Problem 101 Definition of division: \(12 \di... [FREE SOLUTION]

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Elementary Algebra Within Reach

Ron Larson, Kimberly Nolting

$Math Studyset 91影视 Explanations$ Math

6 Edition

Chapter 1: Problem 101

Definition of division: $12 \div 4=$

Short Answer

Expert verified

The result of the division $12 \div 4$ is 3.

Step by step solution

Understanding the Division Operation

The division operation is one of the four basic operations in arithmetic. It is the inverse of multiplication. When we say 12 divided by 4, it means how many times does 4 fit into 12.

Perform the Division

In essence, we ask how often 4 can be subtracted from 12 until it reaches 0. Every time we subtract, we count it. After 3 times of subtracting 4, 12 will become 0. Thus, $12 \div 4 = 3$.

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Key Concepts

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

Basic Arithmetic Operations

Arithmetic operations are fundamental to mathematics. They include addition, subtraction, multiplication, and division. Each has a specific purpose that helps us manipulate numbers.

- **Addition**: Combines values into a larger number. - **Subtraction**: Finds the difference between values. - **Multiplication**: Repeated addition of the same number. - **Division**: The process of distributing a number into equal parts.

Each of these operations has unique properties that make them essential tools in daily calculations and problem-solving. Understanding division in particular is crucial because it often deals with grouping, partitioning, or sharing quantities evenly.

Inverse of Multiplication

Division is often described as the inverse of multiplication. This means if multiplication combines numbers into a larger product, division breaks that product into its original factors.

For example, if we multiply 4 by 3, we get 12. Conversely, if we divide 12 by 4, we find out how many times 4 'fits into' 12, which is 3. This concept of inverse operations can simplify complex problems by reversing the actions, helping us find missing elements in equations easily.

Division by Subtraction

Another way to understand division is to consider it as repeated subtraction. To solve a division problem, such as dividing 12 by 4, we subtract 4 repeatedly from 12 until we reach 0.

- First subtraction: 12 - 4 = 8 - Second subtraction: 8 - 4 = 4 - Third subtraction: 4 - 4 = 0

In this method, we subtracted 4 three times from 12 to reach zero. This result shows us that 12 can be divided by 4 exactly three times, hence 12 梅 4 = 3. This view can make division feel more intuitive, especially for beginners learning fundamental operations.

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91影视

Definition of division: \(12 \div 4=\)

Short Answer

Step by step solution

Understanding the Division Operation

Perform the Division

Key Concepts

Basic Arithmetic Operations

Inverse of Multiplication

Division by Subtraction

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