Question

Which product is positive?

Answer 1

Option D:

$\left(-\frac{2}{5}\right)\left(-\frac{8}{9}\right)\left(\frac{1}{3}\right)\left(\frac{2}{7}\right)$ is positive product.

Solution:

If the negative sign is in even number of times then the product is positive.

If the negative sign is in odd number of times then the product is negative.

To find which product is positive:

Option A:

$\left(\frac{2}{5}\right)\left(-\frac{8}{9}\right)\left(-\frac{1}{3}\right)\left(-\frac{2}{7}\right)$

Here, number of negative signs = 3

3 is an odd number.

So, the product is negative.

Option B:

$\left(-\frac{2}{5}\right)\left(\frac{8}{9}\right)\left(-\frac{1}{3}\right)\left(-\frac{2}{7}\right)$

Here, number of negative signs = 3

3 is an odd number.

So, the product is negative.

Option C:

$\left(\frac{2}{5}\right)\left(\frac{8}{9}\right)\left(\frac{1}{3}\right)\left(-\frac{2}{7}\right)$

Here, number of negative sign = 1

1 is an odd number.

So, the product is negative.

Option D:

$\left(-\frac{2}{5}\right)\left(-\frac{8}{9}\right)\left(\frac{1}{3}\right)\left(\frac{2}{7}\right)$

Here, number of negative sign = 2

2 is an odd number.

So, the product is positive.

Hence option D is the correct answer.

$\left(-\frac{2}{5}\right)\left(-\frac{8}{9}\right)\left(\frac{1}{3}\right)\left(\frac{2}{7}\right)$ is positive product.