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Chapter 1: Problem 71

Perform each indicated operation. $$ (8-1)-12 $$

Short Answer

Expert verified
-5

Step by step solution

01

Evaluate the expression inside the parentheses

First, solve the subtraction inside the parentheses: \(8 - 1\). The result of this operation is 7.
02

Perform the remaining subtraction

Now, subtract 12 from the result obtained in Step 1: \(7 - 12\). The result of this operation is -5.

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Key Concepts

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

Order of Operations
In arithmetic, the order of operations is crucial to getting the correct answer. When solving mathematical expressions, there is a specific order in which operations must be performed:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
This is often remembered by the acronym PEMDAS. Following this order ensures that you handle parentheses first before moving on to other operations. This was the case in the exercise where we first solved the operation inside the parentheses.
Subtraction
Subtraction is one of the basic arithmetic operations. It involves taking one quantity away from another. In our exercise, we performed subtraction twice:
  • First, we subtracted 1 from 8
  • Then, we subtracted 12 from the result we obtained
Remember, it is essential to perform subtraction accurately based on the given order of operations to avoid mistakes.
Parentheses in Arithmetic
Parentheses play a significant role in arithmetic as they dictate which operations should be executed first. Expressions within parentheses are prioritized over other calculations. This means before we tackled any external operations, we had to solve the problem inside the parentheses in our exercise. Once the parentheses are resolved, you can move forward with the remaining operations.

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Most popular questions from this chapter

Decide whether each statement is true or false. \(|-12|<|-20|\)

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. See Example \(9 .\) The quotient of a number and 4 is \(-1\)

Solve each problem. Michigan is projected to lose 3 seats in the U.S. House of Representatives and Illinois 2 in \(2020 .\) The states projected to gain the most seats are California with 9 , Texas with \(5,\) Florida with \(3,\) Georgia with \(2,\) and \(\mathrm{Ari}-\) zona with \(2 .\) Write a signed number that represents the algebraic sum of these changes.

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

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. \(-15,29,8,-6\)
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