Problem 11 - Beginning and Intermediate Algebra

Question

Subtract. See Examples 1 through 5 $$ -6-5 $$

Step-by-Step Solution

Answer

-11

Step 1: Understand the Problem

We're asked to subtract 5 from -6, which is written as \(-6 - 5\). This means we're taking away another 5 from a negative 6.

Step 2: Rewrite the Expression

We can rewrite the problem \(-6 - 5\) as \(-6 + (-5)\) to make it clearer that we are adding a negative number.

Step 3: Add the Numbers

To solve \(-6 + (-5)\), add the numbers while keeping in mind both numbers are negative. This means the total will also be negative. Perform the simple addition: \(-6 + (-5) = -11\).

Key Concepts

Negative Numbers

Negative numbers are those numbers that are less than zero. They are opposite of positive numbers and are usually represented with a minus sign (-) in front. Understanding negative numbers is crucial as they appear often in everyday scenarios such as temperature below zero, debts, or levels below sea.
Negative numbers are on the left side of the number line. As you move further to the left, the numbers become smaller or more negative.

• On a number line: Negative numbers get smaller. Example, -1 is larger than -2.
• Below zero: Anything below zero in temperature is negative.

Understanding how negative numbers interact with other numbers is key to mastering basic arithmetic, especially when dealing with subtraction and addition of integers.

Addition of Integers

Adding integers involves determining if you're moving up or down the number line. When the integers have the same sign, such as both being positive or both negative, the addition is straightforward. You simply add their absolute values.
However, the direction they push you on the number line determines the final sign.

• If both are positive, move to the right, adding.
• If both are negative, move to the left, combining their sizes.

When adding numbers of different signs, the process is slightly different. You find the difference between their absolute values and take the sign of the larger absolute value.

• Different sign addition: The absolute larger maintains its sign. Example: For -6 + 5, think of it as a conflict between sizes and directions.

Understanding Subtraction as Addition

The concept of subtraction can often be reinterpreted as addition, which can simplify calculations involving integers. By turning subtraction into addition, you make it easier to handle especially with negative numbers.
For example, instead of thinking about subtracting a number, consider adding its opposite.

• Example: -6 - 5 becomes -6 + (-5).
• Changing signs: Subtracting positive is like adding negative.

This mental shift tends to make it easier to visualize the problem, especially on a number line. Whenever subtracting, think 'opposite plus'. It simplifies many complex problems into simpler addition tasks that nearly almost anyone can do.