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ELEN [110]
3 years ago
6

Which product is positive?

Mathematics
1 answer:
Natalija [7]3 years ago
4 0

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:

<em>If the negative sign is in even number of times then the product is positive.</em>

<em>If the negative sign is in odd number of times then the product is negative.</em>

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.

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