Fraction Calculator – Definition, Types & Rules

Fraction calculator is a online tool that demonstrates the arithmetic operation for a given fraction. A fraction calculator helps to fasten the calculation procedure, and it further highlights the process to be followed for arithmetic operations. This article aims to discuss the correct approach to use a fraction calculator and further highlight the basics related to fractions, it’s type, method of addition, subtraction, multiplication and division of fractions with rules and examples.

Embibe offers a range of study materials that can be used by students to enhance their preparations. Study materials like PDF of NCERT books, solution sets and previous year question papers. The solution sets are prepared by a team of experts from Embibe who are well aware of the exam pattern and marking scheme followed by CBSE board. Students can follow the solution sets to be understand the correct approach that needs to be followed to answer the exercise questions appropriately.

How Do You Use a Fraction Calculator?

In general, the procedure to use a fraction calculator online is as follows:

Step 1: Insert the fractions and the arithmetic operator in the respective input field

Step 2: Now click the button “Submit” to get the result

Step 3: Finally, the arithmetic operation of fractions will be displayed in the new window.

Using the algebraic formula for addition, subtraction, multiplication, and division of fractions, a fraction calculator will perform the tasks of addition, subtraction, multiplication or division fractions and get you an answer in a reduced fraction form.

Addition:

Subtraction:

Multiplication:

Division

Fraction Calculator Online: Definition

In mathematics, a fraction represents a part of the whole number. It consists of a numerator and denominator where numerator represents the number of equal parts and denominator represents the total amount that makes up a whole.

For example, \(\frac46\) is a fraction where 4 is the numerator, and 6 is the denominator. Fractions can be added, subtracted, multiplied, and divided like all other quantities or numbers.

What Are the Three Types of Fractions?

Let us find out about the types of fractions. There are three types of fractions: proper, improper, and mixed fractions:

Proper Fraction

The top number is a numerator smaller than the bottom number denominator in proper fractions. The proper fraction will always be less than one whole thing, e.g.

Four slices of cake out of a cake that was cut into six: \(\frac46\)

Three rows of a chocolate bar out of the whole chocolate bar, which has five rows: \(\frac35\)

Four parts of lime out of the entire lime that we cut into eight: \(\frac48\)

The general rule, which goes for both positive and negative numbers, is that the absolute value of the fraction is less than one.

Improper Fraction

An improper fraction is a fraction where the numerator is greater than or equal to its denominators. For example, \(\frac84\), \(\frac53\) are improper fractions. Also, an improper fraction always equals to or greater than 1.

Some examples are

Twelve slices of cake, when each cake has eight slices: \(\frac{12}8\)

Eight rows of a chocolate bar. A whole chocolate bar has five rows: \(\frac85\)

Twenty parts of orange, if we cut each orange to 8 equal pieces: \(\frac{20}8\)

Mixed Fraction

Mixed fractions, also termed mixed numerals or mixed numbers, express an improper fraction. They are whole numbers (the number of whole things) and a proper fraction put together. For example, mixed fractions are written as:

How Do You Add Fractions?

We can add fractions in the following manner:

1. When the denominator is the same in both fractions (\(\frac35\) and \(\frac15\))

It is the most simple method where you add numerators and give the denominator, for example:

$\frac{4}{5} +\frac{ 2 }{5}= \frac{(4+ 2)}{5} = \frac{6}{5}$

2. The fractions have different denominators (\(\frac35\) and \(\frac4{10}\)) 

It is a bit more of a complicated case – to add these fractions, you need to find the general denominator.

You can use the LCM method or least common multiple to find the standard number of two denominators. Another option is to multiply your denominators and reduce the fraction later.

3. When you are adding two mixed fractions (\(4\;\frac25\) and \(2\;\frac12\))

One answer for this kind of problem is to change the mixed fraction to an improper fraction and sum it as usual. Let us see an example to convert:

Multiply the whole number by the denominator:

Add the result to you numerator:

That is your new numerator – write it on top of your denominator:

How to Subtract Fractions?

If you are thinking about subtracting fractions and reading through the previous section, take a look at the steps mentioned below:

When you are solving fractions with the same denominator, you must subtract the numerators, for example:

$\frac{3}{5} – \frac{1}{5} = \frac{(3 – 1)}{5} = \frac{2}{5}$

While subtracting fractions with different denominators like \(\frac25\) and \(\frac3{10}\), repeat the procedure from the previous section, but subtracting, not adding in the final step:

(i) Find a common denominator – it is 10.
(ii) Expand the fractions to their equal fractions with a common denominator, as in \(\frac4{10}\) and \(\frac3{10}\).
(iii) Finally, subtract the (top-numbers) or numerator.

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

How Do You Multiply Fractions?

Multiplying fraction is an effortless operation. It is numerator times numerator over denominator times denominator. However, sometimes you also need to simplify the fraction. 

