Question

Can someone please explain to me how I got this wrong? The other options in the image are the ones under the questions and I'm rlly confused. Could anyone fully explain it please?

Answer 1

Answer:
`-(p)/(8)`

This is the fraction -p/8

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Step-by-step explanation:

When we divide by -16, we're really multiplying by -1/16. Fractions and division are very similar ideas.

So we can say,

`2p / -16 = 2p * (-1)/(16)\\\\2p / -16 = (2p)/(1) * (-1)/(16)\\\\2p / -16 = (2p(-1))/(1*16)\\\\2p / -16 = (-2p)/(16)\\\\2p / -16 = (-2p)/(2*8)\\\\2p / -16 = -(p)/(8)\\\\`

The second to last step has a pair of '2's divide and cancel out.

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Another way to think of it is to consider

`(a)/(b) / (c)/(d) = (a)/(b) * (d)/(c)`

The flip from division to multiplication has us apply the reciprocal of the second fraction. In this problem, we have a = 2p, b = 1, c = -16 and d = 1. The steps will be very similar if not identical to what is shown above.