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Chapter 4: Problem 81

Perform the indicated operation. \(-3+(-9)\) (Section \(1.7,\) Table 1.7 )

Short Answer

Expert verified
The result of the operation \(-3+(-9)\) is \(-12\).

Step by step solution

01

Understanding the operation

The operation given is \(-3+(-9)\). This involves two negative numbers. Adding a negative number is the same as subtracting its absolute value, hence the operation can be rewritten as \(-3 - 9\).
02

Performing the operation

Subtract 9 from -3 to obtain \(-12\).

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Key Concepts

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

Negative Numbers
Negative numbers are essential to understand in introductory algebra. They are numbers that are less than zero and are typically represented with a minus sign (-). Negative numbers can be seen as moving to the left on the number line from zero. For instance, if you are at zero and move three steps to the left, you will be at -3. Negative numbers have unique properties, especially when they interact with other kinds of numbers.
  • They are useful in representing debts or temperatures below zero.
  • They follow specific rules when added, subtracted, multiplied, or divided.
  • Combining negative numbers often requires considering their absolute values, which are the numbers without the negative sign.
Understanding these aspects helps in properly managing calculations that involve negative numbers.
Addition and Subtraction
Addition and subtraction are fundamental operations in mathematics. They help us calculate sums and differences, respectively. When dealing with negative numbers, these operations can look different. For example, adding a negative number is the same as subtracting its positive counterpart.
  • In the case of \(-3 + (-9)\), we are adding two negative numbers. This can be rewritten as \(-3 - 9\), which involves subtracting one negative number from another.
  • Subtraction can sometimes increase a negative number's absolute value, as seen in this example.
It's key to practice switching between addition and subtraction forms, especially with negative numbers, to master these operations.
Basic Arithmetic Operations
Basic arithmetic operations form the foundation of more complex mathematical concepts. They include addition, subtraction, multiplication, and division. Each has a unique role and set of rules, particularly when negative numbers are involved.
  • Addition involves combining values. When numbers have the same sign, their absolute values are added together.
  • Subtraction requires taking one value away from another. When involving negative numbers, like subtracting \(-9\) from \(-3\), it can mean increasing the deficit.
  • Being fluent in these operations is essential for solving problems, as it allows for flexibility in rewriting expressions to make them easier to handle, such as converting an addition of a negative number to a subtraction.
Having a solid understanding of these operations equips you to take on more challenging mathematical tasks with confidence.

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Most popular questions from this chapter

In Exercises \(61-68,\) solve each system or state that the system is inconsistent or dependent. $$\left\\{\begin{array}{l} \frac{x}{2}=\frac{y+8}{3} \\ \frac{x+2}{2}=\frac{y+11}{3} \end{array}\right.$$

Involve dual investments. Your grandmother needs your help. She has 50,000 dollar to invest. Part of this money is to be invested in noninsured bonds paying \(15 \%\) annual interest. The rest of this money is to be invested in a government-insured certificate of deposit paying \(7 \%\) annual interest. She told you that she requires a total of 6000 dollar per year in extra income from these investments. How much money should be placed in each investment?

Read Exercise \(72 .\) Then use a graphing utility to solve the systems. $$\left\\{\begin{array}{l}2 x-3 y=10 \\ 4 x+3 y=20\end{array}\right.$$

Determine whether each statement 鈥渕akes sense鈥� or 鈥渄oes not make sense鈥� and explain your reasoning. In dependent systems, the two equations represent the same line.

$$\text { Solve: } 2(x+3)=24-2(x+4)$$
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