Fraction Calculator

Two fractions, four operations, and a simplify tab

Pick Add, Subtract, Multiply, or Divide, then type a numerator and a denominator for each fraction. 3/4 is numerator 3, denominator 4. A whole number is entered as itself over 1, so 2 is 2/1. The Simplify tab takes one fraction and reduces it to lowest terms. There is no calculate button. The green result updates as soon as both denominators are valid, and the worked steps appear underneath.

Every answer is shown three ways. The fraction is the main result, already in lowest terms. The mixed number underneath splits an improper fraction into a whole part and a proper fraction, so 17/4 also reads 4 1/4. The decimal is exact when the fraction terminates and is labelled about when it repeats. The boxes start filled with 1/2 + 1/3, and the examples under the tool load a different problem when you click them.

The plus and minus button in front of each fraction sets its sign. You can also paste a fraction such as −5/8 into the numerator box and it is split into the sign and the two boxes. If a number is a mixed number with a whole part, such as 2 1/2, the mixed fraction calculator on this site handles it with the same steps.

How to add and subtract fractions

Fractions can only be added or subtracted when they have the same denominator. If the denominators already match, add or subtract the numerators and keep the denominator: 5/4 + 7/4 = 12/4, which simplifies to 3. If they differ, the calculator finds the least common denominator, the smallest number both denominators divide into, and rewrites each fraction as an equivalent fraction over it.

1/2 + 1/3 uses a least common denominator of 6. 1/2 becomes 3/6 and 1/3 becomes 2/6, so the sum is 5/6. Subtraction follows the same line with a minus: 3/4 − 1/6 has a least common denominator of 12, so it becomes 9/12 − 2/12 = 7/12. When the second fraction is larger the answer is negative, so 1/4 − 1/2 = 1/4 − 2/4 = −1/4. Multiplying the two denominators together also gives a common denominator, just not always the smallest one. The steps use the least common denominator so the answer needs less reducing at the end.

How to multiply and divide fractions

Multiplying fractions needs no common denominator. Multiply the numerators together and the denominators together: 2/3 × 2/3 = 4/9. When a numerator and the opposite denominator share a factor, the steps cancel it first, so 2/3 × 3/4 becomes 2/1 × 1/4 = 2/4, which is 1/2. Cancelling first keeps the numbers small, but multiplying straight across and simplifying at the end gives the same fraction.

Dividing by a fraction is the same as multiplying by its reciprocal, which is the fraction turned upside down. Keep the first fraction, change the division sign to multiplication, and flip the second one. 3/4 ÷ 2/1 becomes 3/4 × 1/2 = 3/8, and 3/4 ÷ 1/2 becomes 3/4 × 2/1 = 6/4, which simplifies to 3/2 or 1 1/2. Dividing by 0 has no answer, so a second fraction with a numerator of 0 is rejected in the Divide tab.

Simplifying a fraction to lowest terms

A fraction is in lowest terms, also called simplest form, when its numerator and denominator have no common factor greater than 1. To reduce a fraction, divide the top and bottom by their greatest common factor. The greatest common factor of 18 and 24 is 6, so 18/24 = 3/4. If the greatest common factor is 1, the fraction is already as simple as it gets, and the step says so.

The Simplify tab does this for one fraction and then writes the mixed number and the decimal. 8/6 reduces to 4/3, which is 1 1/3 or about 1.333. Every operation on the other tabs ends with the same reduction, so 12/4 becomes 3 and 6/4 becomes 3/2. A 0 numerator reduces to 0 whatever the denominator, and a 0 denominator is rejected because it is undefined.

Reading the mixed number and the decimal

An improper fraction has a numerator at least as large as its denominator. To turn it into a mixed number, divide the numerator by the denominator: the quotient is the whole part and the remainder is the new numerator. 17 ÷ 4 is 4 remainder 1, so 17/4 = 4 1/4. A proper fraction, such as 5/6, has no whole part, so the mixed number line repeats the fraction. A negative result keeps its minus sign in front of the whole number, so −5/4 reads −1 1/4.

The decimal line divides the numerator by the denominator. The decimal is exact when the simplified denominator has no prime factors other than 2 and 5, which is why 3/8 gives 0.375 and 1/3 gives about 0.333333. Everything runs in the browser. Numbers up to twelve digits are accepted in each box, and nothing you type is sent anywhere or stored after you close the tab.