### Video Transcript

What property of multiplication
from the following is used in three-fifths times zero is equal to zero? Option (A) associative
property. Option (B) multiplicative identity
property. Option (C) commutative
property. Option (D) zero product
property. Or is it option (E) multiplicative
inverse property?

In this question, we are given an
equation and asked to identify which of five given properties of multiplication is
used in the given equation.

Letβs start by looking at the given
equation. We can see that on the left-hand
side of the equation, we are multiplying a rational number by zero. And we are saying that this is
equal to zero. We can then recall that this is a
direct application of the zero product property. In general, this property states
that multiplying any rational number by zero gives zero. Hence, the answer to this question
is option (D), the zero product property.

For due diligence, we can also
recall the other four properties of multiplication.

First, we can recall that the
associative property of the multiplication of rational numbers tells us that we can
evaluate the product of rational numbers in any order. In general, we have that if π and
π and π are rational numbers, then π multiplied by π times π is equal to π
times π multiplied by π.

Second, we can recall that the
multiplicative identity property tells us that multiplying any rational number by
one leaves it unchanged. So, if π is a rational number,
then π times one and one times π are both equal to π.

Third, we can recall that the
commutative property of the multiplication of rational numbers tells us that we can
reorder the product of rational numbers. In general, we have that if π and
π are rational numbers, then π times π is equal to π times π.

Finally, we can recall that the
multiplicative inverse property for rational numbers tells us that all nonzero
rational numbers have a multiplicative inverse. In general, we have that if π and
π are nonzero integers, then π over π times π over π is equal to one.

We can see that none of these
properties other than the zero product property are used in the given equation. So the answer is that only option
(D), the zero product property, is used in the equation three-fifths times zero is
equal to zero.