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Chapter 1: Problem 44

Perform each operation. SEE EXAMPLE \(2 .\) (OBJECTIVE 1 ) $$3[-2-(-4)]$$

Short Answer

Expert verified
The solution to the exercise \(3[-2-(-4)]\) is \(6\).

Step by step solution

01

Simplify the Expression Inside the Brackets

The expression inside the brackets is \([-2-(-4)]\). The negative of a negative number becomes a positive number, so \(-(-4)\) becomes \(+4\). Therefore, the expression becomes \([-2 +4]\), which simplifies to \(2\).
02

Perform the multiplication

Next, perform the multiplication. The expression \[3[-2-(-4)]\] has become \[3 * 2\], which equals \(6\).

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Key Concepts

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

Simplification of Expressions
Simplifying expressions is all about making them easier to handle without changing their value. When you simplify an expression, you're generally reducing it to its simplest form. This means removing any unnecessary parts and performing any possible arithmetic operations.

Here's how it works:
  • Focus on one operation at a time, especially operations inside parentheses or brackets.
  • Look for opportunities to perform arithmetic operations such as addition, subtraction, multiplication, or division.
  • Combine like terms whenever possible to reduce complexity.
For example, in the expression given, \([-2 - (-4)]\), converting \(-(-4)\) to \(+4\) allows for immediate simplification to \([-2 + 4 = 2]\). Simplification often involves understanding basic arithmetic and using it strategically.
Negative Numbers in Algebra
Negative numbers can sometimes seem tricky, especially when they appear inside equations or expressions. Understanding how to handle them is essential in algebra. Here are a few pointers to help you:
  • Negative sign of a negative number resolves into a positive. For example, \(-(-4)\) becomes \(+4\).
  • Know that subtracting a negative is the same as adding the positive equivalent. This means \(-2 - (-4)\) is the same as \(-2 + 4\).
  • Treat negative numbers carefully to avoid sign mistakes in calculations.
In the original exercise, noticing that \(-(-4)\) is positive is key to simplifying the expression correctly. Negative numbers might sometimes reverse their role, so always keep track of how they interact within an expression.
Order of Operations
The order of operations is crucial when solving expressions, particularly when they become complex. It refers to the rules that govern which operations should be performed first to ensure a single, unambiguous result. This can be remembered by the acronym PEMDAS:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
In the given expression \(3[-2 - (-4)]\), we started by simplifying the expression inside the brackets as the first step according to PEMDAS.

Once simplified, the next step involves multiplication. By following the order of operations, you ensure consistent results every time. Mastering this concept makes arithmetic operations more straightforward and avoids common calculation pitfalls.

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Most popular questions from this chapter

If the value of \(x\) were doubled, what would happen to the value of \(37 x ?\)

Write each inequality as an equivalent inequality in which the inequality symbol points in the opposite direction. $$3+8>8$$

Which property of real numbers justifies each statement? $$x(y+z)=(y+z) x$$

What is the purpose of using variables? Why aren't ordinary numbers enough?

Can the product of two proper fractions be larger than either of the fractions?
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