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 2/4I 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. 

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. Chris 

