What Divided By -21 Equals -9

What Divided by -21 Equals -9? Unraveling the Math Mystery

This seemingly simple question, "What divided by -21 equals -9?", opens the door to a deeper understanding of fundamental mathematical concepts, particularly division with negative numbers. While the answer itself is straightforward, the journey to finding it provides valuable insights into the rules governing arithmetic operations and their practical applications. This article will not only solve the equation but will also delve into the underlying principles, explore similar problems, and provide practical examples to solidify your understanding.

Understanding Division and Negative Numbers

Before diving into the solution, let's refresh our understanding of division and how negative numbers behave in mathematical operations.

Division: At its core, division is the inverse operation of multiplication. If we say a divided by b equals c (a/b = c), this implies that b multiplied by c equals a (b * c = a). This reciprocal relationship is crucial for understanding how to solve division problems.

Negative Numbers: Negative numbers represent values less than zero. The rules for operating with negative numbers are key:

• Multiplication and Division: When multiplying or dividing numbers with differing signs, the result is negative. If both numbers have the same sign (both positive or both negative), the result is positive.

Solving the Equation: What Divided by -21 Equals -9?

Now, let's tackle the original question: What divided by -21 equals -9? We can represent this mathematically as:

x / -21 = -9

To solve for x, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by -21:

x / -21 * -21 = -9 * -21

This simplifies to:

x = 189

Therefore, 189 divided by -21 equals -9.

Verifying the Solution

To ensure our solution is correct, let's plug the value of x back into the original equation:

189 / -21 = -9

This confirms our answer. The rules of multiplication with negative numbers are clearly demonstrated here: a positive number (189) divided by a negative number (-21) results in a negative number (-9).

Expanding the Understanding: Similar Problems and Applications

The principles demonstrated in solving this equation are applicable to a wide range of mathematical problems. Let's explore some similar examples:

Example 1: What divided by 15 equals -5?

This problem follows the same principles. We set up the equation:

x / 15 = -5

Multiplying both sides by 15, we get:

x = -75

Therefore, -75 divided by 15 equals -5.

Example 2: What divided by -8 equals 12?

Again, we set up the equation:

x / -8 = 12

Multiplying both sides by -8:

x = -96

Therefore, -96 divided by -8 equals 12.

Real-World Applications:

The concept of division with negative numbers appears frequently in various real-world scenarios:

• Finance: Calculating losses or debts. For instance, if a company loses $21 per unit and experiences a total loss of $189, the number of units sold can be determined by dividing -189 by -21.

• Temperature: Representing changes in temperature. A decrease in temperature can be represented by a negative number. Calculating the average temperature change over a period of time often involves division with negative numbers.

• Physics: Calculating velocity or acceleration. Negative values often represent movement in the opposite direction. Determining average speed or acceleration frequently uses division with negative numbers.

Advanced Concepts and Further Exploration

While the initial problem was relatively straightforward, it opens doors to more complex mathematical concepts:

Algebraic Equations: The solution method employed is a fundamental technique in solving algebraic equations. Understanding how to isolate variables and manipulate equations is crucial for success in algebra and beyond.

Signed Numbers and the Number Line: Visualizing numbers on a number line helps to understand the concept of positive and negative numbers and their relationships. This visual representation is especially helpful when working with operations involving signed numbers.

Order of Operations (PEMDAS/BODMAS): When tackling more complex problems, remember the order of operations: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This ensures accurate calculations.

Conclusion: Mastering Division with Negative Numbers

The seemingly simple question, "What divided by -21 equals -9?", serves as a springboard to understanding crucial mathematical concepts. Mastering division with negative numbers, along with a solid grasp of algebraic techniques and the order of operations, forms a strong foundation for tackling more challenging mathematical problems. The examples provided and the discussion of real-world applications highlight the relevance and practicality of these skills, demonstrating their importance across various disciplines. By understanding and applying these principles, you can confidently approach and solve a wide range of mathematical equations. Remember that consistent practice is key to solidifying your understanding and developing proficiency.