Question

Please help.

Maria takes the absolute value of each number in a set of numbers. She notes that for each number, the original number is less than urs absolute value.

Select all the numbers that could be in Maria’s set of original numbers.

Answer 1

-4

-2/3

--> First and second choices

Explanation:

Absolute Value Definition

The absolute value of any number x represented by |x| is defined as follows:

|x| = x if x≥0

|x| = -x if x< 0

In other words, the absolute value of any number is always the positive value of that number

With this definition, let's write the absolute values of the numbers in the given answer choices and see if that given value is less than the absolute value

| - 4 | =-(-4) = 4 ; -4 < 4 So this is a correct choice

| - 2/3 | = + 2/3 ; - 2/3 < 2/3 so this is another correct choice

| 0 | = 0; 0 is NOT less than 0 so not a right choice

| 1/3| = 1/3; absolute and actual values are equal; so NOT less than

| 5 | = 5 so NOT less than

The correct choices are the first two

-4

-2/3

In fact we can generalize by stating that if a number is negative, then that number has to be less than its absolute value