Adding Integers with Different Signs

Oct 13, 2025 by recoveryshake.com 40 views

Understanding the Problem

When dealing with the addition of negative and positive numbers, it's essential to understand the concept of combining integers. The main goal is to find the sum of the given numbers, which involves adding the absolute values of the numbers and then determining the sign of the result based on the number of negative numbers.

Adding Integers with Different Signs

To add integers with different signs, we need to follow a specific procedure. First, we add the absolute values of the numbers, and then we determine the sign of the result based on the number of negative numbers.

Step 1: Add the Absolute Values

The absolute value of a number is its distance from zero on the number line. In this case, we have three numbers: -21, -13, and 20. To add their absolute values, we simply add the numbers without considering their signs.

|-21| + |-13| + |20| = 21 + 13 + 20 = 54

Step 2: Determine the Sign of the Result

Since we have two negative numbers (-21 and -13) and one positive number (20), the result will be negative. This is because the sum of two negative numbers is always negative, and the presence of a positive number does not change the sign of the result.

Finding the Final Answer

Now that we have added the absolute values and determined the sign of the result, we can find the final answer.

(-21) + (-13) + 20 = -54

The final answer is C. $-54$ .

Conclusion

In this problem, we added three integers with different signs and found the sum. We first added the absolute values of the numbers and then determined the sign of the result based on the number of negative numbers. The final answer is C. $-54$ .

Frequently Asked Questions

What is the sum of -21 and -13? The sum of -21 and -13 is -34.
What is the sum of -34 and 20? The sum of -34 and 20 is -14.

Tips and Tricks

When adding integers with different signs, always add the absolute values first.
Determine the sign of the result based on the number of negative numbers.
Practice adding integers with different signs to become more comfortable with the concept.

Real-World Applications

Adding integers with different signs is essential in real-world applications, such as finance, science, and engineering.
Understanding how to add integers with different signs can help you make informed decisions in your personal and professional life.

Common Mistakes

Failing to add the absolute values first.
Determining the sign of the result incorrectly.
Not practicing adding integers with different signs.

Additional Resources

Khan Academy: Adding Integers with Different Signs
Mathway: Adding Integers with Different Signs
IXL: Adding Integers with Different Signs

Frequently Asked Questions

Q: What is the sum of -5 and 3?

A: To find the sum of -5 and 3, we add their absolute values and then determine the sign of the result. The absolute value of -5 is 5, and the absolute value of 3 is 3. Adding these values gives us 5 + 3 = 8. Since we have one negative number (-5) and one positive number (3), the result will be negative. Therefore, the sum of -5 and 3 is -8.

Q: What is the sum of -2 and -4?

A: To find the sum of -2 and -4, we add their absolute values and then determine the sign of the result. The absolute value of -2 is 2, and the absolute value of -4 is 4. Adding these values gives us 2 + 4 = 6. Since we have two negative numbers, the result will be negative. Therefore, the sum of -2 and -4 is -6.

Q: What is the sum of 2 and -1?

A: To find the sum of 2 and -1, we add their absolute values and then determine the sign of the result. The absolute value of 2 is 2, and the absolute value of -1 is 1. Adding these values gives us 2 + 1 = 3. Since we have one positive number (2) and one negative number (-1), the result will be positive. Therefore, the sum of 2 and -1 is 1.

Q: What is the sum of -3 and 2 and -1?

A: To find the sum of -3, 2, and -1, we add their absolute values and then determine the sign of the result. The absolute value of -3 is 3, the absolute value of 2 is 2, and the absolute value of -1 is 1. Adding these values gives us 3 + 2 + 1 = 6. Since we have three negative numbers, the result will be negative. Therefore, the sum of -3, 2, and -1 is -6.

Q: What is the sum of 4 and -2 and 1?

A: To find the sum of 4, -2, and 1, we add their absolute values and then determine the sign of the result. The absolute value of 4 is 4, the absolute value of -2 is 2, and the absolute value of 1 is 1. Adding these values gives us 4 + 2 + 1 = 7. Since we have one positive number (4) and two negative numbers (-2 and -1), the result will be positive. Therefore, the sum of 4, -2, and 1 is 3.