Fractions trip up a surprising number of adults — and virtually every student at some point. Whether you’re helping your kid with homework, splitting a recipe, working through a construction measurement, or solving a math problem, our free Fraction Calculator handles all four operations instantly. Just enter your numerators and denominators and get a fully simplified result — with the step-by-step work shown.
What This Fraction Calculator Can Do
Our calculator handles every common fraction operation:
- ➕ Addition of two or more fractions
- ➖ Subtraction of fractions
- ✖️ Multiplication of fractions
- ➗ Division of fractions
- 🔢 Mixed number calculations (e.g., 2½ + 1¾)
- 📉 Simplify / Reduce a fraction to its lowest terms
- 🔄 Fraction to Decimal conversion
- 🔄 Decimal to Fraction conversion
All results are shown in both simplified fraction form and as a decimal.
What Is a Fraction?
A fraction represents a part of a whole. It consists of two numbers:
- Numerator (top number) — how many parts you have
- Denominator (bottom number) — how many equal parts make up the whole
In the fraction 3/8, the numerator is 3 (you have 3 parts) and the denominator is 8 (the whole is divided into 8 equal parts).
Think of it like a pizza cut into 8 equal slices. If you ate 3 of those slices, you ate 3/8 of the pizza. The remaining 5 slices = 5/8.
Important rule: The denominator can never be zero — a fraction with 0 in the denominator is mathematically undefined.
Types of Fractions You’ll Encounter
| Type | Definition | Example |
|---|---|---|
| Proper Fraction | Numerator < Denominator (value less than 1) | 3/4, 2/7, 5/9 |
| Improper Fraction | Numerator ≥ Denominator (value = or > 1) | 7/4, 9/3, 11/5 |
| Mixed Number | Whole number + a proper fraction | 2¾, 1⅓, 5½ |
| Equivalent Fractions | Different fractions with the same value | 1/2 = 2/4 = 4/8 |
| Simplified Fraction | Fraction reduced to lowest terms | 4/8 simplified = 1/2 |
| Unit Fraction | Numerator is always 1 | 1/2, 1/3, 1/7 |
How to Add Fractions — Step by Step
Adding fractions requires a common denominator — both fractions must have the same number on the bottom before you can add the tops.
Case 1: Same Denominators (Easy)
Just add the numerators and keep the denominator.
3/8 + 2/8 = 5/8
Case 2: Different Denominators (Requires Finding LCD)
Method 1 — Multiply the denominators:
a/b + c/d = (a×d + c×b) / (b×d)
Example: 3/4 + 1/6
Step 1: New denominator = 4 × 6 = 24 Step 2: New numerators: 3×6 = 18 and 1×4 = 4 Step 3: 18/24 + 4/24 = 22/24 Step 4: Simplify: 22/24 = 11/12
Method 2 — Find the Least Common Denominator (LCD):
For 3/4 + 1/6:
- Multiples of 4: 4, 8, 12, 16, 20…
- Multiples of 6: 6, 12, 18, 24…
- LCD = 12
Convert: 3/4 = 9/12 and 1/6 = 2/12 Add: 9/12 + 2/12 = 11/12 ✓
The LCD method usually gives you a result that’s already in simpler form.
How to Subtract Fractions — Step by Step
Fraction subtraction works exactly like addition — you just subtract the numerators once you have a common denominator.
Formula: a/b − c/d = (a×d − c×b) / (b×d)
Example: 3/4 − 1/6
Step 1: Common denominator = 24 Step 2: 3/4 = 18/24 and 1/6 = 4/24 Step 3: 18/24 − 4/24 = 14/24 Step 4: Simplify by dividing both by 2: 7/12
How to Multiply Fractions — Step by Step
Multiplying fractions is actually the simplest operation. No common denominator needed.
Formula: a/b × c/d = (a×c) / (b×d)
Example: 3/4 × 2/5
Step 1: Multiply numerators: 3 × 2 = 6 Step 2: Multiply denominators: 4 × 5 = 20 Step 3: Result: 6/20 Step 4: Simplify: 6/20 ÷ 2 = 3/10
Tip: You can also cross-simplify before multiplying to keep numbers smaller: 3/4 × 2/5 → simplify the 2 and 4 by dividing by 2: 3/2 × 1/5 = 3/10 ✓
How to Divide Fractions — Step by Step
Dividing fractions uses the famous “Keep, Change, Flip” method:
- Keep the first fraction the same
- Change the division sign to multiplication
- Flip (take the reciprocal of) the second fraction
Formula: a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)
Example: 3/4 ÷ 2/5
Step 1: Keep 3/4 the same Step 2: Change ÷ to × Step 3: Flip 2/5 to 5/2 Step 4: 3/4 × 5/2 = 15/8 Step 5: Convert to mixed number: 1 and 7/8
Mixed Number Calculations
A mixed number has a whole number part and a fraction part (like 2¾).
To add or subtract mixed numbers, convert to improper fractions first:
2¾ = (2×4 + 3)/4 = 11/4 1⅓ = (1×3 + 1)/3 = 4/3
Now add: 11/4 + 4/3 LCD = 12 → 33/12 + 16/12 = 49/12 = 4 and 1/12
To convert an improper fraction back to a mixed number: Divide numerator by denominator. The quotient is the whole number; the remainder is the new numerator. 49 ÷ 12 = 4 remainder 1 → 4 and 1/12 ✓
How to Simplify (Reduce) a Fraction
To reduce a fraction to its lowest terms, divide both the numerator and denominator by their Greatest Common Factor (GCF).
