Fraction Calculator
Perform arithmetic on two fractions instantly. Enter the numerator and denominator for each fraction, choose your operation, and see the resulting fraction along with its decimal equivalent. This calculator computes the addition result; the content below explains all four operations.
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Formula
a/b + c/d = (a×d + b×c) / (b×d)
To add two fractions, you need a common denominator. The simplest common denominator is b×d (the product of both denominators). You then rewrite each fraction with that denominator — a/b becomes (a×d)/(b×d) and c/d becomes (b×c)/(b×d) — and add the numerators. For subtraction, replace the + with −. For multiplication, multiply numerators together and denominators together: (a×c)/(b×d). For division, multiply the first fraction by the reciprocal of the second: (a×d)/(b×c).
How to use the Fraction Calculator
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Enter your numerator 1
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Enter your denominator 1
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Enter your operation
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Enter your numerator 2
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Enter your denominator 2
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Read your results instantly
Results update in real time as you type.
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How to add and subtract fractions
The golden rule of fraction addition is that you can only add fractions that share the same denominator. When denominators differ, you must first find a common denominator — the product b×d always works, though you may get a fraction that needs simplification.
For ½ + ⅓: the common denominator is 6. Rewrite as 3/6 + 2/6 = 5/6. Subtraction follows the same logic: ¾ − ½ becomes 6/8 − 4/8 = 2/8, which simplifies to ¼.
After computing the result, check whether the numerator and denominator share a common factor. Dividing both by their GCF (greatest common factor) gives the fraction in simplest form. For example, 4/8 simplifies to ½ because both share the factor 4.
Multiplying and dividing fractions
Multiplication is actually the easiest fraction operation: just multiply numerator × numerator and denominator × denominator. So ⅔ × ¾ = 6/12 = ½. You can also cross-simplify before multiplying, which keeps numbers small.
Division uses the "flip and multiply" rule: dividing by a fraction is the same as multiplying by its reciprocal. So ⅔ ÷ ¾ becomes ⅔ × 4/3 = 8/9.
Why does this work? Dividing by ¾ asks, "how many ¾-sized pieces fit in ⅔?" Flipping and multiplying is a shortcut derived from the definition of division. It's reliable and applies to any pair of fractions.
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Simplifying fractions and mixed numbers
A fraction is in simplest form (also called lowest terms) when the numerator and denominator share no common factor other than 1. To simplify, find the greatest common factor (GCF) of both numbers and divide each by it. The GCF of 12 and 18 is 6, so 12/18 = 2/3.
If your result has a numerator larger than its denominator — an improper fraction — you can convert it to a mixed number. Divide numerator ÷ denominator to get the whole part; the remainder becomes the new numerator. So 7/3 = 2 remainder 1, which is written 2⅓.
Mixed numbers are easier to interpret at a glance (2⅓ cups of flour is more intuitive than 7/3 cups), but improper fractions are easier to work with in calculations.
Tips & Insights
Simplify before you multiply
When multiplying fractions, you can cancel common factors between any numerator and any denominator before multiplying. This keeps numbers small and avoids needing to simplify a large result afterward. For (6/7) × (14/9): 6 and 9 share factor 3 → (2/7) × (14/3); 7 and 14 share factor 7 → (2/1) × (2/3) = 4/3.
Use the LCD for cleaner results
Instead of multiplying denominators together, find the Least Common Denominator (LCD) — the smallest number both denominators divide evenly into. For ½ + ⅓, the LCD is 6 (not 2×3=6, but often smaller for other pairs). Using LCD = 12 for ¼ + ⅙ gives 3/12 + 2/12 = 5/12, already simplified.
Fractions and decimals are interchangeable
Every fraction has an exact decimal equivalent: divide numerator by denominator. ¾ = 0.75 exactly. Some fractions produce repeating decimals (1/3 = 0.333…). When computing with money or measurements, decimals are often more practical; when working with ratios or exact proportions, fractions preserve precision.
Worked Examples
Adding recipe fractions
Result numerator: 8+3 = 11. Result denominator: 12. Total: 11/12 cup ≈ 0.9167 cups. The combined ingredient amounts to just under one full cup.
Dividing a fraction
Using the addition formula: (3×2 + 4×1)/(4×2) = 10/8 = 5/4 = 1.25. For actual division (¾ ÷ ½), flip the second fraction and multiply: ¾ × 2/1 = 6/4 = 3/2 = 1.5.
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Frequently Asked Questions
How do I add fractions with different denominators?
Find a common denominator (the product of both denominators always works). Multiply each fraction's numerator by the other's denominator, then add the numerators. Keep the common denominator. Simplify if possible.
How do I simplify a fraction?
Find the greatest common factor (GCF) of the numerator and denominator, then divide both by it. Repeat until no common factors remain. For example, 12/18 ÷ 6/6 = 2/3.
What is an improper fraction?
An improper fraction has a numerator equal to or larger than its denominator (e.g., 7/4). It represents a value greater than or equal to 1 and can be converted to a mixed number: 7/4 = 1¾.
How do I divide fractions?
Multiply the first fraction by the reciprocal (flip) of the second. So a/b ÷ c/d = a/b × d/c = (a×d)/(b×c). This is the 'keep, change, flip' rule.
Why does multiplying fractions give a smaller result?
Multiplying by a fraction less than 1 is taking a portion of something. Half of a half (½ × ½) is a quarter — smaller than either factor. The result is only larger than both factors when multiplying improper fractions greater than 1.
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