Fraction Calculator

A fraction calculator is a free online tool that shows how to do mathematical operations on fractions. The Fraction Calculator speeds up the calculation process by highlighting the steps you need to take when performing arithmetic operations. This article will cover how to use this particular fraction calculator correctly, as well as the fundamentals of fractions, including their type, addition, subtraction, multiplication, and division, as well as rules and examples.

A fraction reveals how many parts of a whole are available to you. You can recognize a fraction by a slash drawn between two numbers. The number on the left or in the upper part is called the "numerator." The number on the right or in the lower part is called the "denominator." For instance, \$\frac{2}{4}\$ is a fraction with two as the numerator and four as the denominator.

There are different types of fractions: proper fractions, improper fractions, mixed fractions, unit fractions, and complex fractions. Some fractions in relation to each other can be equivalent fractions, like fractions, and unlike fractions.

Rules for Using the Fraction Calculator

• Input the fractions into the boxes that have been made available to you (formatted like \$\frac{4}{9}\$, \$\frac{25}{6}\$, or \$\frac{8}{3}\$).

• There are various options of operators that you can select from. These operators include addition, subtraction, multiplication, or division. You can also use an "of" operator when multiplying fractions. Choose the operator needed to solve the math problem.

• After you have entered the fractions and selected the appropriate operator, the final thing to do is click on the "calculate" button to reveal the answer.

Problems this fraction calculator solves

This fraction solver saves you the time you would have spent manually performing the mathematical operation. The fraction calculator helps add, subtract, multiply, divide, and find a fraction of another fraction.

A Practical Example

Below is a practical illustration of how the fraction calculator operates. For instance, you want to perform an addition operation with the following fractions: \$\frac{2}{6}\$ and \$\frac{1}{4}\$.

Let's begin with the fraction on the left side of the addition operator: \$\frac{2}{6}\$ (where 2 is the numerator and 6 is the denominator). Input 2 (numerator) in the numerator box provided and 6 (denominator) in the denominator box.

The fraction calculator provides two boxes on the operator selector's right side. The fraction on the right side of the addition operator is \$\frac{1}{4}\$ (where 1 is the numerator and 4 is the denominator). Input 1 (numerator) in the numerator box and 4 (denominator) in the denominator box.

After successfully entering the fractions and selecting the appropriate mathematical operator (in this case, addition), the fraction calculator will perform the calculation and display the output in the answer box.

You can also perform other math operations on this fraction calculator. All you have to do is select the operator that suits your intended procedure.

One interesting thing about this math fraction calculator is that it gives you a detailed explanation of how you can perform the operation without using the fraction calculator.

Performing mathematical operations on fractions without the use of a fraction calculator

Adding fractions

1. Fractions with a common denominator

Adding fractions that have the same denominator is relatively stress-free and straightforward. You have to sum up the numerators and retain the same denominator.

For example,

$$\frac{5}{9} + \frac{2}{9} = \frac{(5+2)}{9} = \frac{7}{9}$$

2. Fractions with different denominators

Unlike adding fractions with the same denominator, adding fractions with different denominators is more complicated. When adding fractions with different denominators, the first thing to do is to find a common denominator for both fractions.

You can achieve this by finding the lowest common multiple (LCM) of the two denominators. You can also multiply the denominators and break down the fraction later.

After you have gotten a common denominator for the fractions, you can then add the numerators.

For example,

$$\frac{4}{5} + \frac{3}{7} = \frac{(4×7)}{(5×7)} + \frac{(3×5)}{(7×5)} = \frac{28}{35} + \frac{15}{35} = \frac{(28+15)}{35} = \frac{43}{35} = 1{\frac{8}{35}}$$

3. Adding two mixed fractions

One way to add two mixed fractions is to convert them into improper fractions and add them in the usual way. Another way is to add the whole numbers and the fractions separately and write the answer as the sum of the two.

Subtracting fractions

The steps to take when subtracting fractions are similar to the actions you take when adding fractions. When the fractions are of the same denominator, you can proceed to subtract the numerators and retain the same denominator.

For example,

$$\frac{4}{5} – \frac{1}{5} = \frac{(4-1)}{5} = \frac{3}{5}$$

When solving problems that involve subtracting fractions with different denominators, repeat the same steps stated in the previous section. But this time, you will subtract the numerators instead of adding them. For example,

$$\frac{2}{5} – \frac{3}{10} = \frac{4}{10} – \frac{3}{10} = \frac{1}{10}$$

Multiplying fractions

Multiplying fractions is straightforward. All that is required is to multiply both numerators together and multiply both denominators together. In some scenarios, you may have to simplify your result.

For example,

$$\frac{2}{3} × \frac{5}{6} = \frac{(2 × 5)}{(3 × 6)} = \frac{10}{18}$$

You can further simplify the example above into \$\frac{5}{9}\$ by dividing the numerator and the denominator by their Greatest Common Factor (GCF), which in this case is 2.

When faced with the problem of multiplying mixed fractions, always remember to convert the mixed fractions to improper fractions. Then you can multiply both numerators together and multiply both denominators together in the same way as mentioned above.

Dividing fractions

When diving fractions, you have to invert the fraction on the right side of the operator by swapping the numerator with the denominator. Doing this will cause the division operator to change to a multiplication operator. You can now proceed to multiply both numerators together and multiply both denominators together.

For example,

$$\frac{\frac{1}{2}}{\frac{4}{5}} = \frac{1}{2} × \frac{5}{4} = \frac{(1 × 5)}{(2 × 4)} = \frac{5}{8}$$

Fraction of a fraction

The process of finding the fraction of a fraction is the same as that of multiplying fractions.

For example,

$$\frac{2}{5}\ of\ \frac{4}{5} = \frac {(2 × 4)}{(5 × 5)} = \frac{8}{25}$$

Fractions Types

Proper Fractions

A fraction where the numerator is smaller than the denominator is a proper fraction. For example:

$$\frac{2}{3}, \frac{10}{20}, \frac{13}{57}$$

Improper Fractions

An improper fraction is a fraction where the numerator is greater than the denominator. For example:

$$\frac{5}{2}, \frac{21}{10}, \frac{48}{12}$$

Mixed Fractions

A mixed fraction is basically an improper fraction. It is a combination of a natural number and a fraction. For example:

$$2\frac{1}{2}, 3\frac{5}{14}, 17\frac{2}{7}$$

Like Fractions

The fractions that have the same denominator are like fractions. For example:

$$\frac{1}{8}, \frac{2}{8}, \frac{5}{8}$$

Unlike Fractions

Fractions that have different denominators are unlike fractions. For example:

$$\frac{1}{2}, \frac{3}{7}, \frac{7}{11}$$

Equivalent Fractions

If we can simplify fractions to make them equal, they are called equivalent fractions. For example:

$$\frac{1}{3}, \frac{2}{6}, \frac{4}{12}$$

You can simplify all these fractions to \$\frac{1}{3}\$.

Complex Fractions

A complex fraction has a fraction in its numerator, denominator, or both. For example:

$$\frac{\frac{x+1}{x}}{\frac{x-2}{4}}$$

Unit fractions

A fraction with 1 as its numerator and a whole number for the denominator is a unit fraction. For example:

$$\frac{1}{3}, \frac{1}{8}, \frac{1}{24}$$