https://r2.erweima.ai/mathbot/image/1726786010598q6xcyy77.jpg

Let's solve the two problems shown in the image.

### Problem vii:
\[
\frac{1}{2} + \frac{2}{5}
\]

To solve this, we need to find a common denominator. The least common denominator (LCD) between 2 and 5 is 10.

1. Rewrite each fraction with a denominator of 10:
   \[
   \frac{1}{2} = \frac{5}{10}, \quad \frac{2}{5} = \frac{4}{10}
   \]
   
2. Now, add the two fractions:
   \[
   \frac{5}{10} + \frac{4}{10} = \frac{9}{10}
   \]

Thus, the solution to vii is:
\[
\frac{9}{10}
\]

---

### Problem viii:
\[
\frac{5}{6} + \left( -\frac{8}{6} \right)
\]

Since the denominators are already the same, we can directly add the numerators:

1. Add the numerators:
   \[
   5 + (-8) = -3
   \]

2. The result is:
   \[
   \frac{-3}{6}
   \]

3. Simplify the fraction:
   \[
   \frac{-3}{6} = \frac{-1}{2}
   \]

Thus, the solution to viii is:
\[
\frac{-1}{2}
\]

---

Would you like further details or clarification? Here are five related questions to expand on these ideas:

1. How do you find the least common denominator (LCD) for two fractions?
2. How do you simplify a fraction after addition or subtraction?
3. What are the rules for adding and subtracting negative fractions?
4. How do you convert improper fractions to mixed numbers?
5. How would you handle subtraction of fractions with different denominators?

**Tip:** Always check if the result can be simplified after adding or subtracting fractions by finding the greatest common divisor (GCD).

Learn how to add and subtract fractions with examples like 1/2 + 2/5 and 5/6 + (-8/6). Understand the rules for finding a common denominator, simplifying results, and handling negative numbers. Ideal for Grades 5-7.

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