BAC Computer Software

Fractions Complex Calculations and Brackets

Addition and Subtraction of more than two fractions.

As far as using the Fraction Calculator is concerned you process multiple additions and subtractions as a series of additions and subtractions. That is take the first two fractions and perform the required operation then move the result to fraction 1 and enter the next fraction into fraction 2 and perform the next operation. This is then repeated until the sequence is completed.

If you are working it out on paper then you need to find the common denominator of all the denominators (bottoms). The best way to do this is to take the smallest denominator (bottom) and list all of its factors. Then take each factor in turn and test if it is a factor in all of the other denominators (bottoms) (will it divide into all of the other denominators (bottoms)), if it does cross it of the list of factors and divide all the denominators by it and replace them with the result of the division. Once all the factors have been processed multiply all the factors remaining by the reduced denominators, this is the common denominator. Now work out all the equivalent fractions of all the fractions in the calculation (divide each fractions original denominator (bottom) into the common denominator, the number of times it divides it is then used to multiply the numerator (top)). Finally perform all the addition and subtraction operations between these equivalent numerators (tops) to give a result which should be simplified if possible.

Multiplication and Division of more than two fractions.

As far as using the Fraction Calculator is concerned you process multiplication's and divisions as a series of multiplication's and divisions. That is take the first two fractions and perform the required operation then move the result to fraction 1 and enter the next fraction into fraction 2 and perform the next operation. This is then repeated until the sequence is completed.

If you are working it out on paper then first convert all the divisions to multiplication's i.e. turn the fraction following the division operation upside down and this makes the division operation a multiplication. Now find all the factors of all the numerators (tops) and all the denominators (bottoms). Cancel out all common factors between the numerators (tops) and denominators (bottoms), when there are no common factors left multiply out all the remaining numerator (top) factors and all the reaming denominator (bottom) factors. The resulting fraction is the answer.

Mixture of Additions and Subtractions with Multiplication's and Divisions.

Perform all the multiplication's and divisions first rewriting the calculation with only the additions and subtractions left and then when no more multiplication's or divisions left do the additions and subtractions.

For example:

Calculations With Brackets.

Dealing with brackets is very simple.

First if you are given a calculation that has just one pair of brackets then whatever is inside the brackets must be done first. Treat everything inside the brackets as a  separate calculation and do this first. Now  rewrite the fraction replacing the bracketed part of the fraction with result you have just calculated, this is now a fraction calculation with no brackets which has been explained above.

Secondly if there are more than one pair of bracket, we need to remove the brackets a pair at a time. First find a pair of brackets (an opening bracket followed by a closing bracket with no brackets between them. Now perform the calculation between the brackets and rewrite the whole calculation with this pair of brackets and its contents replaced by the result of the calculation of its contents. Repeat this process for another set of brackets and another until there are no brackets. Once all the brackets are gone you will have a fraction calculation with no brackets. Which pair of brackets you do first does not matter (other than there being no further brackets within them).

For example:


One final note on brackets

Sometimes you get something like this:

There is no operation between the first fraction and the bracket when this occurs it mean multiply, i.e. it means this:

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