Fraction Calculator

Are you looking for an all-in-one math calculator that has everything you need for fraction: addition, division, multiplication, subtraction or simplification? You have come across a perfect match, because our Fraction Calculator gives you access to all of that and even more. Additionally, our calculator gives you two extra options: convert fraction to decimal and vice versa. I guess there is nothing more needed to say except that you will love how quick and versatile our calculator is.

Feel free to read the text below thoroughly if you want to learn more about fractions and find information on how to use our calculator. However, if you want to explore more similar tools, specifically math related, check out the list below we’ve prepared for you:

• Integer Calculator
• Parallel Line Calculator
• Perimeter Calculator
• Vector Projection Calculator
• Condense Logarithms Calculator
• Decimal Calculator

What is a fraction – definition?

In math, a fraction represents a portion of a whole or collection. A whole can be any number, section, or quantity, and portion indicates how many parts of the whole we are referring to. 

Example of fraction: You have chocolate and want to share it with your friends. Chocolate is a whole, and the number of people you want to share the chocolate with is the fraction. So, let’s assume you have three friends, and you break the chocolate into eight equal pieces. Therefore, we are talking about a 4/8 fraction.

Explanation: You + 3 of your friends equal 4. So, you are taking 4 out of 8 parts.

Parts of a fraction

Each fraction consists of two main parts: numerator and denominator. In addition, when you write them, you need to put a horizontal line in between. Thus, the line that separates them is called a fractional bar.

A denominator is always positioned as the top number in the fraction, and it tells us how many we are dividing the whole into.

On the other hand, a numerator is placed under the fractional bar and indicates the total number of parts of the whole.

While here, check our Least Common Denominator and GCF and LCM posts.

Origin

If we go back to the roots of the word “fraction”, we will see that it dates back to the time of Old Egyptians and Ancient Rome. It was derived from the Latin word fractio. 

The Egyptians were the first who found an interest in studying fractions. Generally, they used them for mathematical problems as a tool to help them calculate the division of their food, supplies, and money.

In its original form, for instance, in India where people used to write fractions as a numerator over denominator without a line (fractional bar). However, later the Arabs added the line, and even today, when writing fractions, you always separate them with a horizontal line.

Types of fraction

As numerators and denominators can have different values, there are different types of fractions in math.

Proper fractions are fractions that have a bigger denominator than the numerator. For instance, let’s look:

\frac{2}{7}, \frac{1}{3}, \frac{3}{4}, and so on are all proper fractions.

Improper fractions are fractions whose numerators are equal or bigger than the denominator. So, for example, these are all improper fractions:

\frac{5}{3}, \frac{6}{2}, \frac{3}{2}.

Unit fractions are fractions whose numerator is always equal to 1.

For example, \frac{1}{2}, \frac{1}{3}, \frac{1}{6} are all unit fractions.

Mixed fractions (numbers) are a combination of a whole number and a proper fraction.

For instance, 5 \frac{1}{2}, 3 \frac{1}{2}, 2 \frac{4}{8}, and so on.

Equivalent fractions are fractions that, when we simplify them, still represent the same value. To get an equivalent fraction, you need to:

• either multiply both their numerator and denominator by the same value
• or divide them by the same value

For instance, \frac{4}{8} = \frac{4}{2} and \frac{8}{2} = \frac{2}{4}

Like fractions always have the same denominator. So, for example, \frac{1}{3}, \frac{2}{3}, \frac{6}{3} are all like fractions.

Unlike fractions always have different denominators-for instance, \frac{1}{3}, \frac{2}{5}, \frac{3}{8}.

Conversion

Fractions and decimal numbers have always been in direct relation. Therefore, you can write any fraction as a decimal in math and vice versa. So, in this section, you will learn how to convert a fraction to decimal and decimal to fraction.

Fraction to Decimal

How to turn a fraction into a decimal? Well, converting fraction to decimal can sometimes be a piece of cake. For instance, if you have those fractions:

\frac{1}{2}, \frac{1}{3}, \frac{1}{10}, \frac{4}{100}, and more.

You don’t need to use any calculator or a special magic tool. However, chances are pretty low that you will get those simple fractions to calculate most of the time. Because of that, converting fractions to decimals is generally not a breeze, and you should utilize a calculator for that.

