Fraction Calculator – Add, Subtract, Multiply & Simplify
Free fraction calculator: add, subtract, multiply, divide and simplify fractions to lowest terms, with mixed numbers and step-by-step working. Calculations run in your browser.
Method: Exact fraction arithmetic using GCD and LCD. Results depend only on the values you enter.
Fraction Calculator
Choose the operation you need. Calculations run in your browser.
First fraction
Second fraction
Enter fractions and select Calculate to see the answer, worked steps, simplification and decimal check.
This tool uses exact fraction arithmetic (GCD/LCD), never floating-point rounding for the answer. Denominators must not be zero.
Quick Answer
Quick Answer: A fraction calculator adds, subtracts, multiplies, and divides fractions and simplifies the answer to lowest terms. For example, 1/2 + 1/3 = 5/6, not 2/5, because both fractions must first share the common denominator 6. The free Calcrio fraction calculator shows every step, handles mixed numbers, and always gives the simplified result.
How to Use the Fraction Calculator
The tool has six modes so you can start with the operation you need.
Add — Add two fractions, including fractions with unlike denominators. For example, 1/2 + 1/3 = 5/6.
Subtract — Subtract one fraction from another. For example, 2/3 − 1/4 = 5/12.
Multiply — Multiply two fractions and simplify. For example, 3/4 × 2/3 = 1/2.
Divide — Divide one fraction by another by multiplying by the reciprocal. For example, 5/6 ÷ 2/3 = 5/4 = 1 1/4.
Simplify to Lowest Terms — Reduce a fraction by dividing the numerator and denominator by their greatest common divisor (GCD). For example, 12/18 = 2/3.
Mixed Numbers — Work with mixed numbers such as 1 1/2. For example, 1 1/2 + 2 1/4 = 3 3/4.
- Choose a mode that matches the operation you need.
- Enter the fractions (numerator and denominator for each, or a whole number plus a fraction for mixed numbers).
- Select Calculate to generate the result.
- Check the result cards for the answer, the worked steps, and the simplified form.
The calculator runs in your browser and is free to use, with no sign-up. It is useful for homework checks, cooking measurements, and verifying manual work. Denominators must not be zero, and answers are always shown simplified to lowest terms.
What Is a Fraction?
A fraction is a number that represents part of a whole. It is written as numerator over denominator: a/b. The numerator (top number) counts how many parts you have, and the denominator (bottom number) tells how many equal parts the whole is divided into. In 3/4, the whole is divided into 4 equal parts and you have 3 of them.
A proper fraction has a numerator smaller than its denominator, such as 3/4. An improper fraction has a numerator equal to or larger than its denominator, such as 7/4. A mixed number combines a whole number with a proper fraction, such as 1 3/4, which is the same value as 7/4 because 4/4 + 3/4 = 7/4.
Worked Examples
| Problem | Working | Answer |
|---|---|---|
| 1/2 + 1/3 | Common denominator 6: 3/6 + 2/6 | 5/6 |
| 2/3 − 1/4 | Common denominator 12: 8/12 − 3/12 | 5/12 |
| 3/4 × 2/3 | Multiply across: 6/12, then simplify | 1/2 |
| 5/6 ÷ 2/3 | Multiply by the reciprocal: 5/6 × 3/2 = 15/12 | 5/4 = 1 1/4 |
| Simplify 12/18 | Divide top and bottom by GCD 6: 12 ÷ 6 = 2, 18 ÷ 6 = 3 | 2/3 |
| Convert 7/4 | 7 ÷ 4 = 1 remainder 3 | 1 3/4 |
| 1 1/2 + 2 1/4 | Convert: 3/2 + 9/4 = 6/4 + 9/4 | 15/4 = 3 3/4 |
Example: Why 1/2 + 1/3 Is 5/6, Not 2/5
Adding the numerators (1 + 1 = 2) and the denominators (2 + 3 = 5) gives 2/5, but that is wrong: denominators are the size of the pieces, not pieces to be counted. Halves and thirds are different-sized pieces, so they must first be cut into the same size. The least common denominator of 2 and 3 is 6. Convert: 1/2 = 3/6 and 1/3 = 2/6. Now the pieces match, so add the numerators: 3 + 2 = 5, giving 5/6. Check by size: 1/2 is 0.5 and 1/3 is about 0.333, and 0.5 + 0.333 = 0.833, which is 5/6 — while 2/5 is only 0.4, far too small.
Example: Multiplication Cancels Before You Finish
For 3/4 × 2/3, multiply numerators and denominators: 3 × 2 = 6 and 4 × 3 = 12, giving 6/12. Simplify by dividing top and bottom by GCD 6: 6 ÷ 6 = 1 and 12 ÷ 6 = 2, giving 1/2. Check: 3/4 is 0.75 and 2/3 is about 0.667, and 0.75 × 0.667 = 0.5, which is 1/2.
