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Chapter 1: Problem 50

In Exercises \(1-66,\) compute the value of each expression. $$-18+(-3)+(-4)+11$$

Short Answer

Expert verified
-14

Step by step solution

01

- Combine like terms

Start by grouping the negative and positive terms separately. In this case, the negative terms are (-18), (-3), and (-4), and the positive term is 11.
02

- Add negative terms together

First, add the negative terms together: \(-18 + (-3) + (-4) = -18 - 3 - 4\). Start by adding -18 and -3, which gives \(-18 - 3 = -21\). Next, add -21 and -4, which gives \(-21 - 4 = -25\).
03

- Add the positive term

Now add the positive term 11 to the result from the previous step: \(-25 + 11\). Since adding a positive number to a negative number is equivalent to subtracting the positive from the absolute value of the negative number:\(-25 + 11 = -14\).
04

Final Answer

The value of the expression \(-18 + (-3) + (-4) + 11\) is \(-14\).

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Key Concepts

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

Negative Numbers
Understanding negative numbers is essential in arithmetic. A negative number is a number less than zero, indicated by a minus sign. For example, -5 is five units below zero. Negative numbers can represent losses, decreases, or values below a reference point. When working with negative numbers in addition or subtraction:
  • **Adding a negative number** is the same as subtracting its absolute value (e.g., -3 + (-4) = -3 - 4).
  • **Subtracting a negative number** is equivalent to adding its absolute value (e.g., -3 - (-4) = -3 + 4).

In our exercise, we start by recognizing negative terms: -18, -3, and -4. We group them for easier calculation.
Combining Like Terms
Combining like terms is a crucial process in simplifying expressions. Like terms are terms that have the same variables to the same power. In our example with purely numerical terms, we treat all negatives and positives separately.
First, group all the negative terms together: (-18), (-3), and (-4). Adding these negative terms:
  • Start with -18 and add -3: (-18) + (-3) = -21.
  • Then, add -4 to the result: (-21) + (-4) = -25.

    • Now, only the positive term 11 remains, which we will add in the next step.
    Addition and Subtraction
    The final step involves adding or subtracting the results of previous calculations. In our exercise:
    • We need to combine -25 (result of adding all negative terms) with 11 (positive term).
    Adding a positive number to a negative number is like subtracting its absolute value from the negative number:
    -25 + 11, where the positive term 11 reduces the degree of the negative term:
    • = -14 (since 25 - 11 = 14, keeping the negative sign as the magnitude of the negative term remains larger).
    The final result of the expression -18 +(-3) + (-4) + 11 is -14.
    Through these steps, we practice handling negative numbers, combining like terms, and performing addition/subtraction accurately.

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    Most popular questions from this chapter

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