Question

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Without multiplying, determine the sign of the product (−247,634)(183,758).

The sign of the product is positive because a negative multiplied by a positive is a positive.
The sign of the product is negative because a negative multiplied by a positive is a negative.
The sign of the product is negative because the first number is negative.
The sign of the product is positive because the second number is positive.

Answer 1

The product would be negative (second option).

Answer 2

We have a negative number multiplied by a positive number, so our answer is going to be negative.

One way to think about this is in terms of debt. If I owe you money for 3 movie tickets worth $10, we can express this numerically as

3 x (-10)

where the negative sign indicates debt. If I owe you 3 debts, that's naturally going to come out to another debt. In this case

3 x (-10) = -30

which means I owe you $30.