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Chapter 2: Problem 60

Use the rule for order of operations to simplify each of the following. $$[8+(-2)]+[5+(-7)]$$

Short Answer

Expert verified
The simplified expression is 4.

Step by step solution

01

Simplify Inside the First Bracket

We begin by simplifying the expression inside the first pair of brackets: \(8 + (-2)\). Add \(-2\) to \(8\): \(8 - 2 = 6\).
02

Simplify Inside the Second Bracket

Next, simplify the expression inside the second pair of brackets: \(5 + (-7)\). Add \(-7\) to \(5\): \(5 - 7 = -2\).
03

Combine the Results

Now, combine the results from Steps 1 and 2. You add the results from both brackets together: \(6 + (-2) = 6 - 2 = 4\).

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Key Concepts

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

Simplifying Expressions
When simplifying expressions, the goal is to reduce them to their simplest form. This involves performing operations in an expression based on the order of operations, often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
To simplify an expression, you should:
  • First, deal with any operations inside parentheses or brackets. This means solving any inner expressions first.
  • Next, consider exponents (if there are any) after simplifying what's inside the brackets.
  • Finally, perform addition or subtraction, ensuring each step you take simplifies the expression further.
By following these steps, expressions become easier to manage and calculate. Simplification makes complex problems simpler and often provides a clearer path to the correct answer.
Integer Addition
Adding integers is an essential part of simplifying expressions. When working with integers鈥攚hole numbers that can be positive, negative, or zero鈥攜ou should consider both the number and its sign.
  • Add two positive numbers by simply combining them.
  • For two negative numbers, add them together and retain the negative sign, as the overall value will still be negative.
  • To add a positive and a negative number, subtract the smaller magnitude from the larger magnitude. The sign of the larger magnitude remains with the result.
For example, in the original problem, we added \(8 + (-2)\) to get 6, because subtracting 2 from 8 leaves us with 6. Understanding these rules ensures you handle integer addition correctly in various math contexts.
Brackets in Expressions
Brackets鈥攐r parentheses鈥攕erve a crucial purpose in math expressions. They dictate which parts of an expression should be solved first, in adherence to the order of operations.
Here's how brackets function in simplifying:
  • Brackets can serve to group parts of an expression that need solving before proceeding with the rest of the operations.
  • Perform calculations inside the brackets before doing anything outside them to ensure proper simplification.
  • If there are multiple levels of brackets, solve the innermost brackets first.
In the example provided, each part of the bracketed expression was simplified separately before combining the results. By correctly addressing the expressions inside brackets, the problem becomes manageable and less prone to error.

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Most popular questions from this chapter

Simplify as much as possible by first changing all subtractions to addition of the opposite and then adding left to right. $$-10-1+16$$

Find the wind chill temperature if the thermometer reads \(10^{\circ} \mathrm{F}\) and the wind is blowing at 25 miles per hour.

At 11: 00 in the morning in Superior, Wisconsin, Jim notices the temperature is 15 degrees below zero Fahrenheit. Write this temperature as a negative number. At noon it has warmed up by 8 degrees. What is the temperature at noon?

Perform the indicated operations. $$(6+1)(9-4)$$

Subtract. $$-86-31$$
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