Check out this example below:

$\frac{2}{3} \times \frac{ 5}{6} = \left(\frac{2 \times 5}{3\times 6}\right) =\frac{ 10}{18}$

which can late be simplify to \(\frac59\)

While solving the mixed fractions, do not forget that you must always write them as an inappropriate number before multiplication:

\(\begin{array}{l}2\frac12\;\times\;3\frac14\;=\;\frac52\;\times\;\frac{13\;}4=\;(\frac{5\;\times\;13}{2\times4})\;=\frac{65}8=\;8\frac18\end{array}\)

Moreover, when multiplying a fraction by a whole number, learn that you can record the whole number as itself divided by 1:

\(\begin{array}{l}\frac{3\;\times\;5\;}7=\frac31\times\frac57=\frac{(3\;\times\;5)}{1\times7}\;=\frac{15}7\end{array}\)

How to Divide Fractions?

The division of fractions is considerably similar to fraction multiplication. The simple difference here is that you must multiply your first number by correlating the second fraction. 

Take a look at this example:

$\left(\frac{1}{2}\right) ÷ \left(\frac{4}{5}\right) = \frac{1}{2} \times \frac{ 5}{4} = \left(\frac{1 \times 5}{2\times 4}\right) =\frac{ 5}{8}$

So, all you need to do is spin the second fraction upside down (reciprocal) and multiply the fractions.

How Do You Simplify the Fraction?

We constantly like to make our lives simpler even while solving maths. That is how simplifying fractions is such an essential thing to write the fraction in its simplest form. So we also call simplifying fractions reducing fractions.

How Do We Convert a Fraction Into a Decimal?

The simplest way to turn a fraction into a decimal is to use a calculator or a fraction calculator. You can also use a standard pocket calculator or a dedicated tool, the fraction to decimal converter.

Sometimes the fraction is comparatively easy to change into decimal without using tools – like \(\frac12, \frac34\) (or even \(\frac18\)). Now, let us consider that you can figure out how to expand the above fractions to have 10, 100, 1000, and so on in the denominator, respectively:

Check out the examples below:

Multiply the number \(\frac12\) by 5 to get 10 as the bottom number or denominator:

$\frac{1}{2} = \frac{5}{10} = 0.5$

Next, we multiply \(\frac34\) by 25, to get 100 as the bottom number or denominator:

$\frac{3 }{4}= \frac{75}{100} = 0.75$

Multiplying, \(\frac18\) by 125, to get 1000 as the bottom number or denominator:

$\frac{1 }{8}= \frac{125}{1000} = 0.125$

Nevertheless, what if you do not have the Internet or a calculator with you, but only pen and paper. If your fraction does not look so easy to expand as the ones above then, you will probably need to do the long division to the decimal places by hand/manually.

Rules for Fractions – Fraction Calculator

Fractions – Use the slash “/” separating the numerator and denominator, i.e., for five-hundredths, enter 5/100. If you are using mixed numbers, be sure to leave a single space between the whole and fraction part.

The slash divides the numerator (top number or number above a fraction line) and denominator (bottom number).

Mixed numerals (mixed fractions or mixed numbers) write a non-zero integer divided by one space and fraction, i.e., \(1\frac34\). An example of a negative mixed fraction: \(-4\frac12\).

Because slash is both signs for fraction line and division, we suggested use colon (:) as the operator of division fractions, i.e., 1/2 : 3.

Decimals or (decimal numbers) enter with a (.) decimal point. Besides, they are directly changed to fractions – i.e. 1.45.

The colon: and slash / is the symbol of division. It can be used to divide mixed numbers 1 3/4: 5 3/8 or can be used for write complex fractions, i.e. 1/2: 1/3.

The * or asterisk × is the symbol for multiplication.

While \(+\) is addition, minus sign \(-\) is subtraction, and \(()[]\) is mathematical parentheses.

The exponentiation/power symbol is represented as ^ 

FAQs on Fraction Calculator

Here is a list of some frequently asked questions listed below:

Q. What are the seven types of fractions?
A: The seven types of Fractions are: proper fraction, improper fractions, mixed numbers, like fractions, unlike fractions, equivalent fractions, unit fraction.

Q: What is meant by a fraction?
A: A fraction tells us how many parts of a whole we have. You can identify a fraction by the slash that is written between the two numbers. There is a top number known as the numerator, and a bottom number, the denominator. For example, 1/2 is a fraction.

Q. How can a fraction be identified?
A: Fractions have a top number or (numerator) and a bottom number or (denominator) separated by a “-”, which is given in a p/q format, indicating that the numerator is divided by the denominator.

Q: What is a vulgar fraction?
A: When two integers, i.e., (the numerator and denominator) are placed above and below a fraction, the bar is vulgar. Vulgar fraction is also known as ‘common fractions’.

Q: Define mixed fractions?
A: When a fraction consists of a whole number and a fraction, they are called mixed fractions: for example, 8 ¾, 9 ½.

We hope this article on Fraction Calculator was helpful. Understanding fractions will help you solve statistical problems, and also learning the rules and method will help you score good score for the CBSE exams. 

If you have any queries regarding this article, do let us know about it in the comment section below. We will get back to you at the earliest.

Stay tuned on embibe.com for more news and updates!