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Fraction calculator

Online fraction calculator for mathematical calculations in the Philippines

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What is a fraction calculator?

A 12-year-old Isabel Hughes invented the fraction calculator. The calculator performs basic and advanced fraction operations, decimals, mixed numbers, and expressions with fractions combined with integers. This calculator is equally capable of showing detailed information about the fraction calculation procedure. A fraction calculator is an online tool that showcases the arithmetic operation for a given fraction as the value is derived from multiple fractions operations. With an expression, problems with two, three, or more fractions and numbers can be solved.

The two modes of operation of the fraction calculator are the basic and the advanced modes. The speed of calculating increases and the process of executing the arithmetic operations are showcased. The calculator helps to compare and order fractions. 

Order of operations

It is important to note that this calculator follows well-known rules for the order of operations. These order of operations are;

How are fractions calculated?

To understand the operations behind a fraction and its calculation, recognizing the parts of a fraction is important. Fractions are written as one number placed over a line dividing another number below it. The number above is called the numerator, while the number beneath is the denominator. For example, in ½, 1 is the numerator, while 2 is the denominator, which tells how many parts make up the whole number. In ½, 2 as the denominator means there should be two parts in the fraction.

A whole number with a fraction is called a mixed fraction. The addition and subtraction of fractions are done by identifying fractions with the same denominators before making calculations. If the denominators are not the same, each part of a fraction is multiplied by the other fraction’s denominator to find the same denominator. Once the same denominator is found and numerators multiplied if necessary, the addition and subtraction of the numerators can occur with the result placed over a dividing line. The same denominator can be placed below the line. For example, ¾- ²/⁴ = ¼. On all fronts, avoid adding or subtracting denominators.

Whenever there is a large fraction, there would always be a need to simplify. For example, 8/20 + 12/20 = 20/40. This can be simplified to 4/8. The multiplication and simplification of fractions are done by turning mixed fractions or whole numbers into improper fractions. Multiplication becomes easier when proper and improper fractions are involved. If there is a whole number or mixed fraction to be multiplied, it has to be turned into a fraction. For example, multiplying fractions ⅗ by 8, 8 would be turned into a fraction and multiplied. 

When a mixed fraction is present such as 1½, turn it into an improper fraction, 3/2, before multiplying fractions. The numerators and denominators should be multiplied. The numerators should be multiplied with the result written over a dividing line. The denominators are equally multiplied with the result put under the line. For example, multiply ⅓ by ²/⁶, multiply 1 by 2 ( numerator), and 3 by 6 ( denominator). Your answer would be 2/18.

You will need to reduce the result to a simplified fraction in many cases, especially if you started with an improper fraction. Identify the greatest common factor and use it to simplify the numerator and denominator. An example is 2/18; 2 is the greatest common factor, of which the fraction is reduced by 2 to get 1/9.

There is equally the aspect of dividing fractions, and the easiest way to divide fractions is to flip the second fraction before you calculate the sum. An example is 3/2 ÷ ½. Flip the ½ fraction, so it appears as 2/1. The numerators and denominators can be multiplied, which entails multiplying fractions straight across to the numerator. The result is put over a dividing line, and the denominators are multiplied. The results are equally put under a dividing line. An example is 3/2×2/1 = 6/2.

These results can be simplified because we have a case of improper fraction here, where six is above two. Hence, it can be reduced by using the greatest common factor to reduce the fraction. For example, the greatest common factor for 6/2 is 2. Hence, your supplied answer is 3.

How to use a fraction calculator?

The fraction and arithmetic operator is inserted in the respective input field. This means that the fraction is provided in the input fields, and the button to calculate is clicked on to get the results. Once the user submits the query, the arithmetic operation of the fractions will be displayed externally.

Fraction is a part or portion of a whole symbol or thing. In mathematics, a fraction represents a part of a whole number. It consists of the numerator and denominator, where the numerator represents the number of equal parts, and the denominator represents the total amount that makes up a whole. For example, ⅘ is a fraction where 4 is the numerator, and 5 is the denominator. 

The fraction calculator is easy to use. Users popularly use it to perform functions like adding, subtracting, multiplying, dividing, and converting fractions like all other quantities or numbers. There are three keypads or buttons, with each having its distinguishing feature. The most popular use of a fractions calculator is multiplying fractions and dividing them. Students use it to perform tasks such as subtracting fractions and adding them.

One of the buttons represents the whole number, the other represents the fraction numerator, and the second fraction represents the denominator. Despite having just three boxes to work with, the control and the outward result are outstanding for what is essentially a basic program.

Examples of fractions the fraction calculator can solve

Proper fractions

In this type of fraction, the top number is the numerator smaller than the bottom number, which is the denominator. A proper fraction will always be less than the absolute value or thing. An example is four slices of bread shared amongst five people, which is ⅘. Figure 4, in this case, stands for the numerator, while figure 5 is showcasing the denominator.

Improper fractions

For an improper fraction, the numerator is greater than its denominator. For example, ⁸/⁴, where figure 8 is the numerator, while figure 4 is the denominator.

Mixed fractions

They are whole numbers and a proper fraction put together, for example, 1½.

Equivalent fractions

These are fractions that appear different but, in essence, hold the same value. For example, ⅔ is the same as ⁴/⁶.

Simplified fractions

These are fractions reduced to their lowest form. They are lower equivalents of a higher fraction; ⅔ is a simplified version of ⁴/⁶.

Types of fraction calculators

There are multiple types of fraction calculators available online, some of which are:

What are the benefits of using a fraction calculator?

