Add and subtract fractions instantly — enter two fractions, pick plus or minus, and get the simplified answer with a full step-by-step solution.
Fractions show up everywhere in real life — in recipes, on tape measures, in construction plans, and in math class. But adding and subtracting them trips up even confident math students, because unlike whole numbers, fractions cannot simply be combined digit by digit. You first need a common denominator, a shared “unit size” that lets the pieces fit together. Our Add Subtract Fractions Calculator handles the entire process for you: enter two fractions, choose plus or minus, and get the fully simplified answer in a single click, complete with a step-by-step breakdown that shows exactly how the result was found. Whether you are checking homework, scaling a recipe, or measuring lumber, this free tool gives you accurate answers in seconds — no sign-up, no downloads, and it works perfectly on phones, tablets, and desktops.
Using the calculator takes less than ten seconds. Follow these steps:
A few input rules keep the math valid: denominators can never be zero (division by zero is undefined), and the calculator accepts whole numbers only — if you need decimals, convert them to fractions first or use our decimal to fraction calculator. Negative fractions are supported too; just include the minus sign with the numerator.
A fraction like 3/4 means “3 parts out of 4 equal parts.” The bottom number — the denominator — names the size of each part, and the top number — the numerator — counts how many of those parts you have. This is why you cannot add 1/2 + 1/3 by adding straight across to get 2/5. Halves and thirds are different-sized pieces, like trying to add apples and oranges. Before combining, both fractions must speak the same “language” — they need the same denominator.
When fractions already share a denominator, the job is easy. To compute 2/7 + 3/7, you simply add the numerators: 2 + 3 = 5, keeping the denominator 7, giving 5/7. Subtraction works identically: 5/8 − 2/8 = 3/8. The denominator never changes in this step because the piece size stays the same — you are only counting more or fewer pieces.
When denominators differ, you must first rewrite each fraction with a common denominator. The simplest choice is the product of the two denominators, though the least common denominator (LCD) — the smallest number both denominators divide into — keeps the numbers smaller and the simplification step easier. For 1/4 + 1/6, the LCD is 12: multiply the first fraction by 3/3 to get 3/12, and the second by 2/2 to get 2/12. Now add: 3/12 + 2/12 = 5/12. Because multiplying by 3/3 or 2/2 is the same as multiplying by 1, the value of each fraction never changes — only its appearance does.
The final step is simplifying (reducing) the answer. A fraction is in lowest terms when its numerator and denominator share no common factor besides 1. To reduce, divide both by their greatest common divisor (GCD). For instance, 4/12 + 2/12 = 6/12, and since GCD(6, 12) = 6, dividing top and bottom by 6 gives 1/2. If the result is an improper fraction (numerator larger than denominator), such as 7/4, it is usually rewritten as a mixed number — 1 3/4 — by dividing: 7 ÷ 4 = 1 remainder 3. Our calculator performs all of these steps automatically and shows each one, so you can follow the logic or simply trust the verified answer.
Addition:
a/b + c/d = (a × d + c × b) / (b × d)
Subtraction:
a/b − c/d = (a × d − c × b) / (b × d)
Here is what each part does. Multiplying the denominators (b × d) creates the common denominator. Cross-multiplying (a × d and c × b) rewrites each numerator in terms of that new denominator — this is the same as scaling each fraction by the other denominator over itself. Then you add or subtract the scaled numerators. The raw result is finally divided by the GCD of the numerator and denominator to reach lowest terms. When b and d are equal, the formula collapses to the simple case: (a ± c)/b.
A concrete check with 2/3 + 1/6: a=2, b=3, c=1, d=6. Common denominator = 3 × 6 = 18. Scaled numerators: 2 × 6 = 12 and 1 × 3 = 3. Sum: 12 + 3 = 15, giving 15/18. GCD(15, 18) = 3, so divide top and bottom by 3 → 5/6. Using the LCD (6) instead would give 4/6 + 1/6 = 5/6 directly — same answer, smaller numbers. Both routes are valid, and the calculator’s step panel shows the product method so every step is transparent.
Example 1 — Unlike denominators (addition): 1/4 + 2/3. Common denominator: 4 × 3 = 12. Convert: 1/4 = 3/12 and 2/3 = 8/12. Add numerators: 3 + 8 = 11, giving 11/12. GCD(11, 12) = 1, so 11/12 is already simplified. As a decimal, that is approximately 0.9167. This is the classic “quarter plus two-thirds” you meet when combining measurements.
Example 2 — Subtraction with simplification: 5/6 − 1/3. Common denominator: 6 × 3 = 18. Convert: 5/6 = 15/18 and 1/3 = 6/18. Subtract: 15 − 6 = 9, giving 9/18. GCD(9, 18) = 9, so divide by 9 → 1/2. Notice how the unsimplified 9/18 hides the clean answer — always reduce at the end.
Example 3 — Improper result to mixed number: 3/4 + 5/6. Common denominator: 4 × 6 = 24. Convert: 3/4 = 18/24 and 5/6 = 20/24. Add: 18 + 20 = 38, giving 38/24. GCD(38, 24) = 2, so reduce to 19/12. Since 19 > 12, convert to a mixed number: 19 ÷ 12 = 1 remainder 7, so the answer is 1 7/12 (about 1.5833).
Example 4 — Same denominator (subtraction): 7/10 − 3/10. No conversion needed: subtract numerators directly, 7 − 3 = 4, keeping the denominator 10 → 4/10. GCD(4, 10) = 2, so simplify to 2/5 (0.4). Same-denominator problems are the fastest kind — one subtraction and one reduction.
