Multiple fractions calculation could be performed in several steps, each involving the math operations on just a pair of fractions. This technique is utilizing associative property of arithmetic operations and precedence rule, equally applicable to any integer, fractions or mixed numbers.
Precedence rule defines the order of mathematical operations in any expressions, containing multiple numbers.
Precedence of arithmetic operators is defined as follows:
- parenthesis
- unary negation operator (applying minus sign)
- multiplication and division
- addition and subtraction
Precedence of algebraic operators, which also include exponents and radicals (root) operators, is defined as:
- parenthesis
- unary negation operator
- exponents and radicals
- multiplication and division
- addition and subtraction
In the absence of parenthesis, if two or more sequential operators in the expression are having the same level of precedence, the calculations must be performed from left to right, applying the associative property of arithmetic operators as explained below.
Associative property of addition and subtraction:
a + b + c = (a+b) + c , or: a + (b+c)
a + b - c = (a+b) – c, or: a + (b-c)
a - b + c = (a-b) + c, not: a - (b+c)
a - b - c = (a-b) – c, not: a - (b-c)
Parenthesis is used to indicate the order of the operations.
Associative property of multiplication and division:
a * b * c = (a*b) * c , or: a * (b*c)
a * b / c = (a*b) / c, or: a * (b/c)
a / b * c = (a/b) * c, but not: a / (b*c)
a / b / c = (a/b) / c, but not: a / (b/c)
By applying the technique, described above, any arithmetic expression, containing multiple fractions, could be evaluated as a sequence of mathematical operations on just pair of fractions.
Fractions arithmetic in symbolic form is show below as a reminder:
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*b) / (b*d)
a/b / c/d = (a*d) / (b*c)
Following are numeric samples of multiple fractions calculations, containing the operators of the same precedence (all results are reduced to the lowest terms):
1/2 + 2/7 + 1/6 = (1/2 + 2/7) + 1/6 = 20/21
1/2 + 2/7 - 1/6 = (1/2 + 2/7) - 1/6 = 13/21
1/2 - 2/7 + 1/6 = (1/2 - 2/7) + 1/6 = 8/21
1/2 - 2/7 - 1/6 = (1/2 - 2/7) - 1/6 = 1/21
1/2 * 2/7 * 1/6 = (1/2 * 2/7) * 1/6 = 1/42
1/2 * 2/7 / 1/6 = (1/2 * 2/7) / 1/6 = 6/7
1/2 / 2/7 * 1/6 = (1/2 / 2/7) *1/6 = 7/24
1/2 / 2/7 / 1/6 = (1/2 / 2/7) /1/6 = 10 1/2
Online 3 fractions calculator
Multiple fractions calculation could be performed by free online fraction calculator. This popular calculator, rated #1 on Google™ and Yahoo™ is capable of performing arithmetic operations on 3 fractions, integers or mixed numbers simultaneously. Another version of mobile fractions calculator is customized for reduced screen-size devices (Apple iPod Touch or iPhone, Microsoft Zune HD).
Following example demonstrates the practical evaluation of the three-fraction expression 1/3 + 1 1/2 + 3/4 using online fraction calculator:
- Open web browser and navigate it to the web site: www.webinfocentral.com/MATH/Fractions.aspx. Users of mobile devices with reduced screen size should navigate to the mobile page: http://www.webinfocentral.com/Mobile/Fractions.aspx
- Enter the 1st fraction or mixed number into the corresponding text box titled 'Fraction1'. In our example it is just a regular fraction 1/3.
- Select the first arithmetic operator (in our case it is a multiplication “*”) using the drop down control, marked with a small downward pointing triangle, located just below the text box.
- Enter the 2nd mixed number 1 1/2 into the corresponding text box titled 'Fraction2'.
- Select the second arithmetic operator (“+”) using the lower drop down.
- Enter the 3rd fraction 3/4 into the corresponding text box titled ‘Fraction3’.
- Click on the screen button marked with "=" sign to get the result, presented as both mixed number1 1/4 and corresponding decimal: 1.25.
- And voilà (that's it)!
Note: result fractions are reduced to the lowest terms.
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