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

Question

−

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:

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