How do you add fractions with different denominators?

Find the LCD (least common denominator). Convert each fraction to an equivalent fraction with the LCD. Add the numerators and keep the denominator. Simplify if possible. Example: 1/3 + 1/4 → LCD=12 → 4/12 + 3/12 = 7/12.

How do you multiply fractions?

Multiply the numerators together, then multiply the denominators together, then simplify. Example: 2/3 × 3/4 = (2×3)/(3×4) = 6/12 = 1/2. You can also cross-cancel before multiplying to keep numbers smaller.

How do you divide fractions?

Keep the first fraction, change the division sign to multiplication, and flip (take the reciprocal of) the second fraction. Then multiply. Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.

How do you simplify a fraction?

Find the GCD (greatest common divisor) of the numerator and denominator. Divide both by the GCD. Example: 12/18 → GCD(12,18)=6 → 12÷6 / 18÷6 = 2/3. A fraction is fully simplified when the GCD is 1.

How do you convert a fraction to a decimal?

Divide the numerator by the denominator. Example: 3/4 = 3 ÷ 4 = 0.75. For repeating decimals: 1/3 = 0.333... For mixed numbers: convert the whole part and add the decimal. Example: 2 1/4 = 2 + 0.25 = 2.25.

How do you convert a decimal to a fraction?

Write the decimal over a power of 10 matching the number of decimal places, then simplify. Example: 0.75 = 75/100 = 3/4. For 0.333..., recognize it as 1/3. For mixed decimals like 2.5, write 2 + 5/10 = 2 + 1/2 = 2 1/2.

How do you add mixed numbers?

Add the whole number parts together. Then add the fraction parts together using the LCD method. If the fraction sum is improper (≥1), convert it to a mixed number and add the whole number to the running total. Example: 1 2/3 + 2 3/4 = (1+2) + (2/3+3/4) = 3 + 8/12+9/12 = 3 + 17/12 = 3 + 1 5/12 = 4 5/12.

What is the difference between a proper fraction, improper fraction, and mixed number?

A proper fraction has a numerator smaller than the denominator (e.g. 3/4). An improper fraction has a numerator equal to or larger than the denominator (e.g. 7/4). A mixed number combines a whole number and a proper fraction (e.g. 1 3/4). Improper fractions and mixed numbers represent the same value and can be converted between each other.

How do you compare two fractions?

Convert both fractions to a common denominator and compare numerators. Alternatively, convert both to decimals and compare. Example: Is 3/5 > 2/3? LCD=15: 9/15 vs 10/15. Since 9 < 10, we have 3/5 < 2/3.

Fraction Calculator – Add, Subtract, Multiply, Divide Fractions + Mixed Numbers (Free 2026)

Quick Modes — Click to Load

➗ Fraction Calculator

Enter two fractions or mixed numbers. Leave the whole number as 0 for simple fractions.

Operation

Fraction A

Whole

Numerator

Denominator

Fraction B

Whole

Numerator

Denominator

Quick Examples

➗

Enter fractions and click Calculate

Your answer, simplified result, decimal equivalent, and full step-by-step working will appear here instantly.

How It Works

Fraction Arithmetic — Formulas & Step-by-Step Methods

Every fraction operation follows a clear algorithm. Understanding the method — not just the answer — is what this calculator is designed to teach.

Adding & Subtracting Fractions

Different Denominators — LCD Method

a/b ± c/d = (a×d ± c×b) / (b×d) then simplify

Or: find LCD, convert each fraction, add/subtract numerators

Example: 1/3 + 1/4 → LCD = 12

→ 4/12 + 3/12 = 7/12

Multiplying Fractions

Multiplication

a/b × c/d = (a×c) / (b×d)

Multiply numerators, multiply denominators, then simplify

Example: 2/3 × 3/4 = 6/12 = 1/2

Tip: cross-cancel common factors before multiplying

Dividing Fractions

Division — Keep, Change, Flip

a/b ÷ c/d = a/b × d/c

Keep the first fraction, flip the second (take reciprocal), multiply

Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

Simplifying Fractions (Lowest Terms)

