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Chapter 1: Problem 89

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

Short Answer

Expert verified
The result is -5.90617.

Step by step solution

01

- Solve the innermost parentheses

First, solve the innermost parentheses: (-4.8099 - 3.2516) Combine the values:-4.8099 - 3.2516 = -8.0615
02

- Substitute back into the expression

Next, substitute -8.0615 back into the original expression:-9.1237 + [(-8.0615) + 11.27903]
03

- Solve the expression inside the brackets

Add -8.0615 and 11.27903: -8.0615 + 11.27903 = 3.21753
04

- Final addition

Lastly, add -9.1237 and 3.21753: -9.1237 + 3.21753 = -5.90617

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Key Concepts

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

arithmetic operations
Arithmetic operations form the backbone of all mathematical calculations. These operations include addition, subtraction, multiplication, and division. Each one has specific rules and order in which they should be performed. In our exercise, we use subtraction and addition.
When performing arithmetic operations, it's crucial to follow the proper order. This ensures that you get the correct answer. Always start with parentheses; next, perform any multiplications or divisions from left to right, and finally, carry out all additions or subtractions from left to right.
combining like terms
Combining like terms means to simplify expressions by adding or subtracting terms that have the same variables. This concept usually applies to algebraic expressions, but it can also make arithmetic easier.
For example, in our exercise, we simplify the expression by combining \text{\(-4.8099\)} and \text{\(-3.2516\)} first because they are within the innermost parentheses. Once combined, we substitute this back into the original expression to simplify it further. This step-by-step method helps to avoid mistakes and makes complex calculations more manageable.
parentheses in expressions
Parentheses indicate which operations should be performed first. Solving expressions inside parentheses ensures that you follow the proper order of operations. In our example, we address the smallest parentheses first: \text{\((-4.8099 - 3.2516)\)}.
Once simplified, we take this value and substitute it back into the main expression. Following this method ensures clarity and avoids errors in lengthy calculations.
negative numbers
Negative numbers can make math seem tricky, but they follow straightforward rules. When dealing with negative numbers, it's essential to remember:
  • A negative minus a negative is the same as adding the absolute values.
  • Adding a negative is like subtracting the positive version of that number.
  • Subtracting a negative is like adding the positive.

For example, in our exercise, we first dealt with negative numbers inside the parentheses: \text{\(-4.8099\)} and \text{\(-3.2516\)}. This helped to simplify the overall expression. Understanding these rules makes working with negative numbers more manageable.

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Most popular questions from this chapter

Solve each problem. Marcial Echenique owes \(\$ 679.00\) on his Visa account. He returns three items costing \(\$ 36.89, \$ 29.40,\) and \(\$ 113.55\) and receives credit for these on the account. Next, he makes purchases of \(\$ 135.78\) and \(\$ 412.88\) and two purchases of \(\$ 20.00\) each. He makes a payment of \(\$ 400 .\) He then incurs a finance charge of \(\$ 24.57 .\) How much does he still owe?

Decide whether each statement is true or false. \(|-6|<|-9|\)

Perform each indicated operation. $$ \left(-\frac{3}{4}-\frac{5}{2}\right)-\left(-\frac{1}{8}-1\right) $$

Solve each problem. In \(1998,\) undergraduate college students had an average (mean) credit card balance of 1879. The average balance increased \(\$ 869\) by 2000 , then dropped \(\$ 579\) by \(2004,\) and then increased \(\$ 1004\) by \(2008 .\) What was the average credit card balance of undergraduate college students in \(2008 ?\)

Perform each indicated operation. $$ |-4+8|+|6-1| $$
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