Question

Solve and simplify (reduce the fraction into lowest terms).




−

3
15

−

2
5
−
15
3
​
−
5
2
​
=

Answer 1

To solve the expression

\[
-\frac{3}{15} - \frac{2}{5} - \frac{15}{3} - \frac{5}{2},
\]

let's simplify each term first.

### Step 1: Simplifying the fractions

1. **\(-\frac{3}{15}\)**:
\[
-\frac{3}{15} = -\frac{1}{5} \quad (\text{since } 3 \div 3 = 1 \text{ and } 15 \div 3 = 5)
\]

2. **\(-\frac{2}{5}\)**:
\[
-\frac{2}{5} \text{ is already in its simplest form.}
\]

3. **\(-\frac{15}{3}\)**:
\[
-\frac{15}{3} = -5 \quad (\text{since } 15 \div 3 = 5)
\]

4. **\(-\frac{5}{2}\)**:
\[
-\frac{5}{2} \text{ is already in its simplest form.}
\]

### Step 2: Rewrite the expression
Now we can rewrite the entire expression substituting the simplified forms:

\[
-\frac{1}{5} - \frac{2}{5} - 5 - \frac{5}{2}.
\]

### Step 3: Combining \(-\frac{1}{5}\) and \(-\frac{2}{5}\)
\[
-\frac{1}{5} - \frac{2}{5} = -\frac{1 + 2}{5} = -\frac{3}{5}.
\]

Now the expression is:
\[
-\frac{3}{5} - 5 - \frac{5}{2}.
\]

### Step 4: Getting a common denominator
To combine \(-5\) and \(-\frac{5}{2}\), we convert \(-5\) to a fraction with a denominator of 2:
\[
-5 = -\frac{10}{2}.
\]

Now we have:
\[
-\frac{3}{5} - \frac{10}{2} - \frac{5}{2}.
\]

Combining \(-\frac{10}{2}\) and \(-\frac{5}{2}\):
\[
-\frac{10}{2} - \frac{5}{2} = -\frac{10 + 5}{2} = -\frac{15}{2}.
\]

### Step 5: Combine remaining terms
Now we have:
\[
-\frac{3}{5} - \frac{15}{2}.
\]

### Step 6: Getting a common denominator for \(-\frac{3}{5}\) and \(-\frac{15}{2}\)
The common denominator of 5 and 2 is 10. We convert each fraction:

1. **\(-\frac{3}{5}\)**:
\[
-\frac{3}{5} = -\frac{3 \times 2}{5 \times 2} = -\frac{6}{10}.
\]

2. **\(-\frac{15}{2}\)**:
\[
-\frac{15}{2} = -\frac{15 \times 5}{2 \times 5} = -\frac{75}{10}.
\]

### Step 7: Combine the fractions
Now combining \(-\frac{6}{10}\) and \(-\frac{75}{10}\):
\[
-\frac{6}{10} - \frac{75}{10} = -\frac{6 + 75}{10} = -\frac{81}{10}.
\]

### Final Answer
So, the simplified result of the original expression is:

\[
\boxed{-\frac{81}{10}}.
\]