Question

Without multiplying, find the sign of the product. Explain your thinking -27 x 14 x (-10) x (-72) x 45

Answer 1

Negative sign (-)

Step-by-step explanation

We want to find the sign of the product of those numbers without carrying out athe multiplication of those numbers.

To do this, we have to arrange the negatve numbers close to one another:

(-27) * (-10) * (-72) * 14 * 45

We know that the product of an even number of negative signs will produce a positive sign and vice versa. That is:

- => negative

- * - => positive (+)

- * - * - => negative (-)

- * - * - * - => positive (+)

If we continue in that pattern, we see that the product of an odd number of negative signs gives a negative sign (-) and the product of an even number of negative signs gives a positive sign (+).

Since there are 3 negative signs, the product will have a negative sign.