Example: Simplify 24/36
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 GCF = 12
24 ÷ 12 = 2 36 ÷ 12 = 3 Simplified: 2/3 ✓
Converting Fractions to Decimals and Back
Fraction → Decimal
Simply divide the numerator by the denominator.
| Fraction | Division | Decimal |
|---|---|---|
| 1/2 | 1 ÷ 2 | 0.5 |
| 1/3 | 1 ÷ 3 | 0.333… (repeating) |
| 3/4 | 3 ÷ 4 | 0.75 |
| 2/5 | 2 ÷ 5 | 0.4 |
| 7/8 | 7 ÷ 8 | 0.875 |
| 1/7 | 1 ÷ 7 | 0.142857… (repeating) |
Decimal → Fraction
- Write the decimal over its place value (tenths, hundredths, thousandths)
- Simplify
Example: Convert 0.625
- 0.625 = 625/1000
- GCF of 625 and 1000 = 125
- 625 ÷ 125 = 5; 1000 ÷ 125 = 8
- Answer: 5/8 ✓
Common Fraction Mistakes (And How to Avoid Them)
| Mistake | Wrong | Correct |
|---|---|---|
| Adding denominators | 1/3 + 1/4 = 2/7 ❌ | 1/3 + 1/4 = 7/12 ✓ |
| Not simplifying at the end | Leaving answer as 6/12 ❌ | Simplified: 1/2 ✓ |
| Forgetting to flip when dividing | 3/4 ÷ 1/2 = 3/8 ❌ | 3/4 × 2/1 = 6/4 = 3/2 ✓ |
| Wrong mixed number conversion | 2¾ = 6/4 ❌ | 2¾ = 11/4 ✓ |
Real-Life Uses for Fractions in the US
Fractions aren’t just a math class thing. Americans use them constantly:
- Cooking and baking: Recipes use ½ cup, ¾ teaspoon, ⅓ pound
- Construction and carpentry: Lumber is measured in fractions of an inch (2×4, ⅝” drywall, ¾” plywood)
- Sports statistics: Batting averages, shooting percentages, and winning fractions
- Stock market: Historically quoted in fractions (e.g., 14⅜); now in decimals, but fractional understanding still helps
- Medical dosing: Medications in ½ tablet, ¼ dose increments
- Music: Time signatures (3/4, 4/4, 6/8) are fractions representing beats per measure
- Gas prices: Often displayed as whole dollars + fraction cents (e.g., $3.49 9/10 per gallon)
Fraction Reference Chart — Common Fractions and Their Equivalents
| Fraction | Simplified | Decimal | Percentage |
|---|---|---|---|
| 1/2 | 1/2 | 0.5 | 50% |
| 1/3 | 1/3 | 0.333 | 33.33% |
| 2/3 | 2/3 | 0.667 | 66.67% |
| 1/4 | 1/4 | 0.25 | 25% |
| 3/4 | 3/4 | 0.75 | 75% |
| 1/5 | 1/5 | 0.2 | 20% |
| 2/5 | 2/5 | 0.4 | 40% |
| 3/5 | 3/5 | 0.6 | 60% |
| 1/8 | 1/8 | 0.125 | 12.5% |
| 3/8 | 3/8 | 0.375 | 37.5% |
| 5/8 | 5/8 | 0.625 | 62.5% |
| 7/8 | 7/8 | 0.875 | 87.5% |
Frequently Asked Questions (FAQ)
How do you add fractions with different denominators?
Find the least common denominator (LCD) of the two fractions. Convert each fraction to an equivalent fraction with the LCD as the denominator. Then add the numerators and keep the denominator the same. Finally, simplify the result if possible.
How do you simplify a fraction?
Find the Greatest Common Factor (GCF) of the numerator and denominator, then divide both by that number. For example, to simplify 18/24: GCF = 6, so 18÷6 = 3 and 24÷6 = 4, giving you 3/4.
What is 2/3 divided by 4/5?
Using Keep-Change-Flip: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
What is an improper fraction?
An improper fraction has a numerator that is equal to or greater than its denominator, making its value equal to or greater than 1. For example, 9/4 is improper because 9 > 4. It can be converted to the mixed number 2¼.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. For example, 3/8 = 3 ÷ 8 = 0.375.
What is a mixed number?
A mixed number combines a whole number and a proper fraction, such as 3½ or 2¾. To perform calculations with mixed numbers, first convert them to improper fractions.
What does it mean to reduce a fraction to lowest terms?
It means simplifying the fraction so that the numerator and denominator share no common factors other than 1. The fraction 6/9 reduces to 2/3 because both 6 and 9 are divisible by 3.
What is the least common denominator?
The least common denominator (LCD) is the smallest number that is a multiple of both denominators in a fraction problem. Finding the LCD is the key step in adding or subtracting fractions with different denominators.
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- Triangle Calculator — Geometry problems often involve fractional measurements
- Time Calculator — Time problems sometimes involve fractional hours
This Fraction Calculator is for educational and practical use. All calculations are based on standard mathematical conventions.