How to Add and Subtract Fractions (Step-by-Step)
Fractions are one of the first topics in math that trips students up — and keeps tripping adults who have not practiced since school. The rules for adding, subtracting, multiplying, and dividing fractions are actually simple once you see the pattern, but the lack of a common framework confuses people.
This guide provides a repeatable step-by-step process for each operation, works through real examples, covers mixed numbers, and shows how to simplify your answer every time. Bookmark it and come back whenever fractions show up in cooking, construction, or homework.
✨Key takeaways
- To add or subtract fractions, you MUST have a common denominator.
- To multiply fractions, multiply straight across (numerators together, denominators together).
- To divide fractions, flip the second fraction and multiply.
- Always simplify the result by dividing numerator and denominator by their GCD.
Adding fractions with a common denominator
If the denominators are already the same, just add the numerators. 2/7 + 3/7 = (2+3)/7 = 5/7. The denominator stays the same because you are combining parts of the same whole.
If the denominators differ, you need a common denominator. Multiply each fraction by the other's denominator. For 1/3 + 1/4: multiply 1/3 by 4/4 = 4/12. Multiply 1/4 by 3/3 = 3/12. Now add: 4/12 + 3/12 = 7/12.
Subtracting fractions
The process is identical to addition, except you subtract the numerators. 5/8 - 1/4: convert 1/4 to 2/8. Now 5/8 - 2/8 = 3/8.
Watch for negative results. If the first fraction is smaller, the answer is negative: 1/3 - 1/2 = 2/6 - 3/6 = -1/6. The Fraction Calculator handles this automatically and shows step-by-step work.
Multiplying and dividing fractions
Multiplication is the easiest operation. Multiply numerators together and denominators together. 2/3 x 4/5 = 8/15. No common denominator needed.
Division: flip the second fraction (take its reciprocal) and multiply. 3/4 / 2/5 = 3/4 x 5/2 = 15/8 = 1 7/8. Always simplify the result.
Working with mixed numbers
A mixed number like 2 3/4 combines a whole number and a fraction. To use it in calculations, convert to an improper fraction first: multiply the whole number by the denominator, add the numerator. 2 3/4 = (2x4 + 3)/4 = 11/4.
After calculating, convert back: divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator. 17/5 = 3 remainder 2, so 3 2/5.
Simplifying fractions
Find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. For 12/18: GCD(12, 18) = 6. So 12/18 = 2/3.
A fraction is fully simplified when the only common factor of the numerator and denominator is 1. If you are unsure whether your answer is simplified, the Fraction Calculator does it automatically.
Try the calculators referenced in this guide
Put the maths into practice — every calculator is free and runs entirely in your browser.
Frequently Asked Questions
Why do I need a common denominator to add fractions?
Because you can only combine parts that represent the same size. 1/3 and 1/4 are different-sized pieces — you need to convert them to the same size before adding.
Do I need a common denominator to multiply?
No. Just multiply numerators together and denominators together.
What is the GCD and how do I find it?
The Greatest Common Divisor is the largest number that divides both the numerator and denominator evenly. Use the Euclidean algorithm: divide the larger by the smaller, take the remainder, and repeat until the remainder is 0. The last non-zero remainder is the GCD.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. 3/4 = 3 divided by 4 = 0.75.
Can fractions have negative numbers?
Yes. A negative sign can go in front of the fraction, in the numerator, or in the denominator. -3/4, 3/-4, and -(3/4) all represent the same value.
The Precision Calculator Editorial Team
The editorial team at Get Precision Calculator writes practical, formula-driven guides that explain the maths behind every calculator on this site. All content is reviewed for accuracy before publishing.
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