Video: Identifying the Appropriate Multiplication Property given a Certain Multiplication Equation

Which property of multiplication is used in −4/9 × (−9/4) = 1?


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.

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