Which answer choice describing 10:15 is true?

The equation 10:15=10⋅5 is true because multiplication and division are inverse operations.

The equation 10:15=15⋅10 is true because of the commutative property of multiplication.

The equation 10:15=15:10 is true because of the commutative property of division.

The equation 10:15=110⋅15 is true because of inverse division operations.

Looking at the choices, I say all of them are incorrect. But the closest answer would be the second one, but only if a typo error is corrected. Let's investigate each choice.

The equation 10:15=10⋅5 is true because multiplication and division are inverse operations.

Multiplication and division are inverse operations, but the application done here is incorrect. The correct application should be: 10/15 is 2/3. Now if you multiple 2.3 to 15, the answer is 10. The inverse relationship is not an equality. 10/15 is 2/3 and 10*5 is 50. Clearly, they're not equal.

The equation 10:15=15⋅10 is true because of the commutative property of multiplication.

I think this is the answer if it were 10 * 15 = 15*10. That is a proper application of the commutative property of multiplication, which states that the order does not matter when multiplying numbers.

The equation 10:15=15:10 is true because of the commutative property of division.

There is no such thing as commutative property of division. If it were, there will be no proper fractions.

The equation 10:15=110⋅15 is true because of inverse division operations.

110 * 15 is 1650 while 10/15 = 0.6667. These are not equal.