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# Negative numbers and fractions Would this student also say that 1/2 is equal to 2?

## 5 replies on “Negative numbers and fractions”

LSquaredsays:

Wow–the perceived need to have common denominators in every fraction problem strikes again.

SueHellmansays:

There is an approach to dividing fractions that requires students students use common denominators and then simply divide the numerators to get the answer. This seems to be becoming more popular with some teachers. Unfortunately there doesn’t seem to be a comparable process for multiplication so a student taught this way would likely generalize common denominators everywhere. Also, if a teacher is not aware of this and doesn’t try to find out how the student was taught the process in a previous year, then correcting him/her by saying “common denoms are not used in multiply & divide” flies in the face of what the student was taught before and will be utterly confusing.

Mary OSullivansays:

Just found this site!! Love it!! I’ve been teaching 7th & 8th grade math for over 20 years. Most recently, “IDK” has become an answer more than once 🙂

I think the problem with #4 for this student is it comes after #3.
“lets start by reducing”
“ok now I need a common denominator”
“ok now I can reduce”
“ok I need a common denominator again”
“wow I can reduce again”
eventually multiplied 6 by 5 to get 35.
didn’t multiply the 10’s in the denominator (thinking ‘adding rule’)
reduced by a factor of 5 (fortunately they think 35=6*5 so 35/5=6)
and so the final answer is only off by the factor of 10 in the denominator.

SueHellmansays:

[Looking at #3] This student is trying so hard to remember a process & steps that he/she has failed to register that multiplying and then simplifying a fraction by the same factors does not (in this case) go round in a circle. 3/2 x 5/5 rightly gets to 15/10 but then simplifying 15/10 by cancelling numerator and denominator by 5 does not get him/her back to the original starting place. The same problem occurs with the 1/5. This student has turned 3/2 into 3/5 and 1/5 into ½. The poor kid must have been desperate by the time this question was left behind! This is when numbers have no relation to quantities that could be meaningful.