Question

Julia used absolute value to find the distance between 0 and 6 on a number line. She then wrote a similar statement to represent the distance between 0 and −6. Below is her work. Is it correct? Explain.

|6| = 6 and |−6| = −6

Answer 1

Absolute value function.

Explanation:

• The absolute value of a number helps us to calculate the distance between a number and zero, provided the direction does not play an important role.

• The absolute value of a number can never be negative since it is the value of distance.

• The absolute value function is defined as:

`\mid a \mid = a, a > 0\\~~~~~ = -a, a < 0`

So, it is correct to write the statement that distance between 0 and 6 is equal to distance between 0 and -6.

`\mid 6 \mid = 6\\\mid -6 \mid = -(-6) = 6`