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Chapter 3: Problem 98

Perform the indicated operation. $$(-8.919) \div(-0.9)$$

Short Answer

Expert verified
The short answer to this division operation is \(+9.910\).

Step by step solution

01

Recognize Signs

Identify the signs of the numbers involved in the operation. Here, both numbers are negative.
02

Divide the Numbers

Ignore the signs and divide the absolute values of the numbers, which is 8.919 by 0.9, using long division or a calculator.
03

Apply the Rules of Division

Since the rule for dividing two negative numbers is that the answer is positive, the result of the division operation in step 2 is the final answer.

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Key Concepts

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

Identifying Signs in Division
The first step in dividing numbers is to identify their signs. Understanding the signs during division helps us apply the correct rules and get the right answer. When we talk about signs, we mean whether the numbers involved are positive or negative. If a number is negative, it has a minus sign (-) in front of it, like in our original exercise where both numbers are negative: -8.919 and -0.9.

To identify the signs:
  • Observe each number carefully to see whether it has a minus sign (").
  • In our problem, both the dividend (-8.919) and the divisor (-0.9) have minus signs, indicating they are negative numbers.
Recognizing these signs is crucial because it informs us how to handle the numbers during division. This step sets up the framework for correctly applying the division rules later on.
Long Division
Long division is a method used to divide larger numbers, which might not be straightforward with simpler mental math. Here's how it works with two numbers, such as 8.919 divided by 0.9, after initially ignoring the signs.

Steps to perform long division:
  • Firstly, convert the divisor into a whole number if it isn't one already. In this case, 0.9 becomes 9 by moving the decimal one place to the right.
  • The same decimal shift of one place should be applied to the dividend, turning 8.919 into 89.19.
  • Next, start with 89.19 (the adjusted dividend) and divide by 9, following the normal long division process.
  • Bring down one digit at a time as you divide to handle any remaining part of the number.
  • You can use a calculator to double-check your answer when faced with complex numbers.
Long division helps to systematically break down the division process into manageable steps, ensuring accuracy even when handling tenths and decimals.
Rules of Division with Negative Numbers
When dividing numbers, especially negative ones, special rules apply to ensure we get the correct answer. The basic principle involves looking at the signs of both numbers involved in the division and applying the rules to determine the sign of the answer.

Here are the essential rules:
  • If both numbers have the same sign (either both positive or both negative), the answer is positive. Since our exercise involves two negative numbers, the answer is positive.
  • If the numbers have different signs (one positive and one negative), the answer is negative.
In our example, because both -8.919 and -0.9 are negative, when we divide them after focusing on their absolute values, the result is a positive number. Hence, understanding these rules saves time and guarantees that the solution aligns with mathematical conventions.

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Most popular questions from this chapter

Use the given property of addition to complete the statement. The Inverse Property of Addition $$?+(-18)=0$$

Simplify. $$-13+9-(-10)-4$$

Mathematics The distance \(d\) between point \(a\) and point \(b\) on the number line is given by the formula \(d=|a-b| .\) Find \(d\) when \(a=6\) and \(b=-15\)

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Simplify. $$-16-47-63-12$$
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