Write each group of numbers from greatest to least.

(f) [tex]-\frac{5}{4} + | -1 |, \left| -\frac{2}{3} \right|, -\left| \frac{1}{2} \right|[/tex]

A. [tex]-\frac{5}{4} + | -1 | ; \left| -\frac{2}{3} \right| ; -\left| \frac{1}{2} \right|[/tex]
B. [tex]-\frac{5}{4} + | -1 | ; \left| \frac{1}{2} \right| ; \left| -\frac{2}{3} \right|[/tex]
C. [tex]\left| -\frac{2}{3} \right| ; -\left| \frac{1}{2} \right| ; -\frac{5}{4} + | -1 |[/tex]
D. [tex]\left| -\frac{2}{3} \right| ; -\frac{5}{4} + | -1 | ; -\left| \frac{1}{2} \right|[/tex]
E. [tex]-\left| \frac{1}{2} \right| ; -\frac{5}{4} + | -1 | ; \left| -\frac{2}{3} \right|[/tex]

Answer: (A)



Answer :

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]