To solve the task of ordering the given expressions from least value to greatest value, we will first evaluate each of them. Here are the steps for solving this:
### Step 1: Evaluate each expression
1. Expression 1: [tex]\( -4.8 \times 3.2 \)[/tex]
[tex]\[
-4.8 \times 3.2 = -15.36
\][/tex]
2. Expression 2: [tex]\( 2 \frac{1}{4} + \left( -1 \frac{2}{5} \right) \)[/tex]
Convert the mixed numbers to improper fractions:
[tex]\[
2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{9}{4}
\][/tex]
[tex]\[
-1 \frac{2}{5} = -1 - \frac{2}{5} = -\frac{7}{5}
\][/tex]
Combine these values:
[tex]\[
\frac{9}{4} + \left( -\frac{7}{5} \right)
\][/tex]
In order to add these fractions, they need a common denominator.
[tex]\[
\frac{9}{4} = \frac{45}{20}, \quad -\frac{7}{5} = -\frac{28}{20}
\][/tex]
Now add them:
[tex]\[
\frac{45}{20} - \frac{28}{20} = \frac{17}{20} = 0.85
\][/tex]
3. Expression 3: [tex]\( \frac{4.32}{3} \)[/tex]
[tex]\[
\frac{4.32}{3} = 1.44
\][/tex]
4. Expression 4: [tex]\( -2 \frac{3}{5} - \left( -1 \frac{2}{5} \right) \)[/tex]
Convert the mixed numbers to improper fractions:
[tex]\[
-2 \frac{3}{5} = -2 - \frac{3}{5} = -\frac{13}{5}
\][/tex]
[tex]\[
-1 \frac{2}{5} = -1 - \frac{2}{5} = -\frac{7}{5}
\][/tex]
Rearrange the expression:
[tex]\[
-\frac{13}{5} - \left( -(-\frac{7}{5}) \right) = -\frac{13}{5} + \frac{7}{5}
\][/tex]
Combine these values:
[tex]\[
-\frac{13}{5} + \frac{7}{5} = -\frac{6}{5} = -1.20
\][/tex]
### Step 2: Order the expressions from least value to greatest value
We have computed the values as follows:
1. Expression 1: [tex]\( -15.36 \)[/tex]
2. Expression 2: [tex]\( 0.85 \)[/tex]
3. Expression 3: [tex]\( 1.44 \)[/tex]
4. Expression 4: [tex]\( -1.20 \)[/tex]
Now we will arrange these values from least to greatest:
[tex]\[
-15.36 < -1.20 < 0.85 < 1.44
\][/tex]
Thus, the correct order of the expressions is:
[tex]\[
-4.8 \times 3.2 \quad < -2 \frac{3}{5} - \left( -1 \frac{2}{5} \right) \quad < 2 \frac{1}{4} + \left( -1 \frac{2}{5} \right) \quad < \frac{4.32}{3}
\][/tex]
So, the ordered expressions from least to greatest value are:
[tex]$-4.8 \times 3.2$[/tex] [tex]\(<\)[/tex] [tex]$-2 \frac{3}{5} -\left(-1 \frac{2}{5}\right)$[/tex] [tex]\(<\)[/tex] [tex]$2 \frac{1}{4}+\left(-1 \frac{2}{5}\right)$[/tex] [tex]\(<\)[/tex] [tex]$\frac{4.32}{3}$[/tex]
