Micah and Joel each have a set of five rational numbers. Although their sets are not the same, their sets of numbers have absolute values that are the same. Show an example of what Micah and Joel could have for numbers. Give the sets in order and the absolute values in order.

Enrichment Extension: Show an example where Micah and Joel both have positive and negative numbers.

[tex]A = \left\{\dfrac{1}{2},\dfrac{1}{3},-\dfrac{1}{4}, \dfrac{1}{5},-\dfrac{1}{6}\right\},\quad B = \left\{-\dfrac{1}{2},-\dfrac{1}{3},\dfrac{1}{4}, -\dfrac{1}{5},\dfrac{1}{6}\right\}[/tex]

So that every element of A is different from every element of B, but if you apply the absolute values all numbers become positive, and the two sets become identical.

keshavgandhi04 keshavgandhi04 · Answer 2 · 2022-01-29T14:04:39+01:00

Micah and Joel each have a set of five rational numbers,their sets are not the same, their sets of numbers have absolute values that are the same. We have to show an example of what Micah and Joel could have for numbers the absolute values in order will be 1, 2, 3, 4, 5

According to the question, we will arrange the numbers in ascending(from lower value to higher value) or descending order (from lower value to higher value).

Order of the positive numbers = order of the absolute values and their
Order of the negative numbers = opposite to the order absolute values.

We can see if Micah is having numbers 1, 2, 3, 4, 5, then the order of their absolute values of the numbers will be 1, 2, 3, 4, 5.

Similarly,

Joe is having numbers -5, -4, -3, -2, -1 then the order of the absolute value will be also 1, 2, 3, 4, 5.

And if Micah have the numbers -5, -3, -1, 2, 4, then the absolute values of these numbers will be 1, 2, 3, 4, 5.

Similarly ,

Joe is having numbers -4, -2, 1, 3, 5 then their order of the absolute values is also 1, 2, 3, 4, 5.

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