Cross Math
FAQ

Frequently Asked Questions

Answers to common questions about fraction calculations, formulas, and conversions.

A fraction calculator is an online math tool that adds, subtracts, multiplies, and divides fractions, mixed numbers, and whole numbers. The fraction calculator returns the result in simplified form, as a decimal, as a percentage, and with a step-by-step solution showing every operation.
Yes, this fractions calculator online handles mixed numbers in all 4 operations. Enter the whole number, numerator, and denominator in the input fields. The calculator converts mixed numbers to improper fractions automatically, performs the operation, and converts the result back to a mixed number.
A proper fraction has a numerator smaller than the denominator (like 3/4), and an improper fraction has a numerator equal to or greater than the denominator (like 7/4). A proper fraction has a value between 0 and 1. An improper fraction has a value of 1 or more and can be converted to a mixed number (7/4 = 1¾).
The Least Common Denominator (LCD) is the smallest number that both denominators divide into evenly. To find the LCD: list the multiples of each denominator and identify the smallest number that appears in both lists. For 1/3 and 1/4, multiples of 3 are {3, 6, 9, 12, 15...} and multiples of 4 are {4, 8, 12, 16...}. The LCD is 12. Using prime factorization is faster for large denominators.
The fastest way to simplify a fraction is to divide both the numerator and denominator by their Greatest Common Factor (GCF). For 24/36: factors of 24 include {1, 2, 3, 4, 6, 8, 12, 24}, factors of 36 include {1, 2, 3, 4, 6, 9, 12, 18, 36}. The GCF is 12. So 24 ÷ 12 = 2 and 36 ÷ 12 = 3. The simplified fraction is 2/3.
The Greatest Common Factor (GCF) is the largest number that divides two numbers evenly, and the Least Common Denominator (LCD) is the smallest number that two denominators divide into. GCF is used to simplify fractions (reduce to lowest terms). LCD is used to add or subtract fractions with different denominators. For 12 and 18: GCF = 6, LCD = 36.
Fractions, decimals, and percentages are 3 representations of the same value. Fraction to decimal: divide numerator by denominator (3/4 = 0.75). Fraction to percentage: divide numerator by denominator and multiply by 100 (3/4 = 75%). Decimal to fraction: write the decimal over the appropriate power of 10 and simplify (0.6 = 6/10 = 3/5).
Fractions need a common denominator for addition and subtraction because the denominator defines the size of each part. Adding 1/3 and 1/4 directly is like adding 1 apple-third and 1 apple-fourth — the parts are different sizes. Converting to a common denominator (12) makes the parts equal: 4/12 + 3/12 = 7/12. Multiplication and division do not need a common denominator.
To reduce a fraction to lowest terms, divide both the numerator and denominator by their Greatest Common Factor (GCF) until the GCF equals 1. For 18/24: GCF of 18 and 24 is 6. Divide: 18 ÷ 6 = 3 and 24 ÷ 6 = 4. The fraction 3/4 is in lowest terms because GCF(3, 4) = 1.
Yes, the fraction calculator supports negative fractions in all operations. Enter a negative sign (−) with the numerator. The calculator follows standard sign rules: negative × negative = positive, negative × positive = negative, and subtracting a negative equals adding.