Adding, subtracting, multiplying, or dividing fractions by hand requires careful attention to common denominators, simplification, and mixed number conversions. Our free Fraction Calculator handles all four operations instantly and automatically simplifies the result to its lowest terms — saving you time and eliminating calculation errors. Enter any two fractions and choose the operation.
Fractions are used constantly in cooking recipes, carpentry measurements, financial ratios, and school math. Whether you need to add 3/4 cup to 1/3 cup or figure out half of a fraction for a recipe adjustment, this calculator gives you the exact answer right away.
How Fraction Operations Work
Each of the four arithmetic operations follows a specific rule when applied to fractions. Understanding these rules helps you verify results and work with fractions more confidently.
Addition and Subtraction: Find a common denominator (the lowest common multiple of both denominators), convert each fraction, then add or subtract the numerators. Example: 1/3 + 1/4 → common denominator = 12 → 4/12 + 3/12 = 7/12.
Multiplication: Multiply numerators together and denominators together, then simplify. Example: 2/3 × 3/5 = (2×3)/(3×5) = 6/15 = 2/5.
Division: Multiply the first fraction by the reciprocal of the second (flip the second fraction). Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
Worked Examples
Example 1 — Recipe scaling: A recipe calls for 3/4 cup of flour. You want to make 1/2 of the recipe. Multiply: 3/4 × 1/2 = 3/8 cup of flour.
Example 2 — Adding unlike fractions: 2/5 + 1/3. LCM of 5 and 3 = 15. Convert: 6/15 + 5/15 = 11/15.
Example 3 — Subtracting fractions: 7/8 − 1/4. Convert 1/4 to 2/8. Result: 7/8 − 2/8 = 5/8.
Example 4 — Dividing fractions: How many 1/4 servings are in 3/4 of a pie? 3/4 ÷ 1/4 = 3/4 × 4/1 = 12/4 = 3 servings.
Common Fraction Equivalents
| Fraction | Simplified | Decimal | Percentage |
|---|---|---|---|
| 1/2 | 1/2 | 0.500 | 50% |
| 1/3 | 1/3 | 0.333… | 33.3% |
| 1/4 | 1/4 | 0.250 | 25% |
| 2/4 | 1/2 | 0.500 | 50% |
| 3/4 | 3/4 | 0.750 | 75% |
| 2/3 | 2/3 | 0.667 | 66.7% |
| 4/8 | 1/2 | 0.500 | 50% |
| 3/6 | 1/2 | 0.500 | 50% |
Tips for Working With Fractions
The greatest common divisor (GCD) is your best friend when simplifying fractions. To find it, list the factors of both the numerator and denominator and find the largest number they share. For 12/18: factors of 12 are 1, 2, 3, 4, 6, 12; factors of 18 are 1, 2, 3, 6, 9, 18. GCD = 6. Divide both by 6: 12/18 = 2/3.
When adding fractions with large denominators, the easiest approach is to multiply the denominators together to get a common denominator, even if it is not the lowest one. You can always simplify at the end. For example, 3/7 + 2/9: use 63 as the common denominator → 27/63 + 14/63 = 41/63, which is already fully simplified.
Frequently Asked Questions
How do I add fractions with different denominators?
Find the least common multiple (LCM) of both denominators. Convert each fraction to an equivalent fraction using the LCM as the new denominator, then add the numerators and keep the denominator. Finally, simplify the result if possible.
How do I simplify a fraction to its lowest terms?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For example, 18/24: GCD = 6. 18÷6 = 3, 24÷6 = 4. Simplified = 3/4.
What is a mixed number?
A mixed number combines a whole number and a fraction, such as 2 3/4. To convert to an improper fraction, multiply the whole number by the denominator and add the numerator: 2 3/4 = (2×4 + 3)/4 = 11/4.
Can you divide by a fraction?
Yes. Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a/b is b/a. So a ÷ c/d = a × d/c. For example, 5 ÷ 1/2 = 5 × 2/1 = 10.
What happens when I multiply two fractions less than 1?
The result is always smaller than either of the two original fractions. For example, 1/2 × 1/3 = 1/6, which is less than both 1/2 and 1/3. This is why multiplying fractions can seem counterintuitive — the result gets smaller, not larger.
How are fractions used in everyday life?
Fractions appear in cooking (3/4 cup, 1/2 teaspoon), construction and carpentry (lumber measurements like 3/8 inch), music (time signatures like 3/4 or 4/4), probability (1 in 4 chance = 1/4), finance (interest rates, ratios), and many other contexts.