Let's face it. Math tutor does not need a license to teach (at least in North America). So anyone with some kind of degree can claim to be a well qualified math tutor and the consequence, sometimes, is poor kids suffered since they can not judge if they have been taught in the correct way or not. I have written other articles to point out some problems on how some math tutors have taught math concepts or math algorithms in a very ineffective way. This article will point out a problem that many math tutors think there is a fast tip to add 2 fractions when the denominators are different but potentially this fast tip method could cause problems when kids go to high school.
The question is to add 7/12 and 2/3 and my grade 6 student told me that his tutor taught him to just multiply 12 and 3 to get common multiple 36 and then add 3 x 7 and 2 x 12 as the numerator. So the answer will be 45/36. To further reduce the denominator and numerator to get the simplified answer. On the surface the child may think he has found a great tutor since it is easy to add 2 fractions without going through the concept of finding the lowest common multiple, but doing a bit more research, I find out that this method really does children no good but probably will even harm them in their future math learning. Quickly comes to my mind, the reasons are as follows.
What happens when the children need to add 3 or 4 fractions? The product of 3 or 4 numbers will be very large.
The concept the children learn at elementary school math should be able to transfer to their high school math then this simple approach of multiplication method to attempt to get common denominator will present problems. For example, 1/(x-2) + 1/(x-2)(x-3), the correct way will be to find the LCD as (x-2)(x-3) and then add 2 fractions. But use the multiplication method the children were taught in elementary school, then the common denominator becomes (x-2)^2 (x-3) and an easy fraction addition becomes a complicated polynomial expansion on the numerator.
The correct way of teaching adding 2 fractions with different denominators is still to teach children to use lowest common denominator, not multiplying 2 denominators to get an inflated common multiple.
It is important for parents to hire a math tutor who knows how to teach the correct way.
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