A fraction calculator helps to fasten the calculation procedure and further highlights the process to be allowed for arithmetic operations. A fraction calculator gives step-by-step help on fraction problems.

Functions of a fraction calculator

It gives step-by-step help on fraction problems. Apart from that, a fraction calculator is used for basic operations such as addition, subtraction, multiplication, and division of fractions. A fraction calculator is used for advanced operations, and complex expressions can be evaluated using a fraction calculator. An example is ((2×⅔/ 14.5) + ⅓+⅔×( pi/²))^½.

A fraction calculator is used to solve simple fractions in both modes. For example, ¾ and ½ are examples of simple fractions. It can also be used to solve mixed fractions in both modes. The values for the arithmetic operation space are left between the whole part and the fraction part. Furthermore, a fraction calculator is used to solve decimal fractions. A dot (.) is used as a decimal separator when inputting the values. An example is 1.5. A fraction calculator further highlights the process to be allowed for arithmetic operations

How to use a keyboard for online fraction calculations?

By typing the fraction on a PC, use the division symbol to type a fraction. The first thing to be done is to enter the numerator of the fraction, which is the top number, after which the division key or forward slash is pressed (/) before entering the denominator, which is the bottom number. An example would look like ⁴/³².

To type a whole number with a fraction, simply type the whole number with a space attached. Then include the fraction by entering the numerator, the division key, or forward slash before entering the denominator. An example would look like 1 ½.

Keyboard shortcuts for common fractions can be used. A few common fractions have keyboard shortcuts that can be used by holding down the Alt key and typing the code numbers. You would have something like this 

½ = Alt + 0189

¼ = Alt + 0188

¾ = Alt + 0190

The auto-formatting feature in Word programs can be used. A feature can convert a fraction typed to a fraction symbol, which features the numerator and denominator separated by the horizontal bar using the slash symbol. The function of this feature is usually on by default. However, if it is not activated, go to the Word options in the dialogue box, click on Proofing, and click on Auto-correct options. Autocorrect can either be turned on or off, enabling you to edit how certain things are corrected. Please, note that this function does not work for all fractions.

An equation field in Word programs can also be used to type a fraction. The steps involved are the following:

  1. Open Microsoft Word and click on the section of the document you intend to create a fraction.

  2. Click Ctrl + F9 to insert a set of brackets. A grey box would mark the brackets after clicking.

  3. Type “EQ\F(a, b) into the space between the brackets, without including the parentheses. For example, to show the fraction ²/8, you would type “EQ\F(2,8) between the brackets.

  4. The next step is to delete any blank spaces between the brackets and the “EQ\F(a, b) function. If these blank spaces are not deleted, an error message would be received when trying to turn the equation to a fraction.

  5. Press Shift+F9 to create the fraction.

The subscript and superscript formatting can type fractions in word programs. The font in Word can be formatted such that it appears as a superscript text or subscript text. This would enable you to manipulate the font so that it appears as a fraction. The steps involved in achieving this are the following:

  1. Type the numerator and highlight it.

  2. From the menu, select Format, then click on Font before selecting Superscript.

  3. Press the Ctrl+spacebar to clear the formatting for the next step.

  4. Type a forward slash(/). Then type the denominator and highlight it.

  5. Then select Format, Font, and Subscript in that order.

  6. Press the Ctrl + spacebar to clear the formatting again and move on with your typing.

How to perform complex tasks using a fraction calculator?

There are multiple ways to perform complex tasks using a fraction calculator. Some of which are described below.

Method of lowest common denominator multiplication 

Convert mixed numbers to improper fractions. When possible, reduce all fractions and find the least common denominator of all fractions appearing within the complex fraction. Multiply all numerators together and multiply all denominators together. In the final fraction result, reduce, simplify, and convert to mixed numbers if an improper fraction is showcased.

For example, calculate 2½ × 3½.

The first thing to do from the steps above is to change the mixed numbers into improper fractions. 

2½ = ⁵/²,  while 3½ = ⁷/².

The numerator is 5  and 7 in each fraction, the top number, while the denominator is 2 (least common denominator).

Hence, we have ⁵/² and ⁷/². The least common denominator, in this case, is 2.

The next thing is to multiply the numerator together, which is 5×7= 35.

Multiply the denominators together, 2×2=4.

Thus, ⁵/² × ⁷/²= ³⁵/⁴.

From here, the final fraction result is an improper fraction, which must be converted or changed into a mixed number.

³⁵/⁴ changed to a mixed number becomes 8¾.

Method of fractions by fraction division

The first thing to do is convert mixed numbers to improper fractions and reduce all fractions when possible. Here the main fraction line(/) means dividing fractions. Therefore, invert the second term ( flip the second term) and multiply the operands. When possible, reduce, simplify, and convert any final fraction results to mixed numbers.

For example, calculate ⅕÷ ⅗.

There are no mixed numbers in this case, and the fraction has been reduced from the question. All you have to do is invert or flip over the second fraction in order to simplify fractions.

The second fraction is ⅗; when it’s flipped, it becomes ⁵/³.

You can then multiply this flipped second term of the fraction with the first term of the fraction.

What you would have will be:

⅕ × ⁵/³ = ⁵/¹⁵ (the numerator in each fraction multiplies each other, and the denominator multiplies each other). The final fraction result shows ⁵/¹⁵, which does not need any further simplification as it is a proper fraction. For instance, if the final result here had shown ¹⁶/⁵, this is an improper fraction, which will need further simplification. In this case, the answer would have been left in mixed numbers. 

¹⁶/⁵ will become 3⅕.