Question

Use positive or negative integers to fill in the blanks so that the product is -36. Justify your answer.

-3 * 12 = -36

Answer 1

To get a product of -36 using the integer -3, the other number must be 12 because multiplying a negative by a positive number results in a negative product, as per the rules for multiplying integers.

Step-by-step explanation:

To determine what integers to use for the multiplication to get a product of -36, we consider the rules of multiplication involving integers. Because the desired product is negative, one integer should be positive and the other should be negative, since multiplying two numbers with opposite signs results in a negative product. Given that one of the numbers in the equation is -3, we need to find a positive number that when multiplied by -3 gives us -36.

The correct positive integer to multiply with -3 to get -36 is 12.

This is because (-3) × 12 = -36.

We have verified that the product of a negative and a positive integer is indeed a negative number, which is consistent with the rules of multiplication for integers.