Are we talking about calculator? You can turn fractions into decimals in a second with our all-in-one Fraction Calculator. However, check out our Fraction to Decimal Converter if you need a more thorough way.

Decimal to Fraction

What if you need an opposite way conversion – decimal numbers to fraction? Follow the steps below we prepared to ease it for you:

Let’s assume we have a number 0.6:

• First, you need to get rid of decimal points, by multiplying it by 10/100/1000 depending on the decimal count. In our case, multiply 0.6 by 10 to remove one decimal point: 0.6 \times 10 = 6
• Then, we need to give this number a denominator, which is always 1. Since we have multiplied the numerator by 10, you have to do the same things for the denominator: 1 \times 10 = 10
• Now, we got this fraction \frac{6}{10}
• Before finishing it up, let’s simplify the fraction by dividing both numerator and denominator by 2: \frac{6}{2} and \frac{10}{2}
• There you go, we have our fraction \frac{3}{5} in the simplest form that we got from a decimal 0.6

Math Operations with Fractions

Fractions are like other numbers in math; thus, we can add, multiply, divide, subtract and simplify them.

Adding Fractions

How to add fractions in math? There are three common scenarios when adding fractions; thus, we will cover each.

Scenario one: Equal denominators

If two fractions have the same denominator, we add them by keeping the same denominator and only adding their numerators.

For example: \frac{2}{4} + \frac{3}{4} = \frac{5}{4}

Scenario two: Different denominators

If you have two or more fractions with an unlike denominator, the rule says that you can add them by first finding the common number of their denominators.

For example: \frac{1}{3} + \frac{4}{9} = \frac{3 + 4}{9} = \frac{7}{9}

Scenario three: Mixed fractions (numbers)

In the case of mixed numbers, the most common way to add them is to turn them into improper fractions and then add them. So, if you need a thorough and explained process of adding mixed numbers, check out our Mixed Number Calculator.

Subtracting Fractions

What about subtraction? Fortunately, subtracting fractions works pretty much the same way as adding them. Therefore, we will not repeat the steps, as we have already explained everything.

You can see the three possible scenarios in the “adding fractions” section, and you can apply all of them to subtracting fractions, as well. The only difference is the operation symbol, thus for subtraction, change it to minus instead of plus and follow the same procedure.

Multiplying Fractions

Multiplication of fractions is a piece of cake, and pretty much you can do it without any tool.

How to multiply fractions \frac{7}{9} and \frac{2}{3}?

Multiply the numerator of the first fraction by the one of the second fraction. Additionally, repeat the same thing for denominators:

7 \times 2 and 9 \times 3 = \frac{14}{27}

After multiplying them, see if you can further simplify them. If not, leave it like that, and boom – you are done!

Dividing Fractions

How to divide fractions? Dividing fractions is very similar to their multiplication. Generally, we use the same approach, but instead of multiplying the two fractions, we first turn the second fraction into its reciprocal before calculating them.

Once you have the second fraction turned upside down, multiply their respective numerators and denominators.

Division example: \frac{2}{4} \div \frac{3}{5} = \frac{2}{4} \div \frac{5}{3} = \frac{2 \times 5}{4 \times 3} = \frac{10}{12} = \frac{5}{6}

Simplifying Fractions

How to simplify fractions? Simplifying or reducing fractions means writing fractions in their simplest form. Generally, you can’t simplify all fractions, only some of them. To simplify a fraction, you need to find a number by which both numerator and denominator can be divided.

For example: \frac{2}{8} = \frac{2}{2} and \frac{8}{2} = \frac{1}{4}

Fraction Calculator – How to Use

We already mentioned that you could use all the common operations such as addition, multiplication, division, and subtraction with fractions. So, if you need to calculate them, we highly recommend using our comprehensive Fraction Calculator instead of manually doing the math.

How to use our calculator?

• Select an operation from the list in the calculator
• Enter all the parameters required for the particular operation in the calculator
• The calculator returns and displays the result.

Fraction Calculator – Example

Let’s use the calculator now and see how to turn a decimal into a fraction.

Scenario: Convert 0.06 to a fraction

Note: If the digits of decimal numbers are repeating, you can set this option “Decimal has repeating digits” to “Yes”.

1. Select “convert decimal to fraction” from the list
2. Enter all the parameters required
3. Fraction Calculator returns and displays the result: 0.06 = \frac{3}{50}

FAQ