# Fraction Calculator

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## Table of Contents

## How to use the fraction calculator

To use **our fraction simulator** simply enter the requested data
in the form, these are: the fractions you want to work with and the type of operation you want to
perform: addition, division, subtraction, or multiplication.

Finally, you can select the “*Simplify the result*” box so that the
online calculator does just that with the resulting fraction.

Once all this is done, click on “*Calculate*” so that our tool gives you
the result you are looking for in a matter of seconds in an easy and automated way.

However, if you want to learn how to perform some of these operations by hand, we have made an effort to explain how to do it step by step, in the simplest way possible and always guided by examples so you don't miss any steps.

If you want to become an expert in fractions **keep reading and we will tell
you everything you need to know.**

## What is a fraction

Given a fraction:

$$\frac{a}{b}$$

Where **a** and **b** are positive
integer values, it is a geometric concept where a unit is divided into **b**
parts of which **a** are taken. The value located at the top of the
fraction, **a**, is called the **numerator**,
while the value located at the bottom, **b**, is called the **denominator.**

We unconsciously use fractions daily, whether when dividing an hour into portions:

$$\frac{1}{4}\ of\ an\ hour$$

When shopping at the market:

$$\frac{1}{2}\ kilograms$$

Or the most common example, when wanting to divide and share a cake by cutting it into portions, in this case, each portion represents a fraction of the cake. If we have divided the cake into 5 equal portions, each represents:

$$\frac{1}{5}\ of\ a\ cake$$

## Interpretation of fractions

### Fraction as part of a whole:

The “whole” as a continuous object (cake, square, etc.) or as a discrete set (set of animals, pencils, etc.) when divided into equal portions yields a fraction that represents that portion. For example:

$$\frac{1}{4}\ of\ the\ cake$$

### Fraction as quotient:

When you want to share or divide a number of objects equally. For example, if there are 20 candies to be shared among 4 people, each would get 5 candies, that is:

$$\frac{20}{4}\ of\ the\ total$$

### Fraction as ratio:

Frequently used to compare two magnitudes, for example:

The area of the red triangle, compared to the area of the rectangle, is:

$$\frac{1}{2}$$

### Fraction as operator:

In this interpretation, the fraction is considered as a mathematical operation. For example:

$$9\ is\ \frac{3}{4}\ of\ 12$$

## How to calculate the fractions of a number

In this article, we will explain step by step how to **calculate the fractions
of a specific number,** using examples and explaining the arithmetic of the
calculations.

Didactically speaking, it is convenient to introduce the method for calculating fractions always from a practical point of view, starting with a problem from everyday life with which anyone can identify.

Let's give an example of this type: Juan has 9 apples and eats 1/3. How many apples has he eaten?

Simply multiply the number 9 by the numerator of the fraction, and it would generate a new fraction:

$$\frac{9}{3} = 3$$

These are the apples that Juan has eaten. If it's not entirely clear to you, keep reading, because we are going to cover all possible operations with fractions.

## How to multiply a number by a fraction

If the problem is in written format, the first step you should carry out is to extrapolate the data into numbers. If, on the other hand, the problem is already in numeric format, you can skip this step.

For example, if the statement says one third times eight, it will be a multiplication. In this case, if we reformulate it numerically, we obtain:

$$\frac{1}{3} \times 8$$

At this point, **multiply the whole number by the fraction.** When
working with whole numbers, the only necessary operation is to multiply the figure in question by
the numerator of the fraction, that is, the number that is on the top.

The denominator, however, always remains the same, this will be the case in all calculations that have to do with multiplication.

In our example, we will obtain:

$$\frac{1}{3} \times 8 = \frac{8}{3}$$

Divide the numerator by the denominator, that is, divide the product obtained in the previous step by the denominator of the fraction.

At this point, the fraction obtained could be a fraction in which the numerator is greater than the denominator. In other words, you will have to simplify a fraction to the minimum terms.

In our example, after performing the multiplication, we have obtained the fraction:

$$\frac{8}{3}$$

The result of this operation will not be a whole number, that is, it will have decimals or, in other words, it will be a division that will generate a remainder.