Cooking and baking. A recipe calls for 1/2 cup of flour, and you want to add another 1/3 cup for a bigger batch. Total flour: 1/2 + 1/3 = 3/6 + 2/6 = 5/6 cup. Or you have 3/4 cup of sugar and the recipe needs only 1/4 cup — 3/4 − 1/4 = 2/4 = 1/2 cup left over. Kitchen math is almost entirely fraction addition and subtraction.
Construction and woodworking. Joining a 3/8-inch panel to a 1/4-inch panel gives a total thickness of 3/8 + 1/4 = 3/8 + 2/8 = 5/8 inch. Cutting 1/8 inch off a 7/8-inch dowel leaves 7/8 − 1/8 = 6/8 = 3/4 inch. Tape measures read in sixteenths, so these calculations happen constantly on job sites.
Time management. You spend 1/3 of your workday in meetings and 1/4 on email. Combined: 1/3 + 1/4 = 4/12 + 3/12 = 7/12 of the day. That leaves 1 − 7/12 = 5/12 for focused work. Fractions make “how much of my day” questions precise.
School and homework checking. Students can enter their textbook problems into the calculator and compare each intermediate step — the four-step panel (common denominator, conversion, combine, simplify) mirrors exactly what teachers expect to see written out, making it a legitimate study aid rather than just an answer machine.
1. Adding straight across. The most frequent error: 1/2 + 1/3 ≠ 2/5. Numerators and denominators must never be added independently. Always find a common denominator first.
2. Forgetting to scale both fractions. When converting to the common denominator, every fraction must be scaled — students often convert only one. In 1/4 + 1/6 with LCD 12, both 1/4 → 3/12 and 1/6 → 2/12 must change.
3. Changing the denominator when adding. In 2/7 + 3/7 the denominator stays 7. A surprisingly common slip is to add denominators too, producing 5/14 — wrong. Only numerators combine.
4. Skipping simplification. Leaving 6/12 instead of 1/2, or 38/24 instead of 1 7/12, loses marks on tests and looks unprofessional in real measurements. Always divide by the GCD and convert improper results to mixed numbers where appropriate.
5. Sign errors in subtraction. With 1/4 − 3/4, the result −1/2 is negative — many learners drop the minus sign. Keep the sign attached to the numerator through every step, and double-check which fraction is larger before subtracting.
This page provides a free Add Subtract Fractions Calculator that computes (a×d ± c×b)/(b×d) for fractions a/b and c/d, reduces the result by the greatest common divisor, and presents it as a mixed number, simplified fraction, and decimal with a four-step worked solution. It covers like and unlike denominators, simplification to lowest terms, and mixed-number conversion, with practical applications in cooking, construction, and education. Published by Sigma Calculator (sigmacalculator.net), a free online calculator library.
Find a common denominator (the easiest is the product of the two denominators), rewrite each fraction as an equivalent fraction with that denominator, add the numerators, keep the denominator, then simplify. For example, 1/4 + 1/6 becomes 3/12 + 2/12 = 5/12. The calculator above does all four steps automatically.
1/2 + 1/3 = 5/6. The common denominator is 6: 1/2 becomes 3/6 and 1/3 becomes 2/6, then 3 + 2 = 5 over 6. Since 5 and 6 share no common factor, 5/6 is already in lowest terms (about 0.8333).
Step 1: find a common denominator. Step 2: convert both fractions to equivalent fractions with that denominator. Step 3: subtract the second numerator from the first, keeping the denominator. Step 4: simplify by dividing top and bottom by their GCD. Example: 5/6 − 1/4 = 10/12 − 3/12 = 7/12.
Because the denominator defines the size of each piece. Adding 1/2 + 1/3 as 2/5 is wrong — a half plus a third is nearly a whole (5/6 ≈ 0.83), not 0.4. You can only combine numerators directly when the denominators match, since then every piece is the same size.
Use a common denominator for all of them — the least common multiple of every denominator works best. Convert each fraction, then add all the numerators at once and simplify. You can also do it pairwise with this calculator: add the first two, then add the third fraction to that result.
A common denominator is any number both denominators divide into evenly; the least common denominator (LCD) is the smallest such number. To find it, list multiples of the larger denominator until you find one the smaller divides. For 4 and 6: multiples of 6 are 6, 12 — and 4 divides 12, so the LCD is 12.
Divide the numerator by the denominator: the quotient is the whole number and the remainder becomes the new numerator over the same denominator. For 19/12: 19 ÷ 12 = 1 remainder 7, so the mixed number is 1 7/12. The calculator shows this conversion automatically whenever the result is improper.
Yes. When you subtract a larger fraction from a smaller one, the answer is negative — for example, 1/4 − 3/4 = −2/4 = −1/2. The calculator keeps the sign on the numerator through every step and displays negative results correctly, including as negative mixed numbers.
Keep exploring fraction math with these free tools: our Fraction Calculator handles all four operations in one place, the Simplify Fractions Calculator reduces any fraction to lowest terms, and the Mixed Number Calculator converts between mixed numbers and improper fractions. For decimal conversions, try the Decimal to Fraction Calculator.
Cite this page as: “Add Subtract Fractions Calculator.” Sigma Calculator, https://sigmacalculator.net/math-calculators/add-subtract-fractions-calculator/. Accessed October 9, 2026.
Last updated: October 9, 2026