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Math & School
Fraction Calculator — Add, Subtract, Multiply & Divide Fractions
The fraction math behind recipes, tape measures, lumber cuts and homework
Fractions are everywhere in American daily life, even when you don't call them by name. They run through every recipe (¾ cup of flour, ⅓ teaspoon of salt), every tape measure (a 5/16" drill bit, a board cut to 2 1/2 feet), every wrench set, and a big chunk of school homework from 3rd grade through algebra. The math itself is simple once you know the rules — the trouble is that each operation follows a different rule, and mixing them up is the #1 mistake.
A fraction is just a division waiting to happen: the numerator (top) divided by the denominator (bottom). 3/4 means 3 ÷ 4 = 0.75.
Here are the four rules this calculator uses:
Add / Subtract — you need a common denominator first. The safe method: cross-multiply. a/b ± c/d = (a·d ± c·b) / (b·d). Example: 1/2 + 1/3 = (1·3 + 1·2) / (2·3) = 5/6.
Multiply — the easy one. Just go straight across: a/b × c/d = (a·c) / (b·d). Example: 2/3 × 3/4 = 6/12 = 1/2.
Divide — flip the second fraction and multiply (the "keep, change, flip" trick): a/b ÷ c/d = (a·d) / (b·c). Example: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2.
After any operation, you reduce to lowest terms by dividing the top and bottom by their greatest common divisor (GCD). 6/12 → divide both by 6 → 1/2. Then, if the top is bigger than the bottom (an improper fraction like 7/4), you can rewrite it as a mixed number: 7 ÷ 4 = 1 remainder 3, so 7/4 = 1 3/4.
The most common mistake: adding the bottoms. 1/2 + 1/3 is not 2/5. You never add or subtract denominators — you find a common one first. This calculator does that for you and shows the work, so you can check your own homework or your tape-measure math line by line.
This tool takes two fractions and any of the four operations, then returns the answer reduced to lowest terms, written as an improper fraction, as a mixed number, and as a decimal. It handles negatives and improper inputs, and it will flag a divide-by-zero (a denominator of 0, or dividing by the fraction 0).
📖 See also: How to Calculate a Tip (and Split the Bill)
Calculator
Fill in the fields and click "Calculate" for instant results.
📰 Formula
• Add / Subtract: a/b ± c/d = (a·d ± c·b) / (b·d) • Multiply: a/b × c/d = (a·c) / (b·d) • Divide: a/b ÷ c/d = (a·d) / (b·c) • Reduce: divide top and bottom by GCD(top, bottom) • Mixed number: whole = top ÷ bottom, remainder = top mod bottom
📰 Formula
• Add / Subtract: a/b ± c/d = (a·d ± c·b) / (b·d) • Multiply: a/b × c/d = (a·c) / (b·d) • Divide: a/b ÷ c/d = (a·d) / (b·c) • Reduce: divide top and bottom by GCD(top, bottom) • Mixed number: whole = top ÷ bottom, remainder = top mod bottom
🧪 Worked examples
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Example 2
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Example 3
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Example 4
⚠️ Common mistakes
- Adding or subtracting the denominators (1/2 + 1/3 is 5/6, never 2/5).
- Forgetting to flip the second fraction before dividing.
- Leaving the answer unreduced (6/12 should simplify to 1/2).
- Dividing by a fraction equal to zero, or entering a 0 denominator.
💡 Tips
- Multiplication is the only operation where you go straight across — no common denominator needed.
- To divide, keep the first fraction, change ÷ to ×, and flip the second (keep–change–flip).
- A whole number like 3 is just 3/1 — type 3 as the numerator and 1 as the denominator.
Embed this calculator on your site
Copy the code below and paste it into the HTML of your site or blog.
<iframe src="https://www.calcnimbus.com/embed/fraction-calculator" width="100%" height="500" frameborder="0" style="border:1px solid #eee;border-radius:12px"></iframe>
❓ Frequently asked questions
How do I add two fractions with different denominators?
Give them a common denominator, then add the numerators. The cross-multiply method: a/b + c/d = (a·d + c·b) / (b·d). So 1/2 + 1/3 = (3 + 2)/6 = 5/6.
Why can't I just add the bottom numbers?
Because the denominator tells you the size of each piece. Halves and thirds aren't the same size, so you must convert them to a common piece size first. 1/2 + 1/3 = 5/6, not 2/5.
How do I multiply fractions?
Multiply straight across — tops together and bottoms together. 2/3 × 3/4 = 6/12, which reduces to 1/2. No common denominator is needed for multiplication.
How do I divide fractions?
Keep the first fraction, change division to multiplication, and flip the second fraction (its reciprocal). 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2.
What does it mean to reduce a fraction to lowest terms?
Divide the numerator and denominator by their greatest common divisor (GCD) until no whole number above 1 divides both. 8/12 → both ÷ 4 → 2/3.
How do I turn an improper fraction into a mixed number?
Divide the top by the bottom. The whole-number quotient is the whole part, and the remainder over the original denominator is the fraction part. 7/4 = 1 remainder 3 = 1 3/4.
How do I add a fraction to a whole number, like in a recipe?
Write the whole number as a fraction over 1. To get 2 + 3/4, use 2/1 + 3/4 = (8 + 3)/4 = 11/4 = 2 3/4.
Can this calculator handle negative fractions?
Yes. Put the minus sign on the numerator (for example −3 over 4 for −3/4). The result keeps the correct sign and still reduces to lowest terms.
What's 3/8 plus 1/4 on a tape measure?
Convert 1/4 to 2/8, then add: 3/8 + 2/8 = 5/8. So three-eighths plus one-quarter of an inch is five-eighths of an inch.