Fraction Calculator
Result Summary
No results yet
Enter your details and hit “Calculate” to see your results.
About the Fraction Calculator
Fractions show up everywhere measurement does: recipe scaling (1 3/4 cups halved), lumber and hardware sizes (3/8 inch), fabric yardage, medication doses, and every math class from grade school through algebra. The arithmetic isn’t hard, but it’s easy to slip — adding denominators, forgetting to flip when dividing, or leaving 6/8 unreduced.
This calculator handles proper and improper fractions, mixed numbers, whole numbers, and short decimals in any combination, and always returns the fully simplified result with its decimal equivalent and visible steps — so it works as both a checker and a teacher.
Starting from a decimal like 0.625 instead? Use the Decimal to Fraction Calculator
The Four Fraction Rules
Every fraction operation reduces to one of four rules. With fractions a/b and c/d:
Add: a/b + c/d = (a·d + b·c) / (b·d) Subtract: a/b − c/d = (a·d − b·c) / (b·d) Multiply: a/b × c/d = (a·c) / (b·d) Divide: a/b ÷ c/d = (a·d) / (b·c) — multiply by the reciprocal
Addition and subtraction need a common denominator — that’s what the cross-multiplication builds. Multiplication is straight across, and division flips the second fraction and multiplies. The raw answer often shares a factor top and bottom, so the last step is always to divide both by their greatest common divisor.
Worked Examples
One example of each operation, plus mixed-number cases — every result computed by this calculator:
| Problem | Result | As a decimal |
|---|---|---|
| 1/2 + 1/4 | 3/4 | 0.75 |
| 1/3 − 1/4 | 1/12 | 0.0833… |
| 2/3 × 3/4 | 1/2 | 0.5 |
| 1/2 ÷ 1/4 | 2 | 2 |
| 1 3/4 + 7/8 | 2 5/8 | 2.625 |
| 2 1/2 × 4 | 10 | 10 |
Note the division row: dividing by a fraction smaller than 1 makes the answer bigger — 1/2 ÷ 1/4 asks “how many quarters fit in a half?” and the answer is 2.
Mixed Numbers, Simplifying & Comparing
A mixed number is a whole number plus a fraction: 1 3/4 means 1 + 3/4. To calculate with it, convert to an improper fraction — multiply the whole part by the denominator and add the numerator: 1 3/4 = (1×4 + 3)/4 = 7/4. The calculator does this automatically when you type the mixed form with a space, and converts back for the final answer. Simplifying works the other way: divide numerator and denominator by their greatest common divisor, so 6/8 becomes 3/4.
To compare two fractions, cross-multiply: for 1/3 vs 1/4, compare 1×4 = 4 against 1×3 = 3 — since 4 > 3, 1/3 is larger. The intuition: cutting a pizza into fewer slices makes each slice bigger, so thirds beat quarters even though 4 is the bigger denominator.
Frequently Asked Questions
How do you calculate fractions by hand?
For addition and subtraction, rewrite both fractions over a common denominator (multiply each numerator by the other fraction’s denominator), then add or subtract the tops. For multiplication, multiply straight across. For division, flip the second fraction and multiply. Finish by dividing top and bottom by their greatest common divisor.
Which is bigger, 1/3 or 1/4?
1/3 is bigger. Cross-multiply to check: 1×4 = 4 versus 1×3 = 3, and 4 > 3. Intuitively, splitting something into 3 pieces gives bigger pieces than splitting it into 4 — as decimals, 1/3 ≈ 0.333 and 1/4 = 0.25.
How do I enter a mixed number?
Type the whole part, a space, then the fraction: 1 3/4. The calculator converts it to 7/4 internally, and negative mixed numbers like -2 1/2 work too.
Can I mix fractions with whole numbers and decimals?
Yes. A whole number like 5 is treated as 5/1, and a decimal like 0.75 is converted exactly to 3/4 (up to six decimal places). So 0.75 + 1/4 returns exactly 1.
Why is the answer always simplified?
6/8 and 3/4 are the same value, but convention — and every math teacher — expects lowest terms. The calculator divides numerator and denominator by their greatest common divisor and also shows the unsimplified intermediate step so you can see where the reduction happened.
Can Google’s calculator do fractions?
Typing 1/2 + 1/4 into a search box returns the decimal 0.75, not a fraction. A dedicated fraction calculator keeps exact fractional form — important when the decimal repeats forever, like 1/3 + 1/3 = 2/3 rather than 0.66666667.
Sources & References
- [1]Weisstein, E.W. Fraction — Wolfram MathWorld
- [2]Weisstein, E.W. Mixed Fraction — Wolfram MathWorld
Methodology. This calculator uses standard, peer-reviewed mathematical formulas. It is reviewed and maintained by the Vast Calculators editorial team.
Last updated · July 2026
Results are estimates for general use; verify critical figures independently.