How to calculate Fractions online

Fraction is essentially a number presented as the ratio of two integers, e.g.: 2/3, 5/7, 1/4, 11/5, or in a symbolic form: A/B, where A is called numerator and B is called denominator. Both A and B are integer numbers.

In case the numerator and denominator have non-trivial common divisors (i.e., the divisors which are different from 1) then the fraction could be reduced to the lowest form by dividing both numerator and denominator by greatest common divisor (GCD), for example:

6/8 = (2*3)/(2*2*2) = 3/(2*2)

In this example GCD=2. GCD could be also referred as: greatest common factor (GCF) or largest common factor (LCF); all these terms are used interchangeably.

Decimals are special type of fractions with denominator selected from the set: 10, 100, 1000, or in general, the integer power of 10 (10^i). For example:

0.23 = 23/100

0.037 = 37/1000

Decimals could be converted to fraction precisely, i.e. without any loss of accuracy. Fractions could be converted to the decimals either precisely, or with certain rounding error: the latter conversion will include a repeated sequence of numbers (see the underlined numbers in the following example):

3/4 = 0.75

5/8 = 0.625

2/3 = 0.6 (which means: 0.666666666666666… and so on)

If the value of numerator A is less than the denominator then fraction is called proper or vulgar fraction (the latter term is pretty old but still in use); otherwise the fraction is called improper fraction. For example:

2/3, 4/6, 6/7, 32/33, 101/102 are proper fractions;

3/2, 6/4, 33/32, 102/101 are Improper fractions.

• If both numerator and denominator are equal 0 (i.e. 0/0) then the fraction is undefined
• If numerator is 0 but denominator is not (e.g. 0/5) then the fraction is equal 0
• If denominator is 1 equal (e.g. 2/1) then the fraction is transformed to Integer (2)
• If numerator and denominator are equal non-zero integers (e.g. 7/7) then the fraction is equal 1

Any improper fraction could be presented as mixed number, containing integer and proper fraction. In our examples:

5/2 = 2 1/2 (this notation actually means: 1 1/2 = 1 + 1/2)

3/1 = 3 (this is actually not a fraction but an integer: 3/1 = 3 + 0/1)

33/32 = 1 1/32

Fraction math is based on simple rules outlined below:

• A/B + C/D = (A*D + B*C) / (B*D)
• A/B - C/D = (A*D - B*C) / (B*D)
• A/B * C/D = (A*C) / (B*D)
• (A/B) / (C/D) = (A*D) / (B*C)

In order to calculate fractions you could use free online fractions calculator available at: http://www.webinfocentral.com/MATH/Fractions.aspx. Following steps demonstrates the calculation of: 5 1/4 + 7/8

Step 1. Open web browser  and navigate to the site: http://www.webinfocentral.com/MATH/Fractions.aspx . You should see the "3 Fraction calculator" web page as shown on the image

Step 2. Enter the 1st in the text box titled 'Fraction1'. In general, it could be regular, improper fraction, mixed number or just integer. In our example it is: 5 1/4

Step 3. Select the arithmetic operator “+”(Add) using the drop down control, marked with little triangle pointing downward and located just below the text box for the first Fraction

Step 4. Enter the second number (regular fraction 7/8 as per our example) in the text box marked “Fraction 2”

Step 5. Click on the screen button marked with "=" sign to get the result:

(5 1/4)+(7/8)=6 1/8

and the corresponding decimal equivalent: 6.125