Fraction Calculator
Add, subtract, multiply, divide, simplify, and convert fractions
How to Use This Fraction Calculator
- Choose an operation tab: Basic Ops, Mixed Numbers, Simplify, or Convert
- For basic operations: Enter numerator and denominator for each fraction
- Select the operation (+, -, x, /)
- Click Calculate to see results in fraction, mixed number, and decimal form
- Review step-by-step solution in the Solution Steps section
Example: Add 1/2 + 1/4: Enter Fraction 1 as 1/2, Fraction 2 as 1/4, select +. Result: 3/4 (fraction), 0.75 (decimal). Steps show: Convert to common denominator 4, add numerators 2+1=3, result 3/4.
Tip: When multiplying, cross-cancel before computing to keep numbers smaller. For 2/3 x 9/4: cancel 3 and 9 first to get 2/1 x 3/4 = 6/4 = 3/2.
Why Use a Fraction Calculator?
Fractions appear constantly in cooking, construction, music, and everyday measurements. This calculator handles all common fraction operations with clear step-by-step explanations.
- Doubling or halving recipes (2/3 cup x 2 = 4/3 = 1 1/3 cups)
- Adding measurement fractions in woodworking (3/8" + 5/16")
- Calculating fabric or material portions
- Helping with homework showing work
- Converting between fractions and decimals for calculators
- Comparing sizes (which is bigger: 5/8 or 7/12?)
Understanding Your Results
Results appear in three forms: simplified fraction, mixed number, and decimal - whichever is most useful for your context.
| Result | Meaning | Action |
|---|---|---|
| Proper fraction (numerator < denominator) | Value is less than 1 | Common in measurements and recipes |
| Improper fraction (numerator >= denominator) | Value is 1 or greater | Convert to mixed number for readability |
| Mixed number (whole + fraction) | Combines whole and fractional parts | Easier to visualize: 7/4 = 1 3/4 (one and three-quarters) |
Meaning: Value is less than 1
Action: Common in measurements and recipes
Meaning: Value is 1 or greater
Action: Convert to mixed number for readability
Meaning: Combines whole and fractional parts
Action: Easier to visualize: 7/4 = 1 3/4 (one and three-quarters)
Note: The simplify tab shows GCD calculation. Always express final answers in lowest terms unless the problem requires otherwise.
About Fraction Calculator
Formula
a/b + c/d = (ad + bc)/(bd) | a/b x c/d = (ac)/(bd) | a/b / c/d = (ad)/(bc) Addition finds a common denominator by cross-multiplication. Multiplication is straight across. Division flips the second fraction (reciprocal) and multiplies.
Current Standards: In cooking, common fractions are 1/4, 1/3, 1/2, 2/3, 3/4. In construction (US), measurements use 1/16, 1/8, 1/4, 1/2 inch increments. Metric countries often use decimals instead.
Frequently Asked Questions
How do I add fractions with different denominators?
Find a common denominator (usually LCD), convert each fraction, then add numerators. For 1/3 + 1/4: LCD = 12. Convert: 4/12 + 3/12 = 7/12. You can also cross-multiply: 1/3 + 1/4 = (1x4 + 1x3)/(3x4) = 7/12.
Why do I flip the second fraction when dividing?
Dividing by a number is the same as multiplying by its reciprocal. 6 / 2 = 6 x 1/2 = 3. For fractions: (1/2) / (3/4) asks 'how many 3/4s fit in 1/2?' Flip and multiply: 1/2 x 4/3 = 4/6 = 2/3. So 2/3 of a (3/4) fits in (1/2).
How do I convert a decimal to a fraction?
Count decimal places, use that power of 10 as denominator, simplify. 0.75 = 75/100 = 3/4. For 0.625: 625/1000 = 5/8. For repeating decimals: 0.333... = 1/3, 0.666... = 2/3. Set x = 0.333..., then 10x = 3.333..., subtract: 9x = 3, so x = 1/3.
What's the fastest way to compare fractions?
Cross multiply and compare. For 5/8 vs 7/12: calculate 5x12 = 60 and 7x8 = 56. Since 60 > 56, we have 5/8 > 7/12. Alternatively, convert to decimals: 5/8 = 0.625 and 7/12 = 0.583..., confirming 5/8 is larger.
How do I work with mixed numbers?
Convert to improper fractions first. For 2 1/2: multiply whole by denominator (2x2=4), add numerator (4+1=5), keep denominator: 5/2. Now you can calculate normally. After computing, convert back: if numerator >= denominator, divide to get whole part and remainder fraction.