Problem 12 - Prealgebra

Question

Draw a number line from 10 to 10 and use it to add the following numbers. $$-7+3$$

Step-by-Step Solution

Answer

The sum of -7 and 3 is -4.

Step 1: Understanding the Number Line

A number line is a horizontal line with numbers placed at intervals. In this problem, we need a number line that ranges from -10 to 10, where negative numbers are to the left of zero and positive numbers are to the right of zero.

Step 2: Identifying the Starting Point

The expression (-7 + 3) starts with the number -7. Locate -7 on the number line as our starting point for the addition problem.

Step 3: Moving Forward on the Number Line

To add 3 to -7, move 3 units to the right on the number line from the starting point of -7. Each step towards the right represents the addition of 1.

Step 4: Finding the Result

After moving 3 units to the right from -7, you land on the number -4. Thus, -7 + 3 = -4.

Key Concepts

Basic Arithmetic

In basic arithmetic, especially when learning about number lines, we engage in simple operations like addition and subtraction. Number lines help us visualize these calculations. They're quite straightforward to understand. Picture a straight line with evenly spaced numbers on it, kind of like a ruler, which makes seeing the numbers' order very easy.
This simplicity allows us to easily perform operations like addition and subtraction. The numbers increase as we go to the right and decrease as we move left. In the exercise, when you have an equation like \(-7 + 3\), the idea is to start at \(-7\) on the number line, and then make moves to the right, since you are adding, which means moving in the positive direction.

Negative Numbers

Negative numbers are numbers less than zero. They're interesting because they add a whole new dimension to arithmetic and number lines. Imagine the number line extending to the left of zero, into what might feel almost like a backward zone. This is where negative numbers reside. They are used in many real-world scenarios, like measuring temperatures below freezing or calculating bank account overdrafts.
To understand and work with them on a number line, remember:

• Numbers further left are smaller.
• When you add or move towards the right, you're increasing the value.
• Adding a smaller positive number to a larger negative number actually makes the overall value less negative (or more positive).

So in our problem, starting at \(-7\) and adding \(3\) means moving closer to zero, landing on \(-4\). Each step taken to the right on the number line adds another positive unit, gradually reducing negativity.

Positive Numbers

Positive numbers are on the right side of zero on the number line and represent values greater than zero. They are what we typically count with in everyday situations, like money, objects, or distance. Understanding positive numbers is crucial for operations like addition on a number line since you add in that positive direction. For instance, when you add a positive number, you're moving to the right, marking an increase.
In our exercise, to solve \(-7 + 3\), once you locate \(-7\), adding \(3\) is visualized by moving 3 steps to the right, arriving at \(-4\). This is because positive numbers counteract negativities, nudging the outcome toward zero.
A few key points about positive numbers:

• They represent quantities you can measure and count.
• When added to negative numbers, they bring the total closer to zero or positive territory.
• They simplify complex arithmetic operations by lighting the way clearly towards higher values.

At the end of moving positively, your calculation feels tangible and straightforward with a number line guiding the path.