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Chapter 5: Problem 32

Divide. $$-9.1 \div(-3)$$

Short Answer

Expert verified
3.0333

Step by step solution

01

Understand the Signs

Recognize that dividing two negative numbers will yield a positive result. This is because a negative divided by a negative is positive.
02

Divide the Absolute Values

Ignore the signs and divide the absolute values of the numbers. Compute \( 9.1 \div 3 \).
03

Perform the Division

Calculate \( 9.1 \div 3 \). This gives \( 3.0333... \).
04

Determine the Sign

Since the original division is between two negative numbers, the result is positive. Therefore, \(-9.1 \div -3 = 3.0333... \).

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are simply numbers with a value less than zero. They are represented with a minus sign (-) in front of them. For example, -3 is a negative number. When working with negative numbers, remember that they follow certain rules that are different from positive numbers. Negative numbers can be tricky, but once you master the basics, they become much easier to work with. Remember that a negative number is always less than zero. Hence, -3 is less than 0, and -7 is even less than -3.
What is Absolute Value?
The absolute value of a number is its distance from zero on the number line, regardless of direction. This means that the absolute value of both 3 and -3 is 3. We write the absolute value of a number using two vertical lines. For example, the absolute value of -9.1 is written as \(|-9.1| = 9.1\). Absolute value can be especially useful when dividing or multiplying numbers because it simplifies the calculation by removing the signs. After computing the absolute values, you reapply the sign rules to get the final result.
Sign Rules in Division
When dividing two numbers, the signs of the numbers play a crucial role in determining the final result. Here are the basic rules to remember:
  • If you divide a positive number by another positive number, the result is positive.
  