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Chapter 2: Problem 30

Add. $$-45+21$$

Short Answer

Expert verified
Answer: The result of adding -45 and 21 is -24.

Step by step solution

01

Identify the absolute values

In this step, we find the absolute values of both numbers: Absolute value of -45 is 45, and absolute value of 21 is 21.
02

Subtract the absolute value of the smaller number from the absolute value of the larger number

Now, we will subtract the smaller absolute value from the larger absolute value: 45 - 21 = 24
03

Determine the sign of the result

Since the larger absolute value is from -45, the sign of the result will be negative.
04

Combine the sign and the result from Step 2

Now, we combine the sign (negative) from Step 3 and the result from Step 2 (24): $$-45 + 21 = -24$$

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Key Concepts

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

Absolute Value
Understanding the absolute value of a number is crucial when working with integers. Absolute value tells us how far a number is from zero on the number line, without considering direction. It is always a positive value or zero.
For example, the absolute value of
  • -45 is 45
  • 21 is 21
The absolute value is written using vertical bars:
  • The absolute value of -45 is \(|-45| = 45\)
  • The absolute value of 21 is \(|21| = 21\)
This concept helps us compare the sizes of numbers without worrying about their signs.
Subtraction of Integers
Subtraction of integers might seem tricky, but it becomes simpler when thinking in terms of absolute values. To subtract integers, you often find the difference between their absolute values.
  • Find the absolute values of each number. For -45, it鈥檚 45; for 21, it鈥檚 21.
  • Subtract the smaller absolute value from the larger one: \(45 - 21 = 24\)
The result provides the magnitude of the difference between the numbers. The next step is determining the correct sign based on the original numbers, which leads us to our next concept.
Negative Numbers
Negative numbers represent values less than zero, positioned to the left of zero on the number line. When adding a negative number to a positive number, imagine shifting left from the positive number's position.
A crucial part of working with negative numbers is understanding their impact on subtraction. In the expression
  • -45 + 21
we first find the absolute values. Since 45 is greater than 21, subtraction results in 24. Because
  • -45 is greater in magnitude than 21
the result takes the sign of -45, making it
  • -24
This interaction highlights how negative numbers affect results, making it essential to consider both absolute values and signs for accurate calculations.

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Most popular questions from this chapter

For Exercises \(1-74,\) simplify. $$\frac{20+12(-3)}{3^{2}-1}$$

Prep Exercise 8 For the following equation, complete the related division equation used to solve the equation. \(3 x=-15\) \(x=\) ____ solve and check. $$7 p=28$$

Complete the sentence. The absolute value of \(-18\) is _____________

Prep Exercise 8 For the following equation, complete the related division equation used to solve the equation. \(3 x=-15\) \(x=\) ____ solve and check. $$-18 m=0$$

For Exercises \(1-74,\) simplify. $$\\{12[-2-(-5)]-40\\} \div \sqrt{25-9}$$
See all solutions

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