The lengths of three sides of a triangle are in the ratio 3: 4: 5. the perimeter of the triangle is 156 centimeters. what is the difference in length between the longest and shortest sides?

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this

so, converting firstly the mixed fractions to improper fractions and then "adding".