Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 23, 2024

Simplify the absolute value of the negative fraction -6/5.

STEP 1

Assumptions
1. We need to simplify the expression $-\left|-\frac{6}{5}\right|$ .
2. The vertical bars denote the absolute value, which is the non-negative value of the number inside.

STEP 2

First, we need to evaluate the absolute value of $-\frac{6}{5}$ .
$\left|-\frac{6}{5}\right|$

STEP 3

The absolute value of a number is its distance from zero on the number line, regardless of direction. Therefore, the absolute value of $-\frac{6}{5}$ is the same as the absolute value of $\frac{6}{5}$ .
$\left|-\frac{6}{5}\right| = \left|\frac{6}{5}\right|$

STEP 4

Since $\frac{6}{5}$ is a positive number, its absolute value is simply itself.
$\left|\frac{6}{5}\right| = \frac{6}{5}$

STEP 5

Now, we apply the negative sign in front of the absolute value to the result from STEP_4.
$-\left|\frac{6}{5}\right| = -\frac{6}{5}$

STEP 6

The simplified form of the original expression is thus the negative of the fraction $\frac{6}{5}$ .
$-\left|-\frac{6}{5}\right| = -\frac{6}{5}$
The expression simplifies to $-\frac{6}{5}$ .

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