Hi, I am a planning on becomming a teacher and i am asked to find out what is wrong with these probelms and how i would go about showing a student what is wrong with them!! Math is my weak subject so if you can please help! Thanks! Cindy

Error in patterns:
13/35=1/5; 27/73=2/3; 16/64=1/4

4/5+2/3=6/8; 2/5+3/4=5/9; 7/8+1/3=8/11

2/3*3=6/9; 1/4*6=6/24; 4/5*2=8/10

Hi Cindy,

In the first set of examples

13/35=1/5; 27/73=2/3; 16/64=1/4

the student is "cancelling" the common digit found in the numerator and denominator in reducing the expression.

You must explain to a student that in order to do any cancelation between the numerator and denominator, it must be a common factor, not a common digit. That is, if both numerator and denominator can be divided by the same number, you may divide the numerator and the denominator by that number to reduce the fraction to simplest form.

In the second set of examples

4/5+2/3=6/8; 2/5+3/4=5/9; 7/8+1/3=8/11

the student is adding the fractions by adding the numerators together and the denominators together.

In order to add fractions, they must have a common denominator. Once fractions have a common denominator, they may be added by adding the numerators while leaving the denominator the same. The easiest way to find a common denominator for two fractions is to multiply the two denominators together.

In the last set of examples

2/3*3=6/9; 1/4*6=6/24; 4/5*2=8/10

the student is multiplying both the numerator and denominator by the whole number rather than just the numerator.

Any whole number can be written as a rational expression (fraction) with a denominator of 1. When multiplying fractions you multiply numerator by numerator and denominator by denominator. Since the denominator of the whole number is 1, the denominator of the product will be the same as the denominator of the fraction and the whole number is only multiplied with the numerator of the fraction.

Hope this helps,


I want to add something to Leeanne's answer. When you do a problem I think it is important to ask yourself if the answer makes sense. For the "problem" 4/5+2/3=6/8 think of this situation. You are cleaning up after a pizza party. One pizza was cut into fifths and there are four pieces remaining. Another was cut into thirds and there are two pieces remaining. Thus, altogether you have four fifths plus two thirds of a pizza remaining. This is certainly more than one pizza! On the other hand six eights of a pizza is less than one so 4/5+2/3 can't possibly be 6/8.

In a similar way 2/3*3 can't be less than one. Three times two thirds of a pizza is more than one pizza.

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