Find each sum or difference. See Example 1. -6 - 5

Verified step by step guidance

1. Identify the operation involved in the expression. Here, it is a subtraction: \(-6 - 5\).
2. Recall that subtracting a positive number is the same as moving left on the number line. So, \(-6 - 5\) means starting at \(-6\) and moving 5 units to the left.
3. Rewrite the subtraction as an addition of a negative number: \(-6 - 5 = -6 + (-5)\).
4. Add the two negative numbers by adding their absolute values and keeping the negative sign: \(|-6| + |-5| = 6 + 5 = 11\), so the result is \(-11\).
5. Express the final sum as \(-11\), which is the result of the original expression.

Key Concepts

Understanding Addition and Subtraction of Integers

Adding and subtracting integers involves combining positive and negative numbers on the number line. When subtracting a positive number from a negative number, you move further left on the number line, making the result more negative.

Sum and Difference Operations

The sum refers to the result of adding two numbers, while the difference is the result of subtracting one number from another. Recognizing whether to add or subtract is essential to correctly solving expressions like -6 - 5.

Number Line Visualization

Visualizing integers on a number line helps understand how sums and differences work, especially with negative numbers. Moving left indicates subtraction or adding negative values, which clarifies why -6 - 5 results in a more negative number.