Fraction Calculator

How to Use the Fraction Calculator

1. Select the operation — addition, subtraction, multiplication, or division.
2. Enter Fraction 1 — type the numerator (top number) and denominator (bottom number) in the first row.
3. Enter Fraction 2 — do the same for the second fraction. Negative fractions are supported (use a minus sign in the numerator).
4. View results instantly — the simplified fraction, mixed number form, decimal equivalent, and percentage appear automatically.
5. Simplify a single fraction — expand the "Simplify a single fraction" section to reduce any fraction to lowest terms.

How to Add and Subtract Fractions

Adding or subtracting fractions requires a common denominator. The process: find the Least Common Denominator (LCD) of both fractions, convert each fraction to an equivalent form with the LCD, then add or subtract the numerators while keeping the denominator the same, and finally simplify.

Example: 2/3 + 3/4

LCD of 3 and 4 = 12. Convert: 2/3 = 8/12, 3/4 = 9/12. Add numerators: 8 + 9 = 17. Result: 17/12. As a mixed number: 1 5/12 (since 17 ÷ 12 = 1 remainder 5). As a decimal: 1.4167.

The LCD equals the LCM of the denominators. For denominators 4 and 6, the LCM (LCD) is 12 because 12 is the smallest number both 4 and 6 divide into evenly. You can also always use the product of the denominators as a common denominator — it just may not be the least, meaning more simplification at the end.

Adding Mixed Numbers

To add mixed numbers like 2 1/3 + 1 3/4: convert both to improper fractions first (7/3 and 7/4), then apply the LCD method: LCD = 12, so 28/12 + 21/12 = 49/12 = 4 1/12.

How to Multiply and Divide Fractions

Multiplication is the simplest fraction operation: multiply numerator by numerator and denominator by denominator, then simplify. (2/3) × (3/8) = 6/24 = 1/4. A helpful shortcut is cross-cancelling before multiplying: notice 3 appears in both 2/3 and 3/8, so cancel it: (2/1) × (1/8) = 2/8 = 1/4.

Division uses the "Keep-Change-Flip" (KCF) rule:

1. Keep the first fraction exactly as it is.
2. Change the division sign to multiplication.
3. Flip (find the reciprocal of) the second fraction.

Example: (5/6) ÷ (2/3). Keep 5/6, change to ×, flip 2/3 to 3/2: (5/6) × (3/2) = 15/12 = 5/4 = 1 1/4. The reason KCF works: dividing by a fraction is the same as multiplying by its reciprocal, since dividing by x is multiplying by 1/x.

Simplifying Fractions Using GCF

A fraction is in its simplest (reduced) form when the numerator and denominator share no common factors other than 1 — when their GCF equals 1. To simplify, find the GCF and divide both numbers by it.

Example: Simplify 36/48. Find GCF(36,48): prime factorize both — 36 = 2²×3², 48 = 2⁴×3. GCF = 2²×3 = 12. Divide: 36÷12 = 3, 48÷12 = 4. Simplified: 3/4.

You can also simplify step by step by dividing by small common factors until none remain: 36/48 → divide by 2 → 18/24 → divide by 2 → 9/12 → divide by 3 → 3/4. Both methods reach the same result.

Fraction Calculations: Common Examples

What is 1/2 + 1/4?

1/2 + 1/4 = 3/4. LCD = 4. Convert 1/2 = 2/4. Add: 2/4 + 1/4 = 3/4.

What is 3/4 − 1/3?

3/4 − 1/3 = 5/12. LCD = 12. Convert: 9/12 − 4/12 = 5/12.

What is 2/3 × 3/4?

2/3 × 3/4 = 1/2. Multiply: (2×3)/(3×4) = 6/12. Simplify using GCF 6: 1/2.

What is 5/6 ÷ 5/3?

5/6 ÷ 5/3 = 1/2. Keep 5/6, flip 5/3 to 3/5: (5/6)×(3/5) = 15/30 = 1/2.

What is 7/8 as a decimal?

7/8 = 0.875. Divide 7 by 8. As a percentage: 87.5%.

How do I simplify 12/16?

12/16 = 3/4. GCF(12,16) = 4. Divide both by 4: 12÷4 = 3, 16÷4 = 4.

What is 1/3 as a decimal?

1/3 = 0.33333... (repeating). This is a repeating decimal, often written as 0.3̄ or 0.333.

What is 5/4 as a mixed number?

5/4 = 1 1/4. 5 ÷ 4 = 1 remainder 1. So the whole number is 1 and the remainder fraction is 1/4.

What is 2/5 + 3/10?

2/5 + 3/10 = 7/10. LCD = 10. Convert 2/5 = 4/10. Add: 4/10 + 3/10 = 7/10.

What is the reciprocal of 3/7?

The reciprocal of 3/7 is 7/3 = 2 1/3. To find the reciprocal, swap numerator and denominator. Reciprocals are used in division: dividing by 3/7 is the same as multiplying by 7/3.

People Also Search For

How to add fractions with different denominators step by step

Step 1: Find the LCD (LCM of the denominators). Step 2: Convert each fraction. Step 3: Add numerators. Step 4: Simplify. For 1/4 + 2/5: LCD = 20. Convert: 5/20 + 8/20 = 13/20. Already in lowest terms.

What does it mean to simplify a fraction?

Simplifying means reducing to lowest terms — dividing numerator and denominator by their GCF until GCF = 1. A fraction like 6/9 can be simplified to 2/3 (GCF = 3). A simplified fraction has the same value but uses smaller numbers.

How do fractions relate to division?

A fraction a/b literally means a divided by b. 3/4 means 3 ÷ 4 = 0.75. This is why dividing fractions uses the reciprocal — dividing by b/c is the same as multiplying by c/b, which is dividing by one number and multiplying by another, canceling out.

What is an improper fraction vs a proper fraction?

A proper fraction has a numerator smaller than its denominator (value less than 1), e.g. 3/4. An improper fraction has a numerator equal to or larger than the denominator (value ≥ 1), e.g. 7/4. Improper fractions can be written as mixed numbers: 7/4 = 1 3/4.

How do you compare two fractions?

Convert both fractions to the same denominator (the LCD), then compare numerators. To compare 3/5 and 5/8: LCD = 40. Convert: 24/40 vs 25/40. Since 24 < 25, we have 3/5 < 5/8. Alternatively, convert both to decimals: 0.6 vs 0.625.

Frequently Asked Questions