Fraction Calculator

How to use the fraction calculator

Type each fraction into the stacked boxes — top number (numerator) over bottom number (denominator). For a mixed number such as 1 ½, put the whole number in the box on the left. For a whole number or a decimal, leave the stacked boxes empty and type it on the left. Press ± to make a fraction negative, pick +, −, × or ÷ from the menu, and add up to six fractions with + Add a fraction. The answer updates as you type, in simplest form, as a mixed number and as a decimal, with every step of the working underneath.

Two more modes sit above the boxes: Simplify reduces a single fraction to lowest terms and shows how its greatest common divisor was found, and Decimal → fraction turns decimals — including repeating ones — into exact fractions. All arithmetic uses exact whole numbers, however large, so nothing is ever rounded until the final decimal. Your fractions are saved in the page link, so Share sends the same problem and answer.

How to add and subtract fractions

Fractions can only be added or subtracted when they are cut into the same size pieces, so:

1. Turn mixed numbers into improper fractions: whole × bottom + top, over the same bottom.
2. Find the least common denominator (LCD) — the least common multiple of the denominators.
3. Rewrite each fraction over the LCD, multiplying its top and bottom by the same number.
4. Add or subtract the tops and keep the bottom.
5. Simplify, and turn an improper fraction back into a mixed number.

The general formula a/b + c/d = (a × d + b × c) / (b × d) always works too, but it uses the product of the denominators rather than the smallest common one, so the numbers get bigger and need more simplifying.

Worked example: 1 ½ + ⅔

1. 1 ½ = (1 × 2 + 1)/2 = 3/2.
2. 2 and 3 share no common factor, so the LCD is 2 × 3 = 6.
3. 3/2 = (3 × 3)/(2 × 3) = 9/6, and 2/3 = (2 × 2)/(3 × 2) = 4/6.
4. 9/6 + 4/6 = 13/6. GCD(13, 6) = 1, so it is already in simplest form.
5. 13 ÷ 6 = 2 remainder 1, so the answer is 2 ⅙ — as a decimal 2.1666…, where the 6 repeats (≈ 2.1666666667).

That is exactly what the calculator shows when the page opens.

How to multiply and divide fractions

Multiplying needs no common denominator: multiply the tops together and the bottoms together, then simplify. Mixed numbers must be converted first — multiplying the whole parts and the fraction parts separately is a classic mistake. 1 ½ × 1 ½ = 3/2 × 3/2 = 9/4 = 2 ¼, not 1 ¼.

Dividing by a fraction means multiplying by its reciprocal — flip the second fraction upside down (“keep, change, flip”). ¾ ÷ ⅔ = ¾ × 3/2 = 9/8 = 1 ⅛. It works because dividing by ⅔ asks how many two-thirds fit into ¾, and multiplying by 3/2 answers that. Dividing by zero, including a fraction with 0 on top, has no answer.

Simplifying fractions

A fraction is in simplest form (lowest terms) when the top and bottom have no common factor except 1. Divide both by their greatest common divisor (GCD) and you get there in one step. The calculator finds the GCD with Euclid’s algorithm: divide the larger number by the smaller, then divide the smaller by the remainder, and repeat until the remainder is 0. For 42/56: 56 = 1 × 42 + 14, then 42 = 3 × 14 + 0, so the GCD is 14 and 42/56 = 3/4. For more on factors and multiples, the multiplication table is a handy reference.

Converting decimals to fractions

A terminating decimal is a fraction over a power of ten: 0.375 has three decimal places, so it is 375/1,000, which simplifies to 3/8. A repeating decimal needs one extra trick. Call 0.1666… x. Then 100x = 16.666… and 10x = 1.666…; subtracting makes the endless tails cancel, leaving 90x = 15, so x = 15/90 = 1/6. To enter it here, type 0.1(6).

Common mistakes

• Adding the denominators. ½ + ⅓ is not 2/5; it is 3/6 + 2/6 = 5/6.
• Flipping the wrong fraction. When dividing, flip the second fraction (the divisor), never the first.
• Negative mixed numbers. −2 ⅓ means −(2 + ⅓) = −7/3, not −2 + ⅓ = −5/3.
• Stopping before the simplest form. 6/8 is correct but not finished: divide by the GCD, 2, to get ¾.

For quick decimal arithmetic use the online calculator, and for powers, roots and trigonometry the scientific calculator. To turn a fraction into a percentage, multiply the decimal by 100 or use the percentage calculator.