Education
Fraction Calculator
Last updated: June 19, 2026
A fraction calculator is an arithmetic tool designed to perform operations on fractions and mixed numbers. The calculator automatically computes common denominators for addition and subtraction, simplifies results using the greatest common divisor, and converts improper fractions into mixed numbers. It serves as an educational aid for students learning fraction math, and as a utility for carpenters, chefs, and designers who frequently work with fractional measurements.
Enter two fractions, choose an operation, and the calculator simplifies the result, converts improper fractions to mixed numbers, and shows the decimal value plus step by step work.
Quick Answer
Add, subtract, multiply, and divide proper, improper, or mixed fractions and get simplified results with steps. For example, 1/2 + 1/3 = 5/6.
Fraction 1
Operation
Fraction 2
Step by step
- Common denominator: 4
- Rewrite: 2/4 + 1/4
- Add numerators: 3/4
Simplified answer
3/4
Decimal: 0.75
Examples
1/2 + 1/4
= 3/4 · decimal 0.75
3/4 − 1/8
= 5/8 · decimal 0.625
2/3 × 3/5
= 2/5 · decimal 0.4
3/4 ÷ 2/3
= 9/8 = 1 1/8 · decimal 1.125
How it works
Fractions follow four simple rules for addition, subtraction, multiplication, and division. The calculator runs each rule on your inputs and then simplifies the result by dividing by the greatest common divisor.
Addition
a/b + c/d = (a·d + b·c) / (b·d)
Subtraction
a/b − c/d = (a·d − b·c) / (b·d)
Multiplication
a/b × c/d = (a·c) / (b·d)
Division
a/b ÷ c/d = (a·d) / (b·c)
Simplifying
n/d → (n ÷ gcd) / (d ÷ gcd)
Divide numerator and denominator by their greatest common divisor to put the fraction in lowest terms.
What is a fraction calculator?
A fraction calculator runs the four arithmetic operations on fractions, simplifies the answer to lowest terms, converts improper fractions to mixed numbers, and shows the equivalent decimal. It works on plain fractions like 1/2 or mixed numbers like 1 1/8.
How the fraction calculator works
Each fraction has an optional whole number, a numerator, and a denominator. The calculator:
- Converts any mixed numbers to improper fractions.
- Applies the chosen operation: add, subtract, multiply, or divide.
- Simplifies the result by dividing numerator and denominator by their greatest common divisor.
- Converts an improper result back to a mixed number if applicable.
- Shows the decimal equivalent.
- Prints a short step by step trace of the calculation.
How to add fractions
Find a common denominator, rewrite each fraction with that denominator, then add the numerators. Example: 1/2 + 1/4. The least common denominator is 4. Rewrite 1/2 as 2/4. Then 2/4 + 1/4 = 3/4.
How to subtract fractions
Same as addition, but subtract the numerators. Example: 3/4 − 1/8. The least common denominator is 8. Rewrite 3/4 as 6/8. Then 6/8 − 1/8 = 5/8.
How to multiply fractions
Multiply the numerators to get the new numerator, multiply the denominators to get the new denominator, then simplify. Example: 2/3 × 3/5 = 6/15. The gcd of 6 and 15 is 3, so divide both by 3 to get 2/5.
How to divide fractions
Multiply by the reciprocal of the second fraction. Example: 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8. Convert to mixed form if you prefer: 9/8 = 1 1/8.
How to simplify fractions
Find the greatest common divisor of the numerator and the denominator, then divide both by that number. Example: 12/18. The gcd of 12 and 18 is 6, so 12/18 simplifies to 2/3. A fraction is in lowest terms when its numerator and denominator share no common factor other than 1.
Improper fractions and mixed numbers
An improper fraction has a numerator at least as large as its denominator, like 9/8. A mixed number expresses the same value as a whole part plus a proper fraction, like 1 1/8. To convert improper to mixed, divide the numerator by the denominator: the quotient is the whole part and the remainder over the denominator is the fraction part.
To go the other way (mixed to improper), multiply the whole part by the denominator and add the numerator. For 1 1/8: 1 × 8 + 1 = 9, so the improper form is 9/8.
Worked examples
- 1/2 + 1/4 = 2/4 + 1/4 = 3/4 · decimal 0.75
- 3/4 − 1/8 = 6/8 − 1/8 = 5/8 · decimal 0.625
- 2/3 × 3/5 = 6/15 = 2/5 · decimal 0.4
- 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8 = 1 1/8 · decimal 1.125
Common fraction sums
This calculator shows the step-by-step mathematical work for any pair of fractions. Below is a reference table of common fraction sums:
| Expression | Simplified Result | Decimal (3 places) |
|---|---|---|
| 1/2 + 1/4 | 3/4 | 0.750 |
| 1/3 + 1/3 | 2/3 | 0.667 |
| 1/2 + 1/3 | 5/6 | 0.833 |
| 3/8 + 1/4 | 5/8 | 0.625 |
| 3/4 + 1/4 | 1 | 1.000 |
| 2/3 + 1/2 | 7/6 (1 1/6) | 1.167 |
Common mistakes
- Adding numerators and denominators directly when adding fractions. You only add numerators, and only after using a common denominator.
