Video Transcript
Which property of multiplication is
used in the equation negative four-ninths times negative nine over four equals
one?
Let’s identify what’s actually
happening in this multiplication problem. We take a rational number, negative
four-ninths, and then we multiply that by negative nine over four. And so we should ask ourselves,
what’s the relationship between negative four-ninths and negative nine over
four? Well, we know that to find the
reciprocal of a number, we divide one by that number. So, the reciprocal of negative
four-ninths is one divided by negative four-ninths, and that’s equal to negative
nine over four.
Another way to find the reciprocal
of a number in fractional form is to simply switch the numerator and the
denominator. And so, here we’re multiplying a
number by its reciprocal, and we get one. Another word that we have or a
phrase that we have for the word reciprocal is the multiplicative inverse. It’s so called because when we find
the inverse, we essentially undo an operation. And in this case, we multiply it by
something that gives us the result of one. And so, the property of
multiplication that’s used here is the multiplicative inverse property. This says that if we multiply a
rational number by its reciprocal, we’ll get one.
