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?
Rewrite both fractions over a common denominator, then add only the numerators. The cleanest common denominator is the least common multiple (LCD) of the two bottoms. Take 1/3 + 1/4: the LCD of 3 and 4 is 12, so convert each fraction to twelfths by scaling numerator and denominator together — 1/3 becomes 4/12 and 1/4 becomes 3/12. Add the numerators and keep the denominator: 4/12 + 3/12 = 7/12, which is already in lowest terms. If you do not want to find the LCD, you can always cross-multiply instead: 1/3 + 1/4 = (1x4 + 1x3)/(3x4) = 7/12, then simplify if needed. Subtraction works the same way, just subtracting the numerators.
Why do I flip the second fraction when dividing?
Because dividing by a number is identical to multiplying by its reciprocal — the fraction turned upside down. You can see this with whole numbers: 6 / 2 = 6 x 1/2 = 3. The same rule lets you divide fractions without any new machinery. Dividing asks how many of the second fraction fit into the first, so (1/2) / (3/4) means 'how much of a 3/4 piece fits in 1/2?' Flip the divisor to 4/3 and multiply straight across: 1/2 x 4/3 = 4/6, which simplifies to 2/3 — a 3/4 piece fits 2/3 of the way into 1/2. Another example: 2/3 / 4/5 = 2/3 x 5/4 = 10/12 = 5/6. This calculator reduces the result automatically.
How do I convert a decimal to a fraction?
Count the decimal places, put the digits over that power of 10, then simplify. Each place after the point adds one zero to the denominator: two places means hundredths, three means thousandths. So 0.75 has two decimal places and becomes 75/100, which reduces to 3/4 by dividing both parts by 25. Likewise 0.625 has three places, giving 625/1000, which simplifies to 5/8. Repeating decimals need a small algebra trick: to convert 0.333..., set x = 0.333..., multiply by 10 to get 10x = 3.333..., then subtract the first equation from the second so 9x = 3, giving x = 1/3. By the same method 0.666... = 2/3.
What's the fastest way to compare fractions?
Cross-multiply and compare the two products. Multiply the numerator of each fraction by the denominator of the other, then whichever product is larger sits above the larger fraction. For 5/8 versus 7/12, calculate 5x12 = 60 and 7x8 = 56. Since 60 is greater than 56, and the 60 came from the 5/8 side, 5/8 is the larger fraction. This shortcut works because it is the same as giving both fractions the common denominator 8x12 without writing it out. If you prefer a sanity check, convert to decimals: 5/8 = 0.625 and 7/12 = 0.583..., which confirms 5/8 is larger. For more than two fractions, a common denominator or decimals is usually clearer.
How do I work with mixed numbers?
Convert each mixed number to an improper fraction first, then operate as usual. To make the conversion, multiply the whole number by the denominator and add the numerator, keeping the same denominator. For 2 1/2: multiply the whole by the denominator (2x2 = 4), add the numerator (4 + 1 = 5), and keep the denominator, giving 5/2. With everything in improper form you can add, subtract, multiply, or divide normally. When you are done, turn the result back into a mixed number for readability: divide the numerator by the denominator to get the whole part, and the remainder becomes the new numerator. For example 7/4 gives 1 with remainder 3, so 7/4 = 1 3/4. This calculator shows both forms automatically.