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Chapter 1: Problem 42

In Exercises \(1-72\), compute the value of each expression. $$10-(-3)+1-4$$

Short Answer

Expert verified
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Step by step solution

01

- Simplify the expression inside the parentheses

The first operation is to simplify the expression involving the parentheses. The expression given is: \[10 - (-3) + 1 - 4\] Remember that subtracting a negative number is the same as adding the positive of that number: \[10 - (-3) = 10 + 3\]
02

- Perform the addition

Now add the result from Step 1 to the next number in the expression: \[10 + 3 + 1 - 4\] First, add 10 and 3 to get 13: \[13 + 1 - 4\]
03

- Continue with the next addition

Next, add 1 to the result from Step 2: \[13 + 1 = 14\]
04

- Perform the final subtraction

Finally, subtract 4 from the result of the addition in Step 3: \[14 - 4 = 10\]

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Key Concepts

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

Order of Operations
When solving algebraic expressions, it's important to follow the order of operations. This helps to ensure the calculations are done in the correct sequence.

The order of operations is often remembered by the acronym PEMDAS:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

In the problem given, we need to handle any parentheses first. Even though there are no actual parentheses adding complexity, we do have to deal with a subtraction operation involving a negative number: \(10 - (-3)\). This means it's essential to remember that subtracting a negative is the same as adding the positive of that number.
Integers
Integers are the set of whole numbers and their opposites. They include positive numbers, negative numbers, and zero.

In the given problem, we see the use of both positive and negative integers: \(10 - (-3) + 1 - 4\). It's important to understand how to handle operations with these numbers. When subtracting a negative integer, it鈥檚 equivalent to adding its positive counterpart. So, \(10 - (-3)\) becomes \(10 + 3\).

Understanding integers and their properties will make manipulating algebraic expressions much simpler.
Basic Arithmetic Operations
Basic arithmetic operations include addition, subtraction, multiplication, and division.

Let's break down the problem:
  • Step 1: Simplify the expression involving parentheses or negative signs. Here, \(10 - (-3)\) becomes \(10 + 3\).
  • Step 2: Perform the addition: \(10 + 3 + 1 - 4\). Start by adding 10 and 3 to get 13: \(13 + 1 - 4\).
  • Step 3: Continue with the addition: \(13 + 1 = 14\).
  • Step 4: Finally, perform the subtraction: \(14 - 4 = 10\).


Following these steps systematically ensures accurate results when evaluating expressions.

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Most popular questions from this chapter

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