Mastering the basics of mathematics is a crucial step for any high school STEM student. Understanding adding positive and negative numbers is essential and forms the foundation for more complex math operations.

This article will provide a detailed, step-by-step guide to help you grasp this concept. We’ll cover the addition rules, provide practice problems, and share useful tips. Whether preparing for the ACT® WorkKeys Applied Math exam or simply looking to strengthen your math skills, this guide is designed to help you succeed.

Understanding Positive and Negative Numbers

In mathematics, numbers can be either positive or negative.

Positive numbers are greater than zero. They are often used to represent quantities or values that increase.

On the other hand, negative numbers are less than zero. They typically represent a decrease or loss.

Understanding the difference between these two types of numbers is the first step in mastering addition and subtraction.

The Rules of Addition for Positive and Negative Numbers

Adding positive and negative numbers follows specific rules.

These rules are based on the properties of numbers and the concept of absolute value.

Here are the basic rules for adding positive and negative numbers:

1. The result is always positive adding positive and negative numbers
2. When adding two negative numbers, the result is always negative.
3. When adding a positive number and a negative number, the result depends on their absolute values.

Adding Two Positive Numbers

When you add two positive numbers, the result is always positive.

For example, if you add 3 and 2, the result is 5, which is a positive number.

Adding Two Negative Numbers

When you add two negative numbers, the result is always negative.

For instance, if you add -4 and -3, the result is -7, which is a negative number.

Adding Numbers with Different Signs

When you add a positive number and a negative number, the result depends on their absolute values.

If the absolute value of the positive number is greater, the result is positive.

Conversely, if the absolute value of the negative number is greater, the result is negative.

Visualizing Addition on the Number Line

A number line can be a helpful tool in visualizing the addition of positive and negative numbers.

When adding, you move along the number line in the direction of the number you are adding.

For example, if you start at -2 and add 4, you move four places to the right, ending up at 2.

Practice Problems and Real-World Examples

Practice is key to mastering the addition of positive and negative numbers.

Try solving these problems:

1. -3 + 4
2. 5 + (-7)
3. -2 + (-6)
4. 8 + (-2)

Let’s go through each problem step by step to solve them:

1. For the expression -3 + 4, you start with -3 and then add 4 to it. Imagine starting at -3 on a number line. Moving to the right by 4 units, you pass through -2, -1, and then reach 0. The total after adding 4 is 1. Therefore, -3 + 4 equals 1.
2. Next, we have the equation 5 + (-7). Here, you begin with 5 and add -7, which is the same as subtracting 7 from 5. On the number line, you start at 5 and move 7 units to the left. After moving past 4, 3, 2, and finally to 1 and then 0, you end up at -2. So, 5 + (-7) results in -2.
3. Now, let’s analyze -2 + (-6). In this case, both numbers are negative. When you add two negative numbers, you can think of it as combining their absolute values (which are 2 and 6) and then keeping the negative sign. So, 2 + 6 equals 8, and when you add the negative sign, you get -8. Thus, -2 + (-6) equals -8.
4. Finally, we consider the expression 8 + (-2). Here, you take 8 and add -2, which is the same as subtracting 2 from 8. On a number line, you start at 8 and move 2 units to the left. This brings you down to 7 and then 6. Consequently, 8 + (-2) equals 6.

To summarize:

1. -3 + 4 = 1
2. 5 + (-7) = -2
3. -2 + (-6) = -8
4. 8 + (-2) = 6

Real-world examples can also help. For instance, think of temperature. If it’s -5 degrees and the temperature rises by 7 degrees, it becomes 2 degrees. This is the same as adding -5 and 7.

Tips for Mastering Basic Arithmetic Operations

Consistent practice is crucial for mastering basic arithmetic operations.

Try to solve a few problems every day. This will help you build speed and confidence.

Don’t hesitate to ask for help if you’re stuck. Remember, understanding the basics is key to success in higher-level math.

Need help preparing for the ACT® WorkKeys Applied Math Test?

Albert has hundreds of ACT® WorkKeys practice questions and full-length practice tests to try out.