Sure, let's go through the details of solving this step-by-step.
### Step 1: Simplify the Fractions
First, let's simplify the fractions given in the expressions.
- The fraction [tex]\(-\frac{15}{5}\)[/tex] simplifies to [tex]\(-3\)[/tex] because [tex]\( \frac{15}{5} = 3 \)[/tex] and applying the minus sign gives [tex]\(-3\)[/tex].
- The fraction [tex]\(\frac{3}{5}\)[/tex] stays the same since it is already in its simplest form.
- The fraction [tex]\(-\frac{18}{5}\)[/tex] stays the same as well as it is also in its simplest form.
### Step 2: Perform the Divisions
We need to assess the result of the division of the dividends by the divisors:
#### Expression 1: [tex]\(-\frac{15}{5} - \frac{3}{5}\)[/tex]
1. Simplify [tex]\(-\frac{15}{5}\)[/tex] to get [tex]\(-3\)[/tex].
2. The fraction [tex]\(-\frac{3}{5}\)[/tex] remains as [tex]\(-\frac{3}{5}\)[/tex].
To divide [tex]\(-3\)[/tex] by [tex]\(\left(-\frac{3}{5}\right)\)[/tex]:
[tex]\[
-3 \div \left(-\frac{3}{5}\right)
\][/tex]
To divide by a fraction, we multiply by its reciprocal. The reciprocal of [tex]\(-\frac{3}{5}\)[/tex] is [tex]\(-\frac{5}{3}\)[/tex]:
[tex]\[
-3 \times \left(-\frac{5}{3}\right)
\][/tex]
Multiplying these terms, we get:
[tex]\[
-3 \times -\frac{5}{3} = \frac{15}{3} = 5.0
\][/tex]
So, the result of this division is [tex]\(5.0\)[/tex].
#### Expression 2: [tex]\(-\frac{15}{5} + \frac{3}{5}\)[/tex]
1. Simplify [tex]\(-\frac{15}{5}\)[/tex] to get [tex]\(-3\)[/tex].
2. The fraction [tex]\(\frac{3}{5}\)[/tex] remains as [tex]\(\frac{3}{5}\)[/tex].
Adding [tex]\(-3\)[/tex] and [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[
-3 + \frac{3}{5}
\][/tex]
To add these, convert [tex]\(-3\)[/tex] to a fraction with a common denominator:
[tex]\[
-3 = \frac{-3 \times 5}{5} = \frac{-15}{5}
\][/tex]
Now, add the fractions:
[tex]\[
\frac{-15}{5} + \frac{3}{5} = \frac{-15 + 3}{5} = \frac{-12}{5} = -2.4
\][/tex]
So, the result of this addition is [tex]\(-2.4\)[/tex].
### Step 3: Third Expression [tex]\(-\frac{18}{5}\)[/tex]
This fraction is already in simplified form, so the result remains:
[tex]\[
-\frac{18}{5} = -3.6
\][/tex]
### Step 4: Provided Additional Numbers
The numbers 9 and 12 are given and, based on the context, they appear to be results for specific parts of another question or steps provided:
[tex]\[
\text{Result 1: } 9
\][/tex]
[tex]\[
\text{Result 2: } 12
\][/tex]
### Final Results
After performing the operations and verifying the calculations, we have the following results:
- The division result of [tex]\(-\frac{15}{5}\)[/tex] by [tex]\(-\frac{3}{5}\)[/tex] is [tex]\(5.0\)[/tex].
- The addition result of [tex]\(-\frac{15}{5}\)[/tex] and [tex]\(\frac{3}{5}\)[/tex] is [tex]\(-2.4\)[/tex].
- The simplified fraction [tex]\(-\frac{18}{5}\)[/tex] remains [tex]\(-3.6\)[/tex].
- The given results 9 and 12.
Thus, the final set of results is:
[tex]\[
(5.0, -2.4, -3.6, 9, 12)
\][/tex]
