If pq = 23 and uv = 1/23, find the value of u*q*v*p. Explain which properties you used

Remember that multiplication is commutative, which means the order in which we multiply things doesn't matter.

The order of u * q * v * p (which we can abbreviate uqvp) isn't as important as the fact that we're multiplying all four values together. We could just as easily rewrite the expression as pquv, and it'd represent the same value.

To find this value then, we can simply multiply pq and uv - the values we already know - together.

If we start with the expression pq = 23, we can multiply either side by uv (taking advantage of the multiplication property of equality) to get

pquv = 23uv

And since we know that uv = 1/23, we can use the substitution property of equality to replace the uv on the right side with 1/23:

pquv = 23 (1/23)

The inverse property of multiplication states that any number multiplied by its inverse (its reciprocal) gives us 1. 23 and 1/23 are reciprocals of each other, so 23 (1/23) = 1, which means

pquv = 1

Finally, going back to the second paragraph, we can use the commutative property of multiplication to rearrange the left side of the equation, giving us the solution

uqvp = 1