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Chapter 1: Problem 25

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

Short Answer

Expert verified
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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

Fill in each blank with one of the following: greater than 0, less than 0, equal to \(0 .\) The product or the quotient of two numbers with different signs is _____.

Give a number that satisfies the given condition. A real number that is neither negative nor positive

Solve each problem. A pilot announces to the passengers that the current altitude of their plane is \(34,000\) ft. Because of turbulence, the pilot is forced to descend \(2100 \mathrm{ft}\). Write the new altitude as a signed number.

Fill in each blank with the correct response. The sum of a number and its opposite will always be __________.

To find the average (mean) of a group of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. All even integers between \(-18\) and \(4,\) inclusive
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