Quandaries and Queries


When I was taught to divide a fraction, I was told to multiply the reciprocal. Many times I find I can just divide the fraction, and it saves all the simplifying after.

For example, 4/6 x 9/14 divided by 2/4

I would say 4x9divided by 2=18 over 6x14divided by 4 =21, so the answer is 18/21 but if I multiply the reciprocal, I would end up with 4x9x4 over 6x14x2 which equals 144/168.

So, why are we taught to do it this way? Is it necessary?

Thanks for your time and help.

I'm a high school student, but I guess this is an elementary question.



Hi Angie,

You are completely correct. It is amazing that you noticed it at a young age. It was not until I became a teacher, when some young student asked me to explain division by fractions. I then realized that I had never in my life divided fractions the way I had been taught. I always simplified them first into a single fraction as you explained. It's not just easier to do it your way, but it makes sense -- you are really clearing the fraction 2/4 from the bottom by multiplying top and bottom by 4, and dividing top and bottom by 2.


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