why does multiplying a fraction e.g. enumerator/divisor with divisor/enumerator give 1?I just found out that if you want to get 1 with the fraction: 5 2 Then you multiply it with: 2 5 Does anyone have a good way to think about this?

Question

why does multiplying a fraction e.g. enumerator/divisor with divisor/enumerator give 1?I just found out that if you want to get 1 with the fraction:      5    2  Then you multiply it with:      2    5  Does anyone have a good way to think about this?

Jonathan Bailey · Accepted Answer

This is called The Inverse Property of Multiplication. Take   x, then  x  ⋅      1    x    =  1In your case of   x  =      5    2        5    2    ⋅      1          5      2        =      5    2    ⋅      2    5    =  1

Corinne Woods · Accepted Answer

Even before defining the rational numbers, one usually learns the &#039;prime factor cancellation&#039; game, or how to divide without really trying.For example, if you want apply Euclid&#039;s algorithm to   28 and   16, you can put   28 &#039;on top&#039; and   16 on bottom, writing      28    16    =                    2        2                  7              2      4        =      7          2      2      and then you can say that   16 &#039;goes into&#039;   28 one and three-quarters times.So, we have something that we can call the &#039;numerator/denominator&#039; game. When you create the rational numbers, you hope that it would be helpful to keep this fractional notation. And indeed, it is very useful. If   n is a nonzero number, the multiplicative inverse       n          −      1       can be expressed as       1    n   and you can continue playing the &#039;numerator/denominator&#039; game in new ways.The multiplication of fractional expressions is a blast (you can stick the prime factorizations together), but to add them you need a common denominator (no big deal).For your question, just remember how much fun it is to cancel common terms in the numerator and denominator:      5    2    ∗      2    5    =            5            2              2            5        =            2            5              2            5         (cancel numerator factors /with denominator factors)   =  1

why does multiplying a fraction e.g. enumerator/divisor with divisor/enumerator give 1? I just found out that if you want to get 1 with the fraction: 5/2 Then you multiply it with: 2/5 Does anyone have a good way to think about this?

Open question

Answer & Explanation

New Questions in Pre-Algebra