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Chapter 3: Problem 70

Divide. $$12 \div(-6)$$

Short Answer

Expert verified
-2

Step by step solution

01

Identifying the Numbers

Identify the two numbers in the division operation, which are 12 and -6.
02

Perform the Division

Perform the division, remembering the rule that a positive number divided by a negative number yields a negative result. Therefore, when we divide 12 by -6, we get -2.

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Key Concepts

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

Positive and Negative Numbers
In mathematics, numbers are usually categorized into positive and negative numbers. Positive numbers are greater than zero and typically don't have a sign in front of them, while negative numbers have a minus sign (-) in front to indicate they are less than zero. It's important to differentiate between the two because they behave differently when used in arithmetic operations like division. For example, dividing a positive number by a negative number will result in a negative quotient, as seen in the example of dividing 12 by -6. This is a fundamental concept to understand for handling numbers effectively in both basic and advanced arithmetic.
Division Rules
Division can be thought of as the process of determining how many times one number is contained within another. It鈥檚 essential to follow specific division rules, especially when dealing with positive and negative numbers. Here are some important division rules to remember:
  • When you divide two positive numbers, the quotient is positive.
  • When you divide two negative numbers, the quotient is also positive.
  • When you divide a positive number by a negative number, the result is negative.
  • Similarly, dividing a negative number by a positive number yields a negative result.
This understanding helps in executing division operations accurately. In our initial example, 12 is positive and -6 is negative, leading to a negative result of -2.
Basic Arithmetic Operations
Basic arithmetic operations include addition, subtraction, multiplication, and division. Each operation follows a set of rules and procedures to find a solution. Division is one of these key operations and involves distributing one number by another to find how many times the divisor fits into the dividend. In arithmetic, understanding the interaction between positive and negative numbers is crucial.
  • Addition and subtraction are straightforward but get complex with negative numbers.
  • Multiplication with one or more negative numbers results in a negative product, unless both numbers are negative, which then results in a positive product.
  • Division, as illustrated, can alternate the sign of the quotient based on the combination of signs in the dividend and divisor.
Mastering these operations allows for confidence in problem-solving and lays the foundation for more advanced topics in mathematics.

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