Question

given the rule x/n, describe the values of n for which the output value will be greater the the input value. justify your response.

Answer 1

If we are dealing with only positive numbers: If n is less than 1 but greater than 0, x will get larger.

For example: 10 / 0.2 = 20

Dividing by decimals makes the number in the numerator get larger.

Answer 2

We have the relation X/n

we want to know the value of n for which the output value will be greater than the input, we can writhe this as:

y = x/n

where y is the output and x is the input.

we have that when we multiply a number A for a number greater than 1, we are increasing the value.

when we multiply A by a number smaller than 1 and greater than 0, we are decreasing the value of A.

Is the inverse for the divisions:

This is because supposing that n is smaller than 1, then we can write n = p/q, where q is greater than p.

then we will have:

y = x/n = x/(p/q) = (q*x)/p

so we are multiplying x by a number q, and then dividing the result by a number p that is smaller than q, so overall we have an increase in the value.

So the values of n for which the output value is greater than the input value are the range 0 < n < 1