- Forgetting to simplify the final answer. 6/15 is not wrong, but 2/5 is in lowest terms.
- Confusing the rule for multiplication and division. Multiplication multiplies numerators across; division multiplies by the reciprocal.
- Treating a whole number plus a fraction as a sum without converting first. 1 1/8 means 1 + 1/8, not 1 × 1/8.
- Trying to divide by zero. A denominator can never be 0, and you cannot divide by 0/anything either.
Related tools
- Mixed number calculator to switch between improper fractions and mixed numbers.
- Mixed fraction calculator
- Decimal to fraction calculator for turning a decimal into a simplified fraction.
- Fraction to decimal calculator for the reverse conversion and the percent equivalent.
- Partial fraction decomposition calculator to decompose rational functions into simpler fractions.
- Percentage increase calculator for percentage change between two values.
- Percent error calculator for the gap between an experimental and an accepted value.
- Quadratic formula calculator for solving ax² + bx + c = 0.
- Pythagorean theorem calculator for right triangle side lengths.
- Slope calculator for the slope of a line through two points.
- All education calculators for grades, statistics, and more.
Note. This calculator uses standard arithmetic rules for fractions. Teachers, schools, or textbooks may format steps differently, but the simplified result should match standard fraction arithmetic.
Sources: Fraction arithmetic methodologies and educational steps taught align with national mathematics curriculum standards (Common Core State Standards CCSS.MATH.CONTENT.5.NF). Last reviewed: June 2026.
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Frequently asked questions
Find a common denominator, rewrite each fraction so both share that denominator, add the numerators, and keep the denominator. Then simplify the result by dividing the numerator and denominator by their greatest common divisor. For example, 1/2 + 1/4: the common denominator is 4, so 1/2 becomes 2/4, then 2/4 + 1/4 = 3/4.
Same idea as addition. Find a common denominator, rewrite both fractions to use it, subtract the numerators, and simplify. For example, 3/4 − 1/8: the common denominator is 8, so 3/4 becomes 6/8, then 6/8 − 1/8 = 5/8.
Multiply the numerators together to get the new numerator, multiply the denominators together to get the new denominator, then simplify. For example, 2/3 × 3/5 = (2 × 3) / (3 × 5) = 6/15 = 2/5 after simplification.
Multiply the first fraction by the reciprocal (flipped form) of the second fraction. For example, 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8. The reciprocal turns division into multiplication, which is easier to compute.
Divide the numerator and the denominator by their greatest common divisor. For example, 6/15: the gcd of 6 and 15 is 3, so divide both by 3 to get 2/5. A fraction is in simplest form when its numerator and denominator share no common factor other than 1.
An improper fraction has a numerator that is greater than or equal to its denominator, such as 9/8 or 5/5. It is the same value as a mixed number; for example, 9/8 equals 1 1/8 and 5/5 equals 1. Calculators usually express improper fractions both ways.
A mixed number is a whole number combined with a proper fraction, written as a whole part and a fraction part. For example, 1 1/8 means 1 + 1/8, which is 9/8 as an improper fraction. Mixed numbers are easier to read; improper fractions are usually easier to compute with.
Divide the numerator by the denominator. The quotient is the whole part, and the remainder over the original denominator is the fraction part. For example, 9 ÷ 8 = 1 with remainder 1, so 9/8 = 1 1/8.
Yes. After computing the fraction result, the calculator also shows the decimal equivalent. For example, 3/4 displays as 0.75 and 9/8 displays as 1.125. The decimal is rounded for display but the fraction is exact.
Textbooks sometimes present unsimplified intermediate fractions, leave improper fractions instead of mixed numbers, or use slightly different step ordering. The simplified result should still match. If your textbook keeps the answer as an improper fraction, compare that line to the calculator's simplified result; if it uses a mixed number, compare to the mixed number line.
1/2 + 1/3 equals 5/6. To find the sum, find a common denominator of 6, rewrite the fractions as 3/6 and 2/6, and add the numerators (3 + 2 = 5).
Divide the numerator by the denominator; the quotient is the whole number, and the remainder over the denominator is the fraction. For example, 7/6 equals 1 with a remainder of 1, which translates to 1 1/6.
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