Fraction Solver with Solution Steps

This fraction solver works out arithmetic problems (add, subtract, multiply, divide) between two fractions or mixed numbers, and shows the solution step by step. You enter the two fractions and choose the operation, and it returns the simplified result, the common denominator used (for addition and subtraction), and each intermediate step. The calculator below follows the standard order of operations and simplifies the final answer to its lowest terms.

Formula

For two fractions a/b and c/d (where b and d are not zero):

• 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) (multiply by the reciprocal of the second fraction)

Each variable is an integer: a and c are numerators, b and d are denominators (non‑zero). The result is then simplified by dividing numerator and denominator by their greatest common divisor (GCD).

Worked Example

Using the default values: 1/2 + 1/3.

1. Write both fractions with the common denominator 2×3 = 6.
2. Convert 1/2 to 3/6 (multiply numerator and denominator by 3).
3. Convert 1/3 to 2/6 (multiply by 2).
4. Add the numerators: 3 + 2 = 5, keep the denominator 6.
5. The result is 5/6, which is already in lowest terms.

The calculator shows the result as 0.8333 (decimal) and also the fraction 5/6.

How to Use the Fraction Solver

Enter the four integers (two numerators and two denominators) in the fields. Choose the operation from the drop‑down. The solver immediately displays the simplified fraction and its decimal equivalent. For addition and subtraction, it also shows the common denominator step. You can enter negative numbers for numerators, but denominators must be non‑zero (the calculator enforces a minimum of 1).

Why Show the Solution Steps?

Seeing the steps helps you learn the method, not just get the answer. Many students use a fraction solver to check homework or to understand where they made a mistake. The step‑by‑step breakdown shows the common denominator, the conversion of each fraction, and the final simplification. That is the same process taught in most math textbooks.

Common Mistakes When Solving Fractions Manually

• Forgetting to simplify: Always reduce the final fraction by dividing top and bottom by their GCD.
• Adding denominators directly: 1/2 + 1/3 is not 2/5; you must find a common denominator first.
• Dividing without flipping: Division requires multiplying by the reciprocal of the second fraction.
• Ignoring negative signs: Keep the sign with the numerator; a negative denominator can be moved to the numerator.

Limits of the Calculator

This solver works with two fractions only. It does not handle mixed numbers directly (you must convert them to improper fractions first), nor does it handle variables or algebraic fractions. For very large integers, the intermediate products may become large, but the calculator still simplifies the result. The decimal output is rounded to 4 places, so for repeating decimals (like 1/3 = 0.3333…) the fraction form is exact.

When to Use a Fraction Solver vs. Doing It by Hand

Use the solver when you need a quick check or when the numbers are large. Do it by hand when you are practicing the skill or when you need to show your work for an assignment. Even with a solver, you should understand the steps so you can apply them to real‑world problems like cooking measurements (halving a recipe) or splitting a bill.

Frequently Asked Questions

How do I enter a mixed number like 2 1/2?

Convert it to an improper fraction first: multiply the whole number by the denominator and add the numerator (2×2+1=5), so 2 1/2 becomes 5/2. Then enter 5 as the numerator and 2 as the denominator.

What if the denominator is zero?

A fraction with a zero denominator is undefined. The calculator prevents entering 0 for a denominator to avoid errors. If you see a zero, change it to a non‑zero integer.

Can this solver handle negative fractions?

Yes, enter a negative numerator (or denominator, but the calculator treats the sign as part of the numerator). The result will show the correct sign.

Why is the decimal result rounded?

The decimal display is rounded to 4 decimal places for readability. The fraction form is exact. For example, 1/3 is shown as 0.3333, but the exact value is 1/3.

Does the solver simplify the answer automatically?

Yes, it divides the numerator and denominator by their greatest common divisor. For instance, 2/4 becomes 1/2.

Can I use this for more than two fractions?

No, this solver handles exactly two fractions. For more, you would need to combine them step by step or use a more advanced tool.

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in a | First numerator | - | 1 | 0
in b | First denominator | - | 2 | 1
in c | Second numerator | - | 1 | 0
in d | Second denominator | - | 3 | 1
sel op | Operation | Add=1, Subtract=2, Multiply=3, Divide=4
out result | Result | - | if(op==1, (a*d + b*c) / (b*d), if(op==2, (a*d - b*c) / (b*d), if(op==3, (a*c) / (b*d), (a*d) / (b*c)))) | 4
out num | Numerator | - | if(op==1, a*d + b*c, if(op==2, a*d - b*c, if(op==3, a*c, a*d))) | 0
out den | Denominator | - | if(op==1, b*d, if(op==2, b*d, if(op==3, b*d, b*c))) | 0