Question

help please




Jenna multiplied four numbers together and then divided by -2. The result was a positive value.

Which of the following statements MUST be true?



a.None of the factors were negative.

b.All of the factors were negative.

c.An odd number of factors were negative.

d.An even number of factors were negative.

Answer 1

Rules for multiplying and dividing by negatives:
When you multiply a negative times a negative you get a positive
when you multiply a negative times a positive you get a negative
when you divide a negative by a negative you get a positive
when you divide a negative by a positive you get a negative.

So we know she is dividing by -2 and gets a positive value. This means that she has to be dividing by another negative number from the rules.

So if you multiply two positive numbers you will get a positive back
If you multiply two negative numbers you will get a negative back

These two rules make it so we know A and B are not the correct answer

if we have an even number of factors that are negative we will end up with a negative times a negative which gives us a positive so we can rule out D.

If we have an odd number of factors that are negative, you will have negative times a negative times a negative times a positive. Negative times negative will give you positive. But you have a third negative you are multiplying by so you get another negative number. Then since a negative times a positive is negative you will end up with a negative number.

Since we were looking for a negative number divided by -2 to get a positive number, c is our only option.