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Chapter 1: Problem 149

perform the indicated operation. \(-6 \div(-3)\) (Section 1.7, Example 4)

Short Answer

Expert verified
The result of \( -6 梅 (-3) \) is 2.

Step by step solution

01

Identifying the operation

The operation to be performed is division, indicated by the '梅' symbol.
02

Applying the rule of division for negative numbers

The rule states that when two negative numbers are divided, the result is positive. So, \( -6 梅 (-3) = 2 \).
03

Write down the final answer

After applying the appropriate rule, we find that \( -6 梅 (-3) = 2 \).

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Key Concepts

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

Rules of Division
Division is one of the basic operations in arithmetic, alongside addition, subtraction, and multiplication. It essentially represents the process of breaking a number into equal parts.
To divide two numbers, we follow some fundamental rules that guide the operation, making sure it's carried out correctly:
  • Dividing a number by 1 yields the same number. For example, \(-8 \div 1 = -8\).
  • Any number divided by itself equals 1. For instance, \(-6 \div -6 = 1\).
  • Dividing by zero is undefined in mathematics. Thus, \(a \div 0 \) cannot occur.
  • If a number is divided by another number, we can sometimes simplify or "reduce" the result to its simplest form.
Understanding these rules ensures we handle division tasks correctly, regardless of whether we're working with positive or negative numbers.
Negative Numbers
Negative numbers are numbers that are less than zero. They are typically written with a minus sign in front, such as -2 or -5.
Understanding negative numbers involves grasping how they interact with arithmetic operations like addition, subtraction, multiplication, and division.
Let's explore some vital points:
  • Additive Inverse: The additive inverse of a number is what you add to the number to get zero. For example, the additive inverse of -3 is 3 because \(-3 + 3 = 0\).
  • Multiplying/Dividing Rules: When multiplying or dividing two negative numbers, the result is positive. For example, \-3 \times -4 = 12\ and \-6 \div -3 = 2\.
  • Conversely, if you multiply or divide one positive and one negative number, the result is negative, as in \(-6 \div 3 = -2\).
Being comfortable with negative numbers helps immensely in solving a wide range of mathematical problems.
Basic Arithmetic Operations
Arithmetic operations are the foundation of math. They include addition, subtraction, multiplication, and division, each having its own rules and conventions. Let's break down their essentials:
  • Addition: Adding two positive numbers always results in a positive number. Adding two negative numbers yields a negative result, while adding a positive and a negative number requires subtraction.
  • Subtraction: Subtracting a number is the same as adding its inverse. For example, \(7 - (-3) = 10\) because \(7 + 3 = 10\).
  • Multiplication: When multiplying two numbers with the same sign, the result is positive. However, two numbers with opposite signs multiply to a negative result.
  • Division: Similar to multiplication, dividing two numbers with the same sign results in a positive outcome, and dividing numbers with different signs results in a negative answer.
Mastering these operations involves practice and familiarity with their properties, leading to confident handling of all types of mathematical challenges.

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Most popular questions from this chapter

Simplify each series of additions and subtractions. $$-10-(-5)+7-2$$

Perform the indicated subtraction. $$\frac{1}{5}-\left(-\frac{3}{5}\right)$$

Perform the indicated subtraction. $$\frac{1}{7}-\left(-\frac{3}{7}\right)$$

Simplify each series of additions and subtractions. $$-726-422-921-(-816)$$

A multiplication is expressed as a repeated addition. Find this sum, indicated by a question mark. $$3(-3)=(-3)+(-3)+(-3)=?$$
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