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.