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Mrs. Shen writes the expression |-5| + |3| on the board. Show or explain why the sum |-5| + |3| is the distance between -5 and 3 on a number line.

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27spidersmart

(Short) Answer:

Because the absolute value of a number is the distance between the number and the origin of the line.

Step-by-step explanation:

Mrs. Shen writes the expression |-5| + |3| on the board. Show or explain why the sum |-5| + |3| is the distance between -5 and 3 on a number line.

The definition of absolute value:

For x = 0 or x > 0, | x | = x

For x < 0, | x | = - x

Because the absolute value of a number is the distance between the number and the origin of the line. (0, 0) -5's distance to the line is 5 and 3's distance to the origin of the line is 3. The sum of 5 and 3 is 8. Same with solving the absolute value, |-5| + |3| we get 5 + 3 which is 8 too.

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