Example: Division Flips the Second Fraction
For 5/6 ÷ 2/3, keep the first fraction, change division to multiplication, and flip the second fraction: 5/6 × 3/2 = 15/12. Simplify by dividing top and bottom by GCD 3: 15 ÷ 3 = 5 and 12 ÷ 3 = 4, giving 5/4. As a mixed number, 5 ÷ 4 = 1 remainder 1, so 5/4 = 1 1/4. Check: 5/6 is about 0.833 and 2/3 is about 0.667, and 0.833 ÷ 0.667 = 1.25, which is 1 1/4.
How to Work with Fractions Step by Step
How Do You Add Fractions with Unlike Denominators?
- Find the least common denominator (LCD) — the smallest number both denominators divide into. For 2 and 3, the LCD is 6.
- Convert each fraction to an equivalent fraction with that denominator: 1/2 = 3/6 and 1/3 = 2/6.
- Add the numerators and keep the denominator: 3/6 + 2/6 = 5/6.
- Simplify if possible. 5 and 6 share no common divisor except 1, so 5/6 is already in lowest terms.
Another example: 1/2 + 1/4. The LCD of 2 and 4 is 4. Convert: 1/2 = 2/4 and 1/4 stays 1/4. Add: 2/4 + 1/4 = 3/4.
How Do You Subtract Fractions?
Follow the same steps as addition, but subtract the numerators. For 2/3 − 1/4, the LCD of 3 and 4 is 12. Convert: 2/3 = 8/12 and 1/4 = 3/12. Subtract: 8/12 − 3/12 = 5/12. Check: 2/3 is about 0.667 and 1/4 is 0.25, and 0.667 − 0.25 = 0.417, which is 5/12.
Another example: 7/10 − 3/10. The denominators already match, so subtract the numerators: 7 − 3 = 4, giving 4/10. Simplify by dividing top and bottom by GCD 2: 4 ÷ 2 = 2 and 10 ÷ 2 = 5, giving 2/5.
How Do You Multiply Fractions?
Multiply straight across: numerator × numerator over denominator × denominator, then simplify. For 3/4 × 2/3: 3 × 2 = 6 and 4 × 3 = 12, giving 6/12, which simplifies to 1/2. You may also cancel common factors before multiplying: 3 and 3 cancel, and 2 and 4 share a factor of 2, leaving 1/2 × 1/1 = 1/2.
Another example: 2/3 × 3/4. Multiply across: 2 × 3 = 6 and 3 × 4 = 12, giving 6/12, which simplifies to 1/2. The 3s cancel, which is why the answer is a half.
How Do You Divide Fractions?
Keep, change, flip: keep the first fraction, change division to multiplication, and flip (take the reciprocal of) the second fraction. For 5/6 ÷ 2/3: 5/6 × 3/2 = 15/12 = 5/4 = 1 1/4. Dividing by a fraction smaller than 1 gives a larger answer, which is a useful sanity check: 5/6 divided by 2/3 is larger than 5/6, and 1 1/4 is larger than 5/6.
How Do You Simplify a Fraction to Lowest Terms?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For 12/18, the GCD of 12 and 18 is 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3, giving 2/3. The fraction is in lowest terms when the numerator and denominator share no common divisor except 1.
More examples, each shown with its GCD: 8/12 simplifies by GCD 4 to 2/3 (8 ÷ 4 = 2, 12 ÷ 4 = 3); 15/25 simplifies by GCD 5 to 3/5 (15 ÷ 5 = 3, 25 ÷ 5 = 5); 9/12 simplifies by GCD 3 to 3/4 (9 ÷ 3 = 3, 12 ÷ 3 = 4).
How Do You Work with Mixed Numbers?
Convert each mixed number to an improper fraction first: multiply the whole number by the denominator and add the numerator. For 1 1/2 + 2 1/4: 1 1/2 = (1 × 2 + 1)/2 = 3/2, and 2 1/4 = (2 × 4 + 1)/4 = 9/4. Then find the LCD, 4: 3/2 = 6/4. Add: 6/4 + 9/4 = 15/4. Convert back: 15 ÷ 4 = 3 remainder 3, so 15/4 = 3 3/4.
Converting an improper fraction to a mixed number: divide the numerator by the denominator; the quotient is the whole number and the remainder is the new numerator. For 7/4: 7 ÷ 4 = 1 remainder 3, so 7/4 = 1 3/4. Check: 1 3/4 = 4/4 + 3/4 = 7/4.
Common Mistakes When Working with Fractions
1. Adding Numerators and Denominators
The classic error: 1/2 + 1/3 is not 2/5. Denominators name the piece size, so unlike denominators must be converted to a common denominator first: 3/6 + 2/6 = 5/6.
2. Forgetting to Simplify the Final Answer
6/12 is correct as a value but not finished: it simplifies to 1/2. Always divide top and bottom by their GCD at the end.
3. Flipping the Wrong Fraction When Dividing
In 5/6 ÷ 2/3, only the second fraction flips: 5/6 × 3/2 = 5/4. Flipping the first fraction instead gives 6/5 × 2/3 = 12/15 = 4/5, which is wrong.
4. Using the Larger Denominator Instead of the LCD
For 1/2 + 1/3, the LCD is 6, not 3. Using 3 as the denominator would wrongly treat a half as a third.
