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Chapter 1: Problem 64

In Exercises \(1-66,\) compute the value of each expression. $$520+(-366)$$

Short Answer

Expert verified
The result is 154.

Step by step solution

01

Understand the Problem

The task is to find the result of adding 520 and -366. This involves adding a positive and a negative number.
02

Set Up the Expression

Write the given expression: 520 + (-366)
03

Simplify the Expression

Adding a negative number is the same as subtracting the absolute value of that number. So, the expression simplifies to: 520 - 366
04

Perform the Subtraction

Now, calculate the difference between 520 and 366: 520 - 366 = 154

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Key Concepts

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

Addition of Integers
Adding integers can be simple when you follow a few foundational rules. When dealing with integer addition, the signs of the numbers play a critical role. Here's how to handle various scenarios:
  • Same Sign: If the numbers have the same sign, add their absolute values and keep the common sign. For example, adding 3 and 5 yields 8, and adding -3 and -5 yields -8.
  • Different Signs: If the numbers have different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the larger absolute value. For instance, for the expression 520 + (-366), we recognize that 520 is positive and 366 is negative. We subtract 366 from 520, giving us 154.
Practicing these rules will make integer addition straightforward.
Subtraction of Integers
Subtraction of integers is closely linked to addition. In fact, subtracting a number is the same as adding its opposite. This concept can make subtraction problems easier to manage. Here's how to approach it:
  • To subtract an integer, add its opposite (negative becomes positive, and positive becomes negative). For example, 520 - 366 can be rephrased as 520 + (-366), which quickly shows the relationship between subtraction and addition.
  • Apply the same sign rules as integer addition. Once you've rephrased subtraction as addition, follow the appropriate steps for adding integers with like or unlike signs.
This method simplifies the problem, making it easier to see the result without confusion.
Absolute Value
The absolute value of a number refers to its distance from zero, regardless of its direction on the number line. This concept is fundamental, especially when dealing with different integer operations.
  • Represented as \(|x|\), the absolute value of any number x is always non-negative.
  • The absolute value of positive numbers and zero is simply the number itself. For example, \( |3| = 3 \) and \( |0| = 0 \).
  • The absolute value of a negative number is its positive counterpart. For instance, \( |-3| = 3 \).

In operations, understanding absolute value helps clarify steps, especially when converting between addition and subtraction. For example, the original problem 520 + (-366) simplifies into 520 - 366 by recognizing that adding -366 is equivalent to subtracting 366. This highlights how subtraction can always be reframed as adding a negative, providing a stronger grasp of integer operations.

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Most popular questions from this chapter

Compute the given expression. Round off your answer to two decimal places where necessary. $$12.4-20(0.8)+4.7$$

Fill in the appropriate ordering symbol: either \(<,>,\) or \(=\). 7_____7.

Consider the following statements. If the statement is true, explain why. If the statement is false, explain why and/or give an example illustrating why. (a) Every rational number is an integer. (b) Every integer is a rational number. (c) \(-15\) is greater than \(-10\) (d) The absolute value of \(-15\) is greater than the absolute value of \(-10 .\) (e) A rational number must be positive. (f) An integer must be positive. (g) Every real number is a rational number. (h) Every rational number is a real number.

In Exercises \(1-66,\) compute the value of each expression. $$-48+(-19)$$

Factor the given number into its prime factors. If the number is prime, say so. $$91$$
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