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Chapter 1: Problem 48

In Exercises \(1-66,\) compute the value of each expression. $$-21+15+(-2)+(-3)$$

Short Answer

Expert verified
-11

Step by step solution

01

Identify the Numbers

List all the numbers in the expression: ewline The numbers are -21, 15, -2, -3.
02

Combine Negative Numbers

Add the negative numbers together: ewline (-21) + (-2) + (-3) = -26.
03

Add the Positive Number

Add the positive number to the combined negative result: ewline -26 + 15 = -11.

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Key Concepts

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

addition of integers
In elementary algebra, one of the fundamental concepts is the addition of integers. Integers include all the whole numbers and their negative counterparts.
When adding integers, we follow a few basic rules:
  • If the signs are the same (both positive or both negative), add their absolute values and keep the common sign. For example, \(-3 + (-2) = -5\).
  • If the signs are different, subtract the smaller absolute value from the larger absolute value and use the sign of the larger absolute value. For instance, \(15 + (-3) = 12\).
negative numbers
Understanding negative numbers is crucial in algebra. A negative number is one that is less than zero and is often denoted with a minus sign (-).
When dealing with negative numbers:
  • Adding two negative numbers results in a more negative number. For example, \(-4 + (-5) = -9\).
  • Subtracting a negative number is equivalent to adding its positive counterpart. For example, \(7 - (-3) = 7 + 3 = 10\).
  • When adding a negative number and a positive number, subtract the smaller absolute value from the larger absolute value and take the sign of the larger absolute value.
arithmetic operations
Arithmetic operations are the basic building blocks of mathematics. These operations include addition, subtraction, multiplication, and division.
Here's a quick overview relevant to our solved problem:
  • Addition: Adds numbers together to get a sum.
    Example: \(-21 + 15 = -6\).
  • Subtraction: Finds the difference between numbers.
    Example: \(8 - 3 = 5\).
  • Multiplication: Multiplies numbers to get a product.
    Example: \(-2 \times 3 = -6\).
  • Division: Divides one number by another to get a quotient.
    Example: \(10 / 2 = 5\).
Mastering these operations is essential for solving more complex mathematical problems.

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Most popular questions from this chapter

Compute the given expression. Round off your answer to two decimal places where necessary. $$12.8-9.2(3.4-1.6)$$

We know that multiplication means repeated addition. That is, 4 times 3 means add 3 four times. In view of this and the rule for adding negative integers, what should 4 times \(-3\) be equal to?

Sketch the given set on a number line. $$\\{x | 1 \leq x<3\\}$$

Evaluate the given expression. Remember to follow the order of operations. $$\frac{15+2 \cdot 3}{3+2 \cdot 2}$$

Locate the given number between two successive integers on the number line. For example, if the given number is \(2.6,\) it is located between 2 and 3 on the number line. $$2 \frac{1}{3}$$
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