Question

Which product is negative? (Negative StartFraction 3 over 8 EndFraction) (Negative StartFraction 5 over 7 EndFraction) (one-fourth) (StartFraction 3 over 8 EndFraction) (Negative StartFraction 5 over 7 EndFraction) (Negative one-fourth) (StartFraction 3 over 8 EndFraction) (StartFraction 5 over 7 EndFraction) (one-fourth) (Negative StartFraction 3 over 8 EndFraction) (Negative StartFraction 5 over 7 EndFraction) (negative one-fourth)

Answer 1

`(D)\left(-\frac38\right)\left(-\frac57\right)\left(-\frac14\right)`

Explanation:

The given options are:

`(A)\left(-\frac38\right)\left(-\frac57\right)\left(\frac14\right)\\(B)\left(\frac38\right)\left(-\frac57\right)\left(-\frac14\right)\\(C)\left(\frac38\right)\left(\frac57\right)\left(\frac14\right)\\(D)\left(-\frac38\right)\left(-\frac57\right)\left(-\frac14\right)`

The key to determining which product is negative is to understand the rule of sign multiplication.

Now:

• The product of even negative terms is positive
• The product of odd negative terms is negative.
• The product of positive will always be positive.

In Options A and B, the number of negative signs is even, therefore our result is positive.

In option C, all the terms are positive, therefore our result will be positive.

In Option D, the number of negative signs is odd, therefore our result is negative.