I have to write a program in which I have two fractions. Each fraction has two variables, numerator and denominator. I have to add, subtract, multiply and divide with these fractions, and in the end the fraction has to be simplified. Can anyone here tell me what algorithm I can use to simplify these fractions? An example is if I have 5/10, in the end I need to show 1/2. I've thought of everything but I can't find a way. Thanks to those who help.
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The easiest way to do this is to use the modulus operator.
Let's say you've got 6/8. So you start with the smaller of 6 or 8 and then use the modulous operator:
6%2
this evaluates to 0 meaning the 6 is evenly divisible by 2. Now check 8 %2. This is also 0 meaning that 8 is evenly divisible by 2. Therefore, create a new fraction (6/2) / (8/2) or 3/4.
Then proceed to reduce 3/4 by trying 3%2 (which is 1 so 3 is not divisble by 2) so your fraction is now simplified.
Try 6/9:
6%2 is 0 so try 9%2 which is 1. Therefore, 2 is not a factor.
Next try:
6%3 is 0 so try 9%3 which is also 0 so 3 is a common factor. Therefore, create a new fraction (6/3) / (9/3) or 2/3.
Just remember that your common factors are between 2 and value of the smaller number minus 1. That means 6 has to be tried using 2 through 5 with the modulus operator. -
From the above you could write your own function which finds the greatest common divisor of the two numbers making up the numerator and denominator
{
if(m<n)swap(m,n ); // make n the smallest of the two
while(n>0)
( long r =m%n;
m=n;
n=r;}
return m; //m is the g.c.d.
}Comment
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