Problem 7 - Algebra A Combined Function

Question

Add. See Examples 1 through 12,18, and 19. $$ -14+2 $$

Step-by-Step Solution

Answer

The sum of -14 and 2 is -12.

Step 1: Identify the operation

We are tasked with finding the sum of two numbers: -14 and 2.

Step 2: Understand integer addition

Adding integers involves combining their values. In this case, we have a negative number (-14) and a positive number (2).

Step 3: Visualize number line movement

Starting from -14 on the number line, moving 2 steps to the right brings us to a less negative number, as addition of a positive number moves the value towards zero.

Step 4: Calculate the sum

Starting at -14, move 2 steps to the right: -14, -13, -12. Thus, -14 + 2 equals -12.

Step 5: Confirm the solution

By checking the calculation again, starting from -14 and adding 2 indeed results in -12, confirming the result is correct.

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero. They are typically used to represent values such as debts, temperatures below freezing, and elevations below sea level. On the number line, negative numbers are located to the left of zero.
For example, -3 is less than 0, and -14 is even less than -3. The more negative a number is, the farther it is from zero and the more it represents a smaller value.
When adding negative numbers, you are essentially reducing the total value. This contrasts with adding positive numbers, which increases the total.

Number Line

A number line is a straight, horizontal line that visually represents numbers at equal intervals. It helps us to understand and perform operations with integers more easily.
The center of the number line is zero, with positive numbers extending to the right and negative numbers extending to the left.
When adding integers, the number line is useful as it provides a step-by-step visual guide:

• When you add a positive number, you move to the right.
• When you add a negative number, you move to the left.
• When you subtract a positive number, you move to the left.
• When you subtract a negative number, you move to the right.

Using the number line simplifies understanding movements and helps predict the results of additions and subtractions.

Addition of Integers

The addition of integers can involve both positive and negative numbers. When you add integers, you are combining their values, which can lead to different results depending on the signs of the numbers.
For example, adding two positive integers increases the total value, while adding two negative integers decreases the total value. When adding a positive and a negative integer, the signs dictate whether the sum will be positive, negative, or zero. For instance, when adding -14 and 2, the arithmetic looks like this:

• Start at -14 on the number line.
• Move 2 units to the right since we are adding a positive number.
• You land on -12.

Hence, the sum of -14 and 2 is -12, illustrating how adding a smaller positive number to a larger negative number results in a less negative sum.