Fraction Calculator

Information about Fraction

Fractions are a fundamental concept in mathematics, representing parts of a whole. At their core, a fraction consists of a numerator and a denominator. The numerator indicates how many parts you have, while the denominator shows the total number of parts that make up the whole.

For example, in the fraction \frac{2}{6}, the numerator is 2 and the denominator is 6. Understanding how to perform operations with fractions is crucial, whether you're adding, subtracting, multiplying, or dividing.

If your question includes the “of” keyword instead of any symbol it represents multiplication. you will need to simply perform the multiplication of the fractions. For example: \frac{3}{6} of \frac{5}{7} means \frac{3}{6} \times \frac{5}{7}.

If your problem consists of mixed numbers (whole numbers and fractions) For example 3\frac{1}{5}. You will need to use our Mixed Fractions Calculator.

Addition of Fractions

Fractions require a common denominator if we need to add or subtract them. If the denominators are different, like this fraction operation \frac{2}{6} + \frac{3}{8}, we will need to make the denominators the same. If your denominators are the same, you can skip this step.

To make the denominators the same, we will need to find the Least Common Denominator. You can use our LCD calculator to find out the least common denominators for the provided fraction. In this case, the LCD is 24. It means that we need to find a number that, when multiplied by the denominators will result in 24.

For the first fraction, if we divide 24 by 6, we get 4. It means we need to multiply the numerators and denominators of the first fraction and 4. Same thing for the next fraction. Divide 24 by 8, we get 3. Need to multiply 3 with both numerators and denominators.

We get,

= \frac{2}{6} \times \frac{4}{4} + \frac{3}{8} \times \frac{3}{3}

= \frac{2 \times 4}{6 \times 4} + \frac{3 \times 3}{8 \times 3}

= \frac{8}{24} + \frac{9}{24}

Now, we have the same denominators for both fractions.

If you already had the same denominators you need to continue now from here.

We can now add the numerators of the fractions directly like this and take the denominators as common:

= \frac{8+9}{24}

= \frac{17}{24}

Formula for addition

We can also use this formula to do addition quickly

\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}

Example using numbers:

Q: \frac{2}{6} + \frac{3}{8}

= \frac{2 \times 8 + 6 \times 3}{6 \times 8}

= \frac{16+18}{48}

= \frac{34}{48}

Simplifying them we get:

= \frac{34 \div 2}{48 \div 2}

= \frac{17}{24}

Subtraction of fractions

Subtraction of fractions is similar to addition. We just need to reduce the numbers at the end instead of adding them. We need to make the denominators the same for subtractions too.

Here is the formula for Subtraction.

\frac{a}{b}-\frac{c}{d} = \frac{ad + bc}{bd}

Let's see an example

Q: \frac{2}{5} - \frac{3}{8}

Let's place them as in the formula:

= \frac{2 \times 8 - 3 \times 5}{5 \times 8}

= \frac{16 - 15}{40}

= \frac{1}{40}

Multiplication of fractions

Multiplication of fractions is really easy we just need to multiply the numerators and denominators of both fractions.

The formula is:

\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}

Let's work with an example:

\frac{4}{5} \times \frac{1}{3}

= \frac{4 \times 1}{5 \times 3}

= \frac{4}{15}

Division of fractions

Division of fractions is also really easy, we will just need to flip the numerator and denominator of the second fraction and multiply it with the first fraction.

The formula is

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{ad}{bc}

Let's work with an example

\frac{4}{5} \div\frac{3}{2}

= \frac{4}{5} \times \frac{2}{3}

= \frac{4 \times 2}{5 \times 3}

= \frac{8}{15}