Therefore, 8 divided by 3, would be 2 with a remainder of 2, therefore, as a result, we would get 2 and the following fraction:

$$\frac{2}{3}$$

From a practical point of view, and going back to Juan and the apples, if our protagonist has eight apples, and eats a third of them, how many apples has he eaten?

Well, in this case, 2 apples and 2 thirds of the third, leaving him with 5 apples and a third of the sixth.

## How to simplify a fraction

A fraction in which the numerator is greater than the denominator is known as *improper*.
Before writing the final result of a problem, it is useful to simplify them. For this, a division
between numerator and denominator is followed, taking into account the remainder, if any, in a
fractional form:

Imagine you want to simplify the fraction:

$$\frac{11}{3}$$

For this, divide 11 by three whose result is 3 with a remainder of 2, this remainder will be reformulated in a fractional form, therefore it would be like this:

$$\frac{11}{3} = 3 + \frac{2}{3}$$

The result obtained will be **a mixed number** composed of a whole
number and a fraction. To write the mixed number correctly, you must write the result of the
division (in whole numbers) and then add the remainder in the form of a fraction.

On the other hand, you can also reduce a fraction to the lowest terms, after having performed a multiplication and obtained a fraction. In other words, you will have to find the greatest common divisor between the different numerators and denominators to reduce these figures to prime numbers.

For example, imagine you want to reduce the fraction:

$$\frac{3}{12}$$

In this case, to reduce it to the lowest terms, you will have to divide the numerator and the denominator of the fraction by the greatest common divisor, in this case, 3, to obtain the result of:

$$\frac{1}{4}$$

## How to add and subtract fractions

### Fractions with the same denominator

The natural way to understand the addition of fractions is simply to understand what this operation represents from the concept of what a fraction is. For example:

$$\frac{2}{5}+\frac{1}{5}$$

You can reason as in the example of the cakes, if you divide it into 5 portions and from this you take 2 portions and then take 1, you will have taken 3 portions out of 5. You can then say that

$$\frac{2}{5}+\frac{1}{5}=\frac{3}{5}$$

This idea can be generalized and thus say that:

$$\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$$

And this applies when the fractions have the same denominator.

### Fractions with different denominators

The case where the fractions have different denominators can be resolved by transforming the fractions so that they have the same denominator and thus be able to apply the previous case. For example:

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

By multiplying and dividing the first fraction by 3 and multiplying and dividing the second fraction by 5 in the same way, both are made to have the same denominator, thus the operation is as follows

$$\frac{4}{5}+\frac{1}{3}=\frac{12}{15}+\frac{5}{15}=\frac{17}{15}$$

The previous procedure can be generalized in the following way:

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

The case of **subtraction** can proceed in a similar way to that
of addition, that is:

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

## How to multiply fractions

The multiplication of fractions is one of the operations with fractions easiest to remember, since it is carried out linearly, that is, the numerator is multiplied by the numerator and the denominator by the denominator

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

For example:

$$\frac{3}{2}\times \frac{4}{5}=\frac{(3)(4)}{(2)(5)}= \frac{12}{10}=\frac{6}{5}$$

## How to divide fractions

To perform the division of fractions we can proceed in several ways. The first is to apply the rule of the double C, that is,

$$\frac{a}{b}: \frac{a}{b}=\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{ad}{bc}$$

Another equivalent way consists of inverting or swapping the values of the fraction on the right and then performing the multiplication operation

$$\frac{a}{b} : \frac{a}{b}=\frac{a}{b}\times\frac{d}{c}=\frac{ad}{bc}$$

For example:

$$\frac{2}{3}:\frac{4}{5}=\frac{2}{3}\times \frac{5}{4}=\frac{10}{12}=\frac{5}{6}$$

And that is all you need to know about fractions and their operations. In this article, you
have learned, in addition to using **the fraction calculator,** how to
perform different operations.

If you found the content useful and interesting, do not hesitate **to share it
on your social networks,** thus you will help us increase the diffusion of this
community of calculators and free simulators, making our work easier.

Finally, all that remains for us to ask is that if for any reason you come across typos in
the article or programming errors in the online calculator, **let us know through the
contact page,** so we can solve these problems as soon as possible.