To solve $5 + (-2 \frac{1}{3}) + (-3 \frac{1}{6})$, we follow these steps:

Step 1: Convert mixed numbers to improper fractions

• $-2 \frac{1}{3} = -\frac{7}{3}$
• $-3 \frac{1}{6} = -\frac{19}{6}$

Step 2: Combine terms

Now, we have: $5 + \left( -\frac{7}{3} \right) + \left( -\frac{19}{6} \right)$

Step 3: Express 5 as a fraction

We can write $5$ as $\frac{30}{6}$ to have the same denominator as $\frac{19}{6}$.

Step 4: Find a common denominator

The least common denominator (LCD) of 3 and 6 is 6. So we rewrite the fractions:

• $-\frac{7}{3} = -\frac{14}{6}$

Now the equation looks like: $\frac{30}{6} + \left( -\frac{14}{6} \right) + \left( -\frac{19}{6} \right)$

Step 5: Add the fractions

Now combine all terms over a common denominator of 6: $\frac{30}{6} - \frac{14}{6} - \frac{19}{6} = \frac{30 - 14 - 19}{6} = \frac{-3}{6}$

Step 6: Simplify the fraction

$\frac{-3}{6} = -\frac{1}{2}$

So, the final result is: $5 + \left( -2 \frac{1}{3} \right) + \left( -3 \frac{1}{6} \right) = -\frac{1}{2}$

Would you like more details or have any questions?

Related Questions:

1. How do you convert between improper fractions and mixed numbers?
2. What are the steps to add or subtract fractions with different denominators?
3. How do you simplify fractions after performing operations?
4. Can improper fractions always be simplified?
5. What is the role of the least common denominator in fraction operations?

Tip: Always simplify fractions after performing any addition or subtraction to find the final reduced form.