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The problem asks: "What should be added to \( \left( -\frac{9}{8} + \frac{11}{10} \right) \) to make 1?"

Let's solve it step by step.

### Step 1: Combine the fractions
First, we need to find the sum of \( -\frac{9}{8} + \frac{11}{10} \). To do that, we need a common denominator.

The least common denominator (LCD) between 8 and 10 is 40. Let's convert each fraction:

\[
-\frac{9}{8} = -\frac{9 \times 5}{8 \times 5} = -\frac{45}{40}
\]
\[
\frac{11}{10} = \frac{11 \times 4}{10 \times 4} = \frac{44}{40}
\]

Now, we can add the fractions:
\[
-\frac{45}{40} + \frac{44}{40} = \frac{-45 + 44}{40} = \frac{-1}{40}
\]

### Step 2: Set up the equation
Now, we want to find what number should be added to \( \frac{-1}{40} \) to make 1. Let the number be \( x \). So the equation becomes:

\[
\frac{-1}{40} + x = 1
\]

### Step 3: Solve for \( x \)
To solve for \( x \), add \( \frac{1}{40} \) to both sides:

\[
x = 1 + \frac{1}{40}
\]

Convert 1 to a fraction with denominator 40:

\[
x = \frac{40}{40} + \frac{1}{40} = \frac{41}{40}
\]

### Final Answer:
The number that should be added is \( \frac{41}{40} \).

Do you want more details or have any other questions?

Here are five related questions:
1. How do you find the least common denominator (LCD) for two fractions?
2. What is the process of converting fractions to have a common denominator?
3. How do you add positive and negative fractions?
4. What does it mean to "make 1" in a fraction equation?
5. How can you solve an equation involving fractions and variables?

**Tip:** When adding fractions, always find the least common denominator to simplify the process.

What should be added to (-9/8 + 11/10) to make 1?

This problem explores adding fractions with different denominators and solving a simple equation to find what should be added to (-9/8 + 11/10) to make 1. Suitable for Grade 7-8 students, the solution demonstrates combining fractions and basic equation solving.

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