Simplification — GCD Method

Simplified = (n ÷ GCD) / (d ÷ GCD)

Find GCD(numerator, denominator) using Euclidean algorithm

Example: 12/18 → GCD(12,18) = 6 → 2/3

A fraction is fully simplified when GCD = 1

Worked Example: 1 2/3 + 2 3/4 (Mixed Numbers)

Convert to improper fractions: 1 2/3 = 5/3, 2 3/4 = 11/4

Find LCD(3,4) = 12

Convert: 5/3 = 20/12, 11/4 = 33/12

Add: 20/12 + 33/12 = 53/12

Convert back: 53 ÷ 12 = 4 remainder 5 → 4 5/12

✓ 1 2/3 + 2 3/4 = 4 5/12 (= 4.4167)

Reference Tables

Fraction Reference Tables (2026)

Quick lookup for common fraction conversions. Use the calculator above for any value.

Common Fractions — Decimal & Percentage Equivalents

Fraction	Simplified	Decimal	Percentage	As Mixed Number
1/2	1/2	0.5	50%	1/2
1/3	1/3	0.333333	33.3333%	1/3
2/3	2/3	0.666667	66.6667%	2/3
1/4	1/4	0.25	25%	1/4
3/4	3/4	0.75	75%	3/4
1/5	1/5	0.2	20%	1/5
2/5	2/5	0.4	40%	2/5
3/5	3/5	0.6	60%	3/5
4/5	4/5	0.8	80%	4/5
1/6	1/6	0.166667	16.6667%	1/6
5/6	5/6	0.833333	83.3333%	5/6
1/7	1/7	0.142857	14.2857%	1/7
1/8	1/8	0.125	12.5%	1/8
3/8	3/8	0.375	37.5%	3/8
5/8	5/8	0.625	62.5%	5/8
7/8	7/8	0.875	87.5%	7/8
1/9	1/9	0.111111	11.1111%	1/9
1/10	1/10	0.1	10%	1/10
3/10	3/10	0.3	30%	3/10
7/10	7/10	0.7	70%	7/10
1/12	1/12	0.083333	8.3333%	1/12
5/12	5/12	0.416667	41.6667%	5/12
7/12	7/12	0.583333	58.3333%	7/12
11/12	11/12	0.916667	91.6667%	11/12

Adding Fractions — Common Combinations

Fractions	LCD	Result (Improper)	Simplified	Mixed Number
1/2 + 1/3	6	5/6	5/6	5/6
1/2 + 1/4	4	3/4	3/4	3/4
1/3 + 1/4	12	7/12	7/12	7/12
1/4 + 1/8	8	3/8	3/8	3/8
2/3 + 1/4	12	11/12	11/12	11/12
3/4 + 1/8	8	7/8	7/8	7/8
1/2 + 3/8	8	7/8	7/8	7/8
5/8 + 1/4	8	7/8	7/8	7/8
2/3 + 3/4	12	17/12	17/12	1 5/12
1/3 + 2/5	15	11/15	11/15	11/15

Fraction × Fraction — Common Multiplication Results

Fractions	Multiply	Simplified	Decimal
1/2 × 1/2	1/4	1/4	0.2500
1/2 × 2/3	2/6	1/3	0.3333
2/3 × 3/4	6/12	1/2	0.5000
3/4 × 4/5	12/20	3/5	0.6000
1/3 × 3/4	3/12	1/4	0.2500
1/2 × 3/4	3/8	3/8	0.3750
2/5 × 5/6	10/30	1/3	0.3333
3/8 × 4/9	12/72	1/6	0.1667

FAQ

Fraction Calculator — Frequently Asked Questions

Everything you need to know about adding, subtracting, multiplying, dividing, and simplifying fractions — with step-by-step explanations.

Fraction Calculator — Add, Subtract, Multiply & Divide Fractions + Mixed Numbers (2026)