Скачать или смотреть Reciprocals of Fractions | Multiplying and Dividing Fractions, Multiplicative Inverses

What is the reciprocal of a fraction and why is it important? The reciprocal of a fraction a/b is the number we must multiply a/b by in order to get 1. The reciprocal can be found by "flipping the fraction around", simply swapping the numerator and denominator. Thus, the reciprocal of a/b is b/a. Multiplying these fractions together gives us 1, that is (a/b)*(b/a) = 1.

We need to be careful, however, because if our fraction has a 0 in the numerator, it does not have a reciprocal. If our fraction has a 0 in the numerator, then it is equal to 0. What can we multiply 0 by in order to get 1? There is no such number, and so there is also no reciprocal. If our fraction had a 0 in the denominator to begin with, then it was undefined to begin with, so we should steer clear of it!

If we were to try to find the reciprocal for a fraction of the form 0/b, we might try to flip it around, giving b/0, which is an undefined expression: we cannot have 0 in the denominator of a fraction.

Reciprocals are also handy because if we divide two fractions, say a/b divided by c/d, this is equal to a/b times the reciprocal of c/d, which is a/b times d/c. By hand, multiplying is usually easier than dividing.


I hope you find this video helpful, and be sure to ask any questions down in the comments!

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