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Chapter 1: Problem 34

In Exercises \(1-66,\) compute the value of each expression. $$10+(-6)+1$$

Short Answer

Expert verified
The value of the expression is 5.

Step by step solution

01

Understand the Expression

The expression given is: \(10 + (-6) + 1\).
02

Perform the Addition Inside the Parentheses

Start by adding the first two numbers: \(10 + (-6)\).
03

Calculate the Result of the First Addition

Adding 10 and -6 together: \(10 + (-6) = 4\).
04

Add the Remaining Number

Now add the result from step 3 to the remaining number: \(4 + 1\).
05

Calculate the Final Result

Adding 4 and 1 together: \(4 + 1 = 5\).

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Key Concepts

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

adding_integers
Adding integers is a foundational concept in elementary algebra. It involves combining positive and negative whole numbers to find a total sum.

When you add positive and negative integers:
  • Adding two positive integers always results in a positive sum.
  • Adding two negative integers results in a negative sum.
  • Adding a positive integer and a negative integer requires determining whether the sum is positive or negative based on their absolute values.

    Example:
    To add the numbers 10 and -6, consider this:
    • Start with 10 (a positive number).
    • Move 6 units to the left (because -6 is negative).
    • This lands you at 4, so 10 + (-6) = 4.

    Now that you have 4, adding 1 more results in 5.

    This approach simplifies even complex problems by breaking them into smaller steps.
expression_evaluation
Evaluating expressions involves calculating the value of an algebraic expression. This process can include a variety of operations, such as addition, subtraction, multiplication, and division.

Steps to Evaluate:
  • Identify the components of the expression.
  • Perform operations following the order of operations (PEMDAS/BODMAS), which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
  • Simplify the expression step-by-step.

    Example:
    The expression given is: 10 + (-6) + 1.
    • Start by adding 10 and -6 to get 4.
    • Then, add 1 to 4.

    This step-by-step approach ensures accurate and straightforward evaluations.
integer_operations
Integer operations refer to calculations involving whole numbers, which can be positive or negative. These operations include addition, subtraction, multiplication, and division.

Important Points:
  • When adding integers with different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the larger absolute value.

    Example: 10 + (-6). Subtract 6 from 10 and keep the sign of 10, which results in 4.

  • When adding integers with the same sign, add their absolute values and keep their common sign.

    Example: (-3) + (-2) = -5.

  • Subtraction of integers can be considered as adding the opposite.

    Example: To subtract -6 from 10, you can rewrite it as 10 + 6 = 16.

Being proficient in integer operations builds a solid foundation for mastering more advanced algebraic concepts. Practice these steps regularly to enhance your skills.

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Most popular questions from this chapter

In Exercises \(1-72\), compute the value of each expression. $$-246-327-(-542)$$

In Exercises \(73-84\), evaluate the given expression. $$|2-6|-(2-6)$$

Evaluate the given expression. Remember to follow the order of operations. $$\frac{18-3(4-1)}{2 \cdot 3+3}$$

Compute the given expression. Round off your answer to two decimal places where necessary. $$15.7-35(0.6)-4.6$$

Evaluate the given expression. Remember to follow the order of operations. $$30-(5 \cdot 4)-2$$
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