use a commutative law to find an equivalent expression pq. an equivalent expression pq is= subtract the following -9(-3)=
The Correct Answer and Explanation is:
To apply the commutative law to simplify the expression pqpqpq, we first need to define what the commutative property is. The commutative property states that the order in which you add or multiply numbers does not change the result. Specifically:
- Commutative property of multiplication: a×b=b×aa \times b = b \times aa×b=b×a
Given this, let’s look at the expression pqpqpq. According to the commutative property, we can rewrite this as qpqpqp, since multiplication is commutative. Therefore:pq=qppq = qppq=qp
Now, let’s move on to the second part of the question: simplifying −9(−3)-9(-3)−9(−3).
Step 1: Understanding multiplication of negative numbers
When multiplying two negative numbers, the result will be positive. This is because a negative times a negative equals a positive. Therefore:−9×−3=27-9 \times -3 = 27−9×−3=27
Step 2: Detailed explanation
Multiplying negative numbers works because of the rules for signs in arithmetic:
- When multiplying two positive numbers, the result is positive.
- When multiplying a positive and a negative number, the result is negative.
- When multiplying two negative numbers, the result is positive.
In this case, we are multiplying two negative numbers: −9-9−9 and −3-3−3. According to the rule above, the result will be positive. The product is 272727.
Final answer:
−9(−3)=27-9(-3) = 27−9(−3)=27
By applying the commutative property to the expression pqpqpq, we know that it can be written as qpqpqp, but the numerical simplification of −9(−3)-9(-3)−9(−3) is 27.
