To complete the inequality, let's first establish the locations of the points and their relationships:

• Point a is located between 0 and 1, closer to 1. This means $a$ is positive and less than 1.
• Point b is located between -1 and 0, closer to 0. This means $b$ is negative and greater than -1.
• We are asked to compare $a + b$ and $a - b$.

Key considerations:

1. $a + b$: Since $a$ is positive and $b$ is negative, $a + b$ will be the sum of a small positive number and a small negative number. Depending on the relative magnitudes of $a$ and $b$, the sum could be positive or negative, but it will generally be closer to 0.

2. $a - b$: Subtracting a negative number is the same as adding a positive number. So $a - b$ will be larger than $a$, and closer to 1, since $b$ is negative.

Completing the inequality:

We can infer the following relationships:

• $a + b$ is a value between $-1$ and $0$, because the sum of a small positive number $a$ and a small negative number $b$ will not exceed 0.
• $a - b$ is larger, because subtracting a negative $b$ effectively adds the magnitude of $b$, making the result greater than $a$.

Therefore, the inequality that completes the sentence is: $a + b < a - b$

Summary:

The correct inequality is: $a + b < a - b$

Would you like further explanation or details on any part of this? Here are some related questions to explore:

1. How does the addition of two numbers with opposite signs work mathematically?
2. Can $a + b$ ever exceed $a - b$ in this case? Why or why not?
3. How would the inequality change if $a$ and $b$ were both positive or both negative?
4. What happens to the sum $a + b$ as $a$ gets closer to 1 or $b$ gets closer to -1?
5. How can this concept of addition and subtraction of numbers with different signs be applied in solving equations?

Tip: When adding numbers with different signs, always subtract the smaller absolute value from the larger one and take the sign of the number with the larger absolute value.