Choose any two negative integers. Is the sum of the integers less than or greater than the value of either of the integers? Will this be true no matter which integers you choose? Explain.

Let's break down the problem step by step.

### Step 1: Choose two negative integers.
Suppose we choose two negative integers, \(a\) and \(b\), where \(a < 0\) and \(b < 0\).

### Step 2: Calculate the sum of these integers.
The sum of these two integers is \(a + b\).

### Step 3: Compare the sum to each integer.
Since \(a\) and \(b\) are both negative, their sum will also be negative. Moreover, the sum of two negative numbers is always less than either of the individual numbers. 

Here's why:

- If we compare the sum \(a + b\) to \(a\), we get:
  \[
  a + b < a
  \]
  because \(b\) is negative, so adding \(b\) to \(a\) will decrease the value.

- Similarly, if we compare the sum \(a + b\) to \(b\), we get:
  \[
  a + b < b
  \]
  because \(a\) is also negative, so adding \(a\) to \(b\) will decrease the value.

### Conclusion:
Yes, the sum of any two negative integers will always be less than the value of either of the individual integers. This is true for any pair of negative integers because adding a negative number to another negative number results in a value that is even more negative.

### Why is this true no matter which integers you choose?
This is true because adding two negative numbers together means you're moving further to the left on the number line, which corresponds to a smaller (more negative) value. Therefore, the sum will always be less than either of the integers involved in the sum.

Would you like more details or have any questions?

Here are 5 related questions:

1. What happens when you add a positive integer to a negative integer?
2. How does the product of two negative integers compare to their individual values?
3. If you subtract a negative integer from another negative integer, how does the result compare?
4. How would the sum of a negative and a positive integer behave?
5. Can the sum of two negative integers ever be positive?

**Tip:** Remember, when adding numbers, the sign and magnitude of the numbers significantly affect the result.

Explore why the sum of any two negative integers is always less than the value of either integer individually. Learn through step-by-step reasoning and examples. Suitable for Grades 6-8.

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