5. Adding Mixed Numbers Without Converting
Adding 1 1/2 + 2 1/4 as 3 2/6 is wrong. Convert first: 3/2 + 9/4 = 6/4 + 9/4 = 15/4 = 3 3/4.
6. Dividing by Zero
A denominator of zero has no meaning: 1/0 is undefined. The calculator rejects a zero denominator.
Benefits & Limitations
Benefits
- Adds, subtracts, multiplies, and divides fractions with every step shown.
- Simplifies every answer to lowest terms automatically.
- Handles mixed numbers by converting to improper fractions and back.
- Catches the 1/2 + 1/3 trap by showing the common-denominator step explicitly.
- Free in the browser, on phones, tablets, and desktops, with no sign-up.
Limitations
- The calculator works with exact fractions, so decimal inputs must first be written as fractions.
- It does not solve fraction equations with an unknown; it evaluates the operation you enter.
- Very large numerators and denominators can become hard to read, even though the arithmetic stays exact.
Quick Definitions
| Term | Definition |
|---|---|
| Fraction | A number written as numerator over denominator, such as 3/4: 3 parts out of 4 equal parts. |
| Numerator | The top number of a fraction; it counts the parts you have. In 3/4, the numerator is 3. |
| Denominator | The bottom number of a fraction; it names the size of the parts. In 3/4, the denominator is 4. |
| Proper fraction | A fraction with a numerator smaller than its denominator, such as 3/4. |
| Improper fraction | A fraction with a numerator equal to or larger than its denominator, such as 7/4. |
| Mixed number | A whole number plus a proper fraction, such as 1 3/4, equal to 7/4. |
| Lowest terms | A fraction whose numerator and denominator share no common divisor except 1, such as 2/3. |
| Common denominator | A denominator shared by two fractions so they can be added or subtracted; for 1/2 and 1/3 it is 6. |
| Reciprocal | A fraction flipped over: the reciprocal of 2/3 is 3/2. Used when dividing fractions. |
| Equivalent fraction | A fraction with the same value but different numbers, such as 3/6 = 1/2. |
Frequently Asked Questions
What is a fraction calculator?
It is a free tool that adds, subtracts, multiplies, and divides fractions and simplifies the answer to lowest terms. The free Calcrio fraction calculator shows every step, including the common denominator and the simplification.
Why is 1/2 + 1/3 = 5/6 and not 2/5?
Because halves and thirds are different-sized pieces. Convert both to sixths first: 1/2 = 3/6 and 1/3 = 2/6. Then 3/6 + 2/6 = 5/6. Adding numerators and denominators directly gives 2/5, which is only 0.4, while the true sum is about 0.833.
How do you simplify 12/18 to lowest terms?
Divide the numerator and denominator by their greatest common divisor, 6. 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so 12/18 = 2/3. Since 2 and 3 share no common divisor except 1, 2/3 is in lowest terms.
How do you divide fractions?
Keep the first fraction, change division to multiplication, and flip the second fraction. For 5/6 ÷ 2/3: 5/6 × 3/2 = 15/12 = 5/4 = 1 1/4.
How do you add mixed numbers?
Convert each mixed number to an improper fraction first, then add with a common denominator. For 1 1/2 + 2 1/4: 3/2 + 9/4 = 6/4 + 9/4 = 15/4 = 3 3/4.
Fraction Calculator Methodology
Addition and subtraction. Given a/b and c/d, find the least common denominator L = lcm(b, d). Convert: a/b = (a × (L ÷ b))/L and c/d = (c × (L ÷ d))/L. Then add or subtract the numerators over L. For 1/2 + 1/3: L = 6, 1/2 = 3/6, 1/3 = 2/6, and 3/6 + 2/6 = 5/6. For 2/3 − 1/4: L = 12, 2/3 = 8/12, 1/4 = 3/12, and 8/12 − 3/12 = 5/12.
Multiplication. (a/b) × (c/d) = (a × c)/(b × d), then simplified. For 3/4 × 2/3: (3 × 2)/(4 × 3) = 6/12 = 1/2.
Division. (a/b) ÷ (c/d) = (a/b) × (d/c) = (a × d)/(b × c), then simplified. For 5/6 ÷ 2/3: (5 × 3)/(6 × 2) = 15/12 = 5/4 = 1 1/4.
Simplification. Divide the numerator and denominator by gcd(numerator, denominator). For 12/18: gcd(12, 18) = 6, so 12/18 = 2/3.
Mixed numbers. Convert a mixed number W n/d to an improper fraction as (W × d + n)/d, and convert an improper fraction p/q back by quotient and remainder: p ÷ q = W remainder r gives W r/q. For 7/4: 7 ÷ 4 = 1 remainder 3, so 7/4 = 1 3/4. For 1 1/2 + 2 1/4: 3/2 + 9/4 = 6/4 + 9/4 = 15/4 = 3 3/4.
Validation. Denominators must be nonzero; a zero denominator is rejected as undefined. All results are simplified to lowest terms before display.
References
Try the Fraction Calculator Now
Enter your two fractions above to get the simplified answer with full worked steps — or start with the classic trap, 1/2 + 1/3, and watch it land on 5/6, not 2/5.