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Chapter 1: Problem 25

Find each sum. $$ -2+[5+(-1)] $$

Short Answer

Expert verified
2

Step by step solution

01

Simplify the Expression Inside the Brackets

Start by simplifying the expression inside the brackets. Calculate \[ 5 + (-1) \].
02

Compute 5 + (-1)

Add 5 and -1: \[ 5 + (-1) = 4 \].
03

Substitute Back Into the Equation

Replace the simplified bracket expression back into the original problem: \[ -2 + 4 \].
04

Compute the Final Sum

Add -2 and 4: \[ -2 + 4 = 2 \].

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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 involves combining positive and negative numbers. To handle this, follow these steps:
  • Identify whether the numbers are positive or negative.
  • Combine the values considering their signs.
Positive numbers are straightforward, but negative numbers can be tricky. Think of negative numbers as moving backwards on a number line. For example, adding -2 and 4 can be visualized as starting at the point -2 and moving 4 steps forward to land on 2. This helps in ensuring accuracy.
Substitution Method
The substitution method is often used to simplify complex problems. After simplifying a portion of the expression, replace that part with its result to make the problem easier to solve.
  • Simplify parts of the expression step by step.
  • Substitute the simplified parts back into the original expression.
For example, in the problem \[ -2 + [5 + (-1)] \], you first simplify \[ 5 + (-1) = 4 \]. Then, you substitute this back into the original expression to get \[ -2 + 4 \]. This method breaks down the problem into manageable pieces.
Order of Operations
The order of operations is a hierarchical set of rules used to determine the order in which calculations are performed in a mathematical expression. The order is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right)).
  • Start with calculations inside Parentheses.
  • Then handle any Exponents.
  • Next, perform Multiplication and Division from left to right.
  • Finally, perform Addition and Subtraction from left to right.
Applying this to the problem \[ -2 + [5 + (-1)] \], you first address the operation inside the brackets \[ 5 + (-1) = 4 \], then you proceed to the addition \[ -2 + 4 = 2 \]. This ensures that mathematical expressions are solved correctly.

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Most popular questions from this chapter

Find each difference. $$ 5.7-(-11.6) $$

Decide whether each statement is true or false. \(-|8|>|-9|\)

Decide whether each statement is true or false. \(|13-8| \leq|7-4|\)

The two tables show the heights of some selected mountains and the depths of some selected trenches. Use the information given to answer. \( \)\begin{array}{|l|c|}\hline \text { Mountain } & {\text { Height (in feet) }} \\\ {\text { Foraker }} & {17,400} \\ {\text { Wilson }} & {14,246} \\\ {\text { Pikes Peak }} & {14,110} \\ \hline\end{array} $$ \begin{array}{|l|c|}\hline\text {} & {\text { Depth }( \text { in feet } } \\ {\text { Trench }} & {\text { as a negative number }} \\ {\text { Philippine }} & {-32,995} \\ {\text { Cayman }} & {-24,721} \\ {\text { Java }} & {-23,376} \\ \hline \end{array} $$ What is the difference between the height of Mt. Foraker and the depth of the Philippine Trench?

Perform each indicated operation. $$ -9.1237+[(-4.8099-3.2516)+11.27903] $$
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