Problem 6 - Algebra 1: Concepts and Skills

Question

Use a number line to find the sum. $$ 7+(-3) $$

Step-by-Step Solution

Answer

The sum of 7 and -3 is 4.

Step 1: Identify the Starting Point

On the number line, identify the starting point which will be the first number in the problem, which is 7.

Step 2: Represent the Addition

Next, represent the addition of the second number, -3, on the number line. Since the number is negative, move to the left from the starting point. The number of steps to the left will be equal to the absolute value of the second number, meaning 3 steps to the left since |-3|=3.

Step 3: Find the Sum

The point on the number line where you end up is the sum of the two numbers. Count the numbers on the line to the spot where you landed to find the sum.

Key Concepts

Number Line

A number line is a visual representation of numbers laid out in a straight horizontal line. It is typically used to display positive and negative integers as well as fractions and decimals. Positive numbers are usually represented to the right of zero, while negative numbers appear to the left. This line is an incredibly helpful tool in visualizing the process of adding and subtracting numbers.

To add using a number line, you start at a point corresponding to the first number. If you're adding a positive number, move right. Conversely, if the number you're adding is negative, you move left. For instance, if you add 7 and (-3), you start at 7 and move 3 steps to the left to arrive at the answer 4.

Adding Integers

Adding integers involves combining both positive and negative whole numbers. The basic rules for adding integers dictate that if the signs are the same, you add the absolute values and keep the sign. However, if the signs differ, you subtract the smaller absolute value from the larger absolute value, and retain the sign of the number with the larger absolute value. For example, when adding 7 and (-3), you are actually subtracting the absolute value of -3 from 7 and keeping the positive sign, resulting in 4.

Negative Numbers

Negative numbers are values less than zero, denoted by a minus sign (-). They represent quantities that are lacking or below a standard level, such as temperatures below zero degrees or debts. When using a number line, negative numbers appear to the left of zero, and their position relative to zero visually demonstrates their value. Dealing with negative numbers during addition means subtracting their absolute value from the other number, as they have an inverse effect compared to positive numbers.

Absolute Value

The absolute value of a number is the distance between that number and zero on a number line, disregarding its sign. It is always a non-negative value. Represented by two vertical bars around the number (for instance, \(|-3| = 3\)), the absolute value signifies the magnitude of a number. In the context of adding integers on a number line, when you come across a negative number, you utilize its absolute value to determine the number of steps you take. This ensures a consistent, accurate representation of the addition process, since direction is already determined by the positive or negative sign of the integer.