Answer to Question #200053 in Algebra for Phumzile Zondi

Question

A common error that learner's make is to write 3/5 for the fraction of the whole represented here. Why do you think they do this? What activity or strategy would yo use to try to address this misconception?

Answer 1

(1)"Believing that fractions’ numerators and denominators can be treated as separate whole numbers."

 

Students often add or subtract the numerators and denominators of two fractions (e.g., 2/4 + 5/4 = 7/8 or 3/5 – 1/2 = 2/3). These students fail to recognize that denominators define the size of the fractional part and that numerators represent the number of this part. The fact that this approach is used for multiplication of fractions is another source of confusion.

(2) )Believing that only whole numbers need to be manipulated in computations with fractions greater than one.

 When adding or subtracting mixed numbers, students may ignore the fractional parts and work only with the whole numbers (e.g., 53/5 – 21/7 = 3). These students are either ignoring the part of the problem they do not understand, misunderstanding the meaning of mixed numbers, or assuming that such problems simply have no solution.

Above two are the main errors that are performed by the students. To solve these kind of errors we should teach them the basics of the fraction.They need to understand that

denominators define the size of the fractional part and that numerators represent the number of this part.