Question Video: Identifying the Correct Property of the Multiplication of Rational Numbers Mathematics • 7th Grade

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.

Let’s 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 𝑎 and 𝑏 and 𝑐 are rational numbers, then 𝑎 multiplied by 𝑏 times 𝑐 is equal to 𝑎 times 𝑏 multiplied by 𝑐.

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

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 𝑎 and 𝑏 are rational numbers, then 𝑎 times 𝑏 is equal to 𝑏 times 𝑎.

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 𝑎 and 𝑏 are nonzero integers, then 𝑎 over 𝑏 times 𝑏 over 𝑎 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.