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Chapter 1: Problem 29

Find each sum. $$ [(-9)+(-3)]+12 $$

Short Answer

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Step by step solution

01

Simplify Inside the Brackets

First, simplify the expression inside the brackets: (-9) + (-3).Combining these gives (-12).
02

Substitute the Simplified Value

Next, substitute the simplified value back into the original expression: (-12) + 12.
03

Add the Remaining Numbers

Finally, add the remaining numbers: (-12) + 12 = 0. So, the sum is 0.

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Key Concepts

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

arithmetic operations
Arithmetic operations are the basic building blocks of mathematics. They include addition, subtraction, multiplication, and division. In integer addition, we combine numbers to find the total.

Here are some key points about arithmetic operations:
  • Addition: Combines two or more numbers to form a larger number.
  • Subtraction: Finds the difference between two numbers.
  • Multiplication: Repeated addition of a number.
  • Division: Distributing a number into equal parts.
In our exercise, we primarily deal with addition.

This is the process of summing integers, including both positive and negative numbers. Knowing the rules of arithmetic will help you understand more complex operations later on.
negative numbers
Negative numbers are numbers less than zero and are denoted with a minus sign ( - ). They represent values below zero, like -1, -2, -3, etc.

When adding negative numbers, think of moving further to the left on the number line.
  • Adding two negative numbers combines their absolute values and keeps the sign negative. For instance, \((-9) + (-3) = -12\).
  • When you add a negative number to a positive number, the smaller absolute value of the number is subtracted from the larger absolute value, keeping the sign of the larger absolute value. For instance, \((-12) + 12 = 0\).
Understanding these rules helps in solving the arithmetic operations involving negative numbers, as seen in our example.
simplifying expressions
Simplifying expressions involves reducing them to their simplest form. This process makes them easier to understand and solve.

In our exercise, we simplify the expression step-by-step:
  • First, we handle operations inside any brackets. For example, \((-9) + (-3)\) simplifies to \(-12\).
  • After simplifying within the brackets, replace the original expression with the simpler form to get \(-12 + 12\).
  • Finally, carry out the remaining operation. The remaining expression \(-12 + 12\) simplifies to \0\.
This method breaks down complex expressions into manageable parts, making it easier to find the solution.

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Most popular questions from this chapter

Find each difference. $$ -4.4-8.6 $$

Perform each indicated operation. $$ -3+[(-5-8)-(-6+2)] $$

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

Write a numerical expression for each phrase and simplify. See Examples 7 and \(8 .\) The product of 12 and the difference between 9 and \(-8\)

Solve each problem. Linda Des Jardines owes \(\$ 870.00\) on her MasterCard account. She returns two items costing \(\$ 35.90\) and \(\$ 150.00\) and receives credit for these on the account. Next, she makes a purchase of \(\$ 82.50\) and then two more purchases of \(\$ 10.00\) each. She makes a payment of \(\$ 500.00 .\) She then incurs a finance charge of \(\$ 37.23 .\) How much does she still owe?
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