Lesson PROOF that a number multiplied by its reciprocal is 1

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Why is a number, multiplied by its reciprocal, always equal to one? here's proof.

Suppose that you have a fraction a%2Fb

. Its reciprocal is b%2Fa

. The product of the fraction and its reciprocal is %28a%2Fb%29%2A%28b%2Fa%29

. That's equal to a%2Ab%2Fb%2Fa

. We know from the commutative property (discussed on this site in the pre-algebra section) that b*a is the same as a*b. So, replace b*a with a*b on the bottom of the fraction: a%2Ab%2Fb%2Fa+=+a%2Ab%2Fa%2Fb

. The last fraction clearly has the same numerator as denominator (just like 5%2F5

, for example). A fraction with the same numerator as denominator is equal to one.

So, we just proved that multiplying a number by its reciprocal always gives 1.

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