Question

put in order from least to greatest. -6, |-6|, 1.5, -1\frac{1}{2} \
-6, -1\frac{1}{2}, 1.5, |-6| \
|-6|, 1.5, -1\frac{1}{2}, -6 \
|-6|, -6, -1\frac{1}{2}, 1.5 \
-1\frac{1}{2}, |-6|, 1.5, -6

Explanation:

Step1: Simplify absolute value and mixed number

First, simplify \(|-6|\) which is \(6\), and convert \(-1\frac{1}{2}\) to decimal, \(-1\frac{1}{2}=-1.5\). So the numbers are \(-6\), \(6\), \(1.5\), \(-1.5\).

Step2: Compare negative numbers

For negative numbers, the larger the absolute value, the smaller the number. \(|-6| = 6\) and \(|-1.5| = 1.5\), so \(-6 < -1.5\) (since \(-6\) has a larger absolute value).

Step3: Compare positive numbers

Positive numbers are \(1.5\) and \(6\), and \(1.5 < 6\).

Step4: Order all numbers

Combining the comparisons, the order from least to greatest is \(-6\), \(-1\frac{1}{2}\), \(1.5\), \(|-6|\).

Answer:

\(-6, -1\frac{1}{2}, 1.5, |-6|\) (corresponding to the first option: \(-6, -1\frac{1}{2}, 1.5, |-6|\))