How to Add, Subtract, Multiply and Divide Fractions
How to add fractions with a common denominator, subtract, multiply, divide and simplify them, and convert mixed numbers and decimals, with worked examples.
By Udit Agarwal · Updated October 17, 2026
To add fractions, rewrite them over a common denominator, add the numerators and keep the denominator: 1/4 + 1/6 = 3/12 + 2/12 = 5/12. Subtraction works the same way, multiplication goes straight across (top times top, bottom times bottom), and division multiplies by the reciprocal of the second fraction. Then simplify by dividing the top and bottom by their greatest common divisor.
A fraction such as 3/4 has a numerator (3, the parts you have) over a denominator (4, the equal parts that make a whole). Multiplying or dividing the top and bottom by the same non-zero number gives an equivalent fraction, so 3/4 = 6/8 = 9/12. Every method below relies on that.
A proper fraction is less than 1, such as 3/4. An improper fraction has a numerator at least as large as its denominator, such as 7/4. A mixed number writes the same amount as a whole number and a fraction: 7/4 = 1 3/4.
With the same denominator, add the numerators and keep the denominator: 2/9 + 5/9 = 7/9.
With different denominators, rewrite both fractions over a common denominator first. Adding straight across does not work: 1/2 + 1/3 is not 2/5, which is less than 1/2 on its own. The smallest denominator that works is the least common denominator (LCD), the least common multiple of the denominators.
A sum can come out above 1: 2/3 + 3/4 = 8/12 + 9/12 = 17/12, which is 1 5/12 as a mixed number.
A shortcut skips the search for the LCD: a/b + c/d = (ad + bc)/bd. For 1/4 + 1/6 it gives (6 + 4)/24 = 10/24, which simplifies to 5/12. It always works, at the cost of larger numbers to simplify at the end. The LCM Calculator finds the least common multiple of two or more denominators, which is their least common denominator.
For mixed numbers, add the whole numbers and the fractions separately, then carry: 2 1/3 + 1 3/4 = 3 + 4/12 + 9/12 = 3 + 13/12 = 4 1/12. Converting to improper fractions gets the same result: 7/3 + 7/4 = 28/12 + 21/12 = 49/12 = 4 1/12.
Subtraction follows the same steps: find a common denominator, then subtract the numerators. 5/6 − 1/4 = 10/12 − 3/12 = 7/12. If the second fraction is larger, the answer is negative: 1/4 − 1/2 = 1/4 − 2/4 = −1/4.
Mixed numbers sometimes need borrowing. In 3 1/4 − 1 2/3, the fraction parts become 3/12 and 8/12, and 3/12 is too small to subtract 8/12 from. Borrow 1 from the 3, which turns 3 3/12 into 2 15/12, then subtract: 2 15/12 − 1 8/12 = 1 7/12. Converting to improper fractions avoids the borrowing: 13/4 − 5/3 = 39/12 − 20/12 = 19/12 = 1 7/12.
Multiply the numerators together and the denominators together, then simplify. No common denominator is needed: 2/3 × 9/10 = 18/30 = 3/5.
Cancelling first keeps the numbers small. Divide any numerator and any denominator by a factor they share: in 4/9 × 3/8, the 4 and the 8 share 4, and the 3 and the 9 share 3, leaving 1/3 × 1/2 = 1/6. Multiplying first gives 12/72, which simplifies to the same 1/6.
"Of" means multiply. Three-quarters of 20 is 3/4 × 20/1 = 60/4 = 15, and two-thirds of 3/4 cup is 2/3 × 3/4 = 6/12 = 1/2 cup.
Convert mixed numbers to improper fractions before multiplying: 1 1/2 × 2 2/3 = 3/2 × 8/3 = 24/6 = 4. Multiplying the whole numbers and the fractions separately is a common mistake; here it would give 2 1/3 instead of 4.
To divide by a fraction, multiply by its reciprocal, the fraction turned upside down. A popular memory aid is "keep, change, flip": keep the first fraction, change ÷ to ×, and flip the second.
3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8.
This works because division asks how many of the second amount fit into the first. Six halves fit into 3, and multiplying by the reciprocal gives the same answer: 3 ÷ 1/2 = 3 × 2/1 = 6. Two everyday cases:
Mixed numbers again go to improper fractions first: 2 1/4 ÷ 3/4 = 9/4 × 4/3 = 36/12 = 3. Dividing by zero, or by a fraction equal to zero such as 0/5, is undefined.
A fraction is in lowest terms when the numerator and denominator share no factor other than 1. To get there in one step, divide both by their greatest common divisor (GCD, also called the greatest common factor). For 18/24 the GCD is 6, so 18/24 = 3/4.
For larger numbers, find the GCD with Euclid's algorithm: divide the larger number by the smaller, then divide the smaller number by the remainder, and repeat until the remainder is 0. The last number you divided by is the GCD. For 84/126:
The GCD is 42, so 84/126 = 2/3. Dividing by small common factors one at a time reaches the same answer in more steps: 84/126, 42/63, 14/21, 2/3. The GCF Calculator finds the greatest common factor of two or more positive whole numbers and lists their prime factors.
Mixed number to improper fraction: multiply the whole number by the denominator, add the numerator and keep the denominator. 2 3/4 = (2 × 4 + 3)/4 = 11/4.
Improper fraction to mixed number: divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator: 17 ÷ 5 = 3 remainder 2, so 17/5 = 3 2/5.
Negative mixed numbers trip people up. −2 3/4 means −(2 + 3/4), which is −11/4. Reading it as −2 + 3/4 gives −5/4, a different number. Convert the positive version and put the minus sign back at the end.
Fraction to decimal: divide the numerator by the denominator. 3/8 = 3 ÷ 8 = 0.375, and multiplying by 100 gives the percentage, 37.5%. The percentage guide covers that step in detail.
A fraction in lowest terms gives a terminating decimal only when its denominator has no prime factors other than 2 and 5, as with 3/8 or 7/20. Any other denominator gives a repeating decimal: 1/3 = 0.333…, 5/6 = 0.8333… and 2/7 = 0.285714285714…, where the block 285714 repeats forever.
Decimal to fraction: write the digits over the matching power of 10, then simplify. 0.375 = 375/1000 = 3/8, 0.6 = 6/10 = 3/5 and 2.75 = 275/100 = 11/4 = 2 3/4. The Ratio Calculator can do the reducing: enter 0.375 and 1 as the two terms and it returns 3 : 8.
Repeating decimal to fraction: when the repeat starts right after the decimal point, put the repeating block over as many 9s as it has digits. 0.333… = 3/9 = 1/3, and 0.272727… = 27/99 = 3/11.
| Fraction | Decimal | Percent |
|---|---|---|
| 1/8 | 0.125 | 12.5% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.333… | 33.33% |
| 1/2 | 0.5 | 50% |
| 2/3 | 0.666… | 66.67% |
| 3/4 | 0.75 | 75% |
The Fraction Calculator adds, subtracts, multiplies or divides two fractions. Type each numerator and denominator in its own box and pick +, −, × or ÷; the answer appears as a simplified fraction, a decimal rounded to four places and a mixed number. It uses the methods above: the cross-multiplication shortcut for adding and subtracting, straight across for multiplying, the reciprocal for dividing, and the greatest common divisor to reduce the answer. A copy button copies the calculation and result as text.
The boxes take whole numbers only, with a leading minus sign for a negative number. There is no box for a whole-number part, so convert a mixed number to an improper fraction first (2 1/4 becomes 9/4), and enter a decimal such as 0.5 as a fraction (1/2). The sign always ends up on the numerator, so 1/−2 shows as −1/2, and a whole-number answer appears as 8/1 in the fraction row and 8 as the mixed number. Because the decimal is rounded, 1/3 shows as 0.3333 and 1/32 (0.03125) as 0.0313. A zero denominator, or dividing by a fraction equal to zero, shows an error instead of a result.
To simplify a single fraction, enter it as the first fraction and multiply by 1/1: 84/126 × 1/1 gives 2/3. To combine three or more fractions, work in steps: 1/2 + 1/3 = 5/6, then 5/6 + 1/4 = 13/12, or 1 1/12. The calculation runs in your browser and nothing you type is uploaded.
How do you add fractions with different denominators? Rewrite them over a common denominator, ideally the least common multiple of the denominators, then add the numerators. 1/4 + 1/6 = 3/12 + 2/12 = 5/12. Simplify the result if the top and bottom still share a factor.
How do you simplify a fraction? Divide the numerator and denominator by their greatest common divisor. For 18/24 the GCD is 6, which gives 3/4. The fraction is fully simplified when the only common factor left is 1.
How do you divide fractions? Multiply the first fraction by the reciprocal of the second. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8, or 1 7/8.
Do you need a common denominator to multiply fractions? No. Multiply the numerators together and the denominators together, then simplify: 2/3 × 9/10 = 18/30 = 3/5. Common denominators are only needed for adding and subtracting.
How do you turn a mixed number into an improper fraction? Multiply the whole number by the denominator and add the numerator, keeping the same denominator. 2 3/4 becomes (2 × 4 + 3)/4 = 11/4.
How do you convert a fraction to a decimal? Divide the numerator by the denominator: 3/8 = 0.375. If the denominator in lowest terms has a prime factor other than 2 or 5, the decimal repeats, as 1/3 = 0.333… does.
What is 1/2 + 1/3? 5/6. The common denominator is 6, so 1/2 + 1/3 = 3/6 + 2/6 = 5/6, which is about 0.8333.