2 Fractions addition and subtraction in symbolic form is shown 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*b) / (b*d)
a/b / c/d = (a*d) / (b*c)
3 fractions addition or subtraction could be performed in two different ways:
A). As a single-step steps procedure using the general computational formula shown below:
a/b ± c/d ± e/f = (a*d*f ±c*b*f ± e*b*d) / (b*d*f)
The formula above is further explained by following examples:
a/b + c/d + e/f = (a*d*f +c*b*f + e*b*d) / (b*d*f)
a/b - c/d - e/f = (a*d*f -c*b*f - e*b*d) / (b*d*f)
This computational technique is rather straightforward and presented in a very compact form, but it does not guarantee the result to be in the lowest terms. This will require additional step of reducing fraction to lowest terms, which requires the factoring of nominator and denominator of the result fraction and finding the greatest common factor (GCF).
B). As a two-step procedure by applying the associative property of arithmetic operations, i.e., calculating the pair of the first and second fractions, then taking the result and performing another calculation, which involves the result and the third fraction. Important note: in the absence of parenthesis the order of calculation is from left to right.
Associative property of addition and subtraction:
a/b ± c/d ± e/f = (e/f ± c/d) ± e/f
Parenthesis is used to indicate the order of the operations, namely: from left to right.
Corresponding numeric examples:
1/2 + 2/9 - 1/6 = (1/2 + 2/9) - 1/6 = 13/18 -1/6 = 5/9
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.
3 fractions addition or subtraction could be performed by free online fraction calculators, listed below:
1. Online 3 Fractions Calculator (#1 on Google and Yahoo)
2. Mobile 3 Fractions Calculator
Copyright© 2009 Alexander Bell
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