Add and subtract by aligning denominators, calculating numerators, then reducing. Do not add the denominators of 1/2 and 1/3 to get 2/5. This guide is for learners checking common denominators, signs, working and rounded decimals.
Open the fraction calculator and compare a hand-worked 5/8−1/6=11/24 with the result and working. Numerators and denominators have separate input fields.
Choose the operation before choosing a method
| Operation | First step | Example | Exact result |
|---|---|---|---|
| Add | Align denominators | 1/2+1/3=3/6+2/6 | 5/6 |
| Subtract | Align denominators | 5/8−1/6=15/24−4/24 | 11/24 |
| Multiply | Multiply numerator and denominator pairs | 3/5×10/9=30/45 | 2/3 |
| Divide | Invert only the second fraction | 3/4÷2/5=3/4×5/2 | 15/8 |
Why use common denominators and an LCM?
A denominator counts equal parts of the same whole; a numerator counts how many parts are used. Models with different-sized wholes cannot be compared by adding lengths or areas directly. In sixths, 1/2 has three parts and 1/3 has two, giving 5/6.
As explained in OpenStax, multiplying numerator and denominator by the same nonzero value preserves the fraction. For 3/4+5/6, the least common denominator 12 gives 9/12+10/12=19/12. Using the product 24 gives 38/24, which reduces to the same result. The LCM keeps intermediate numbers smaller.
Use the GCD/LCM guide and GCD/LCM calculator to choose a denominator. If denominators already agree, 3/7+2/7=5/7 without another conversion.
Reduction, negative denominators and mixed numbers
| Input or situation | Method | Result or caution |
|---|---|---|
| Reduce 12/18 | Divide both by GCD 6 | 2/3 |
| 1/−2 | Move the sign to the numerator | −1/2 |
| −1/−2 | Two negative signs cancel | 1/2 |
| 0/5 | Numerator zero, denominator nonzero | 0 |
| −1 2/3, minus on the whole | −(1+2/3) | −5/3 |
| 2 1/4 | (2×4+1)/4 | 9/4 |
For 2 1/4−1 2/3, convert to 9/4−5/3=27/12−20/12=7/12. To write 19/12 as a mixed number, divide 19 by 12: quotient 1, remainder 7, giving 1 7/12. Write −(1+2/3) explicitly to separate a negative mixed number from −1+2/3.
You may cancel common factors in a product before multiplying. Do not cancel terms diagonally across addition. If you reduce individual terms after aligning denominators, check the denominators still agree before adding or subtracting.
Choose the conditions and check
Compare a common denominator and reduced answer
Enter 5/8 and 1/6, choose subtraction, and check 11/24. Reverse it by adding 1/6 back to recover 5/8.
Verify by size, inverse operations and cross-products
| Check | Example | Error it can reveal |
|---|---|---|
| Size | Adding positive 1/3 to 1/2 must increase it | Wrong answer 2/5=0.4 |
| Inverse operation | 11/24+1/6=15/24=5/8 | Sign or denominator errors |
| Cross-products | 11/20=55/100 because 11×100=20×55 | Similar rounded decimals |
| Multiply back | (3/4÷2/5)×2/5=3/4 | Inverting the wrong fraction |
For nonzero b,d, a/b=c/d exactly when ad=bc. 1/3 differs from 3333/10000 because 10000≠9999, even if short decimal displays look alike. Keep fractions through the calculation instead of converting early to a rounded decimal.
Input limits, decimal output and copying
Each numerator and denominator must be an integer with absolute value at most 9999999. A zero denominator or division by zero is rejected. There is no mixed-number entry field or three-fraction input; convert mixed numbers and calculate in pairs while respecting brackets and operation precedence.
| Mode and input | Fraction result | How to read it |
|---|---|---|
| Calculate 9/4−5/3 | 7/12 | Mixed numbers converted first |
| Calculate 3/4÷2/5 | 15/8 | Mixed number 1 7/8 |
| Simplify 12/18 | 2/3 | Decimal 0.6666666667 is approximate |
| Calculate 1/9999999×1/9999999 | 1/99999980000001 | Decimal zero is a rounded display |
| Numerator 10000000 or denominator 0 | Error | Correct the input before using a result |
Within its input limits, the tool uses integer arithmetic for the fraction and rounds the decimal to at most ten places. It uses the product of denominators in its working, so compare reduced answers when your own LCM-based steps look different. Copy includes fraction, mixed number and decimal; label which value is exact in your notes.
Continue with ratios or return for another exercise
The percentage guide connects 1/4=0.25=25%. Review the GCD/LCM guide for denominator choices, or browse the mathematics category.
Choose the conditions and check
Keep the fraction with your working
Choose Simplify and enter 12/18 to check 2/3. Copy it into your own notes; the calculator does not save notes or input history.
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Editorial verification scope
Tools Hub Editorial Team checked the public teaching material and examples on October 29, 2026. Diagrams are original models of a shared whole and the operation rules. Local browser verification covers operations, reduction, signs, input errors, copy and small-screen results.
FAQ
Can I cross-cancel across addition?
No. For 1/2+1/3, use denominator 6 to get 3/6+2/6=5/6. Cancelling factors of a product does not allow cancelling terms of a sum.
How do I enter the negative mixed number −1 2/3?
If the minus applies to the whole mixed number, write −(1+2/3)=−5/3. The expression −1+2/3 is instead −1/3. Convert to an improper fraction before entering it.
Is a zero numerator the same as a zero denominator?
No. 0/5 is zero, but 5/0 is undefined. Dividing 1/2 by 0/5 also divides by zero and is rejected.
If the decimal display is zero, is the fraction zero?
Not necessarily. Decimals are rounded to at most ten places. 1/9999999×1/9999999=1/99999980000001 is positive but displays decimal zero. Use the fraction for the exact answer.
