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Chapter 2: Problem 25

Add. $$84+(-23)$$

Short Answer

Expert verified
Answer: The sum of 84 and -23 is 61.

Step by step solution

01

Compare the magnitudes of the numbers

First, let's compare the magnitudes of the two numbers, 84 and -23. Since 84 is greater than 23, the sum will have the same sign as 84, which is positive.
02

Find the difference between the magnitudes

Next, let's find the difference between the magnitudes of the two numbers: 84 - 23 = 61.
03

Determine the sign of the result

As determined in Step 1, the result will have the same sign as 84, which is positive.
04

Write the result

Finally, we can write the result as a positive number: $$84 + (-23) = 61$$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Positive and Negative Numbers
When adding numbers, it is vital to differentiate between positive and negative numbers. Positive numbers are greater than zero, while negative numbers are less than zero. They are opposite in direction on the number line.
  • Positive numbers: 1, 2, 3, etc.
  • Negative numbers: -1, -2, -3, etc.
In the case of the exercise, we have 84, a positive number, and -23, a negative number. Each type of number affects the result differently during addition.
Knowing their characteristics helps in foreseeing the outcome of an addition where they interact.
Magnitude Comparison in Integer Addition
Magnitude refers to the size or absolute value of a number, without considering its sign. Comparing magnitudes is crucial when adding numbers with different signs since it helps determine the result's overall sign.
For example, to compare the magnitudes of 84 and -23, we look at their values without considering the sign:
  • The magnitude of 84 is 84.
  • The magnitude of -23 is 23.
Since 84 (positive) is greater than 23 (negative), the outcome of their addition will take the sign of the number with the larger magnitude, which is positive in this case.
Addition with Negative Numbers
Adding a positive number and a negative number involves combining their values while considering their signs. Evaluating the difference in their magnitudes reveals the amount by which they influence each other.
  • Step 1: Compare their magnitudes to determine the sign of the sum.
  • Step 2: Subtract the smaller magnitude from the larger to find the result.
  • Step 3: Assign the sign of the larger magnitude to the result.
In our example, adding 84 and -23, the difference in magnitudes is 61 (since 84 - 23 = 61). Considering the steps, we see the positive influence of 84 results in the final positive sum: 61.

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Most popular questions from this chapter

For Exercises \(1-74,\) simplify. $$4 \sqrt{16 \cdot 9}-\left\\{(-4)^{3}+2[18 \div(-2)+(4-(-2))]\right\\}$$

Prep Exercise 6 When dividing two num bers that have the same sign, the result is ___. Prep Exercise 7 When dividing two numbers that have different signs, the result is ___. divide. $$-\frac{28}{4}$$

For Exercises \(1-74,\) simplify. $$\left.\left.\left\\{(-3)^{2}+4\right](8-20) \div(-2)\right]\right\\}+(-5) \sqrt{25 \cdot 4}$$

Simplify. $$|-18|$$

Complete the sentence. The absolute value of \(-16\) is _____________
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