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Chapter 10: Problem 37

Divide. $$ \frac{48.6}{-3} $$

Short Answer

Expert verified
-16.2

Step by step solution

01

- Understand the Division

Identify the numbers involved in the division problem: the dividend (48.6) and the divisor (-3). Recognize that division is the process of finding out how many times the divisor can fit into the dividend.
02

- Perform the Division

Divide 48.6 by 3 without considering the sign first. Perform the division:
03

- Include the Sign

Since the divisor is negative, the result of the division will also be negative. Therefore, the solution is -16.2.

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Key Concepts

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

Understanding the Dividend
In any division problem, the dividend is the number you are dividing up. For instance, in the problem \( \frac{48.6}{-3} \), the dividend is 48.6. Think of the dividend as an amount you're splitting into smaller sections.

The dividend goes inside the division bracket if you are doing long division. Here, it is placed at the top of the fraction.

When working with decimals, remember to keep them aligned during your calculations.

This ensures accuracy and makes the process smoother.
Identifying the Divisor
The divisor is the number by which you are dividing the dividend. In our example, \( \frac{48.6}{-3} \), the divisor is -3.

Essentially, the divisor is how many pieces you want to divide the dividend into.

The divisor can be positive or negative, which impacts the final result.

Always pay close attention to the sign of the divisor.

If the divisor is a negative number, it will change the sign of your answer.

Keep this in mind during all calculations.
Working with Negative Numbers
Dealing with negative numbers in division requires extra care. A negative divisor or dividend will affect the final sign of your result.

If both the dividend and divisor are either both positive or both negative, the result will be positive.

Here, the dividend is positive (48.6), and the divisor is negative (-3), so the result will be negative.

Always double-check the signs when you're finalizing your answer.

Remember:
  • Positive 梅 Positive = Positive
  • Negative 梅 Negative = Positive
  • Positive 梅 Negative = Negative
  • Negative 梅 Positive = Negative
Step-by-Step Solution
Let's break down the division \( \frac{48.6}{-3} \) step-by-step.

Step 1: Identify the numbers: The dividend is 48.6, and the divisor is -3.

Step 2: Ignore the negative sign for a moment and divide 48.6 by 3.

Perform the division: \ 48.6 梅 3 = 16.2 \

Step 3: Because the divisor is negative, your final answer will be negative.

So, \ \frac{48.6}{-3} = -16.2 \

By following these steps, you ensure accuracy and understand each part of the process.

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