To determine the order of the given expressions from greatest to least, let's first evaluate each expression.
Step 1: Evaluate [tex]\( -\frac{5}{4} + |-1| \)[/tex]
- [tex]\(-\frac{5}{4}\)[/tex] is [tex]\(-1.25\)[/tex].
- [tex]\(|-1|\)[/tex] is [tex]\(1\)[/tex].
Thus,
[tex]\[ -\frac{5}{4} + |-1| = -1.25 + 1 = -0.25 \][/tex]
So, the value of [tex]\( -\frac{5}{4} + |-1| \)[/tex] is [tex]\( -0.25 \)[/tex].
Step 2: Evaluate [tex]\( \left|-\frac{2}{3}\right| \)[/tex]
- [tex]\( -\frac{2}{3} \)[/tex] is approximately [tex]\(-0.6667\)[/tex].
- Taking the absolute value gives us [tex]\(\left|-\frac{2}{3}\right| = \frac{2}{3}\)[/tex] which is [tex]\(0.6667\)[/tex].
So, the value of [tex]\(\left|-\frac{2}{3}\right|\)[/tex] is [tex]\(0.6667\)[/tex].
Step 3: Evaluate [tex]\( -\left|\frac{1}{2}\right| \)[/tex]
- [tex]\(\left|\frac{1}{2}\right|\)[/tex] is [tex]\(0.5\)[/tex].
- Taking the negative sign gives us [tex]\(-\left|\frac{1}{2}\right| = -0.5\)[/tex].
So, the value of [tex]\(-\left|\frac{1}{2}\right|\)[/tex] is [tex]\(-0.5\)[/tex].
Now, we have the values of the expressions:
1. [tex]\( -\frac{5}{4} + |-1| = -0.25 \)[/tex]
2. [tex]\( \left|-\frac{2}{3}\right| = 0.6667 \)[/tex]
3. [tex]\( -\left|\frac{1}{2}\right| = -0.5 \)[/tex]
Step 4: Sort these values from greatest to least:
- The greatest value is [tex]\(0.6667\)[/tex].
- Next, [tex]\(-0.25\)[/tex].
- The least value is [tex]\(-0.5\)[/tex].
So, the expressions from greatest to least are:
1. [tex]\( \left|-\frac{2}{3}\right| = 0.6667 \)[/tex]
2. [tex]\( -\frac{5}{4} + |-1| = -0.25 \)[/tex]
3. [tex]\( -\left|\frac{1}{2}\right| = -0.5 \)[/tex]
Thus, the correct order is:
[tex]\[ \left|-\frac{2}{3}\right| ; -\frac{5}{4} + |-1| ; -\left|\frac{1}{2}\right| \][/tex]
So, the correct answer is:
C. [tex]\(\left|-\frac{2}{3}\right| ;-\left|\frac{1}{2}\right| ;-\frac{5}{4}+|-1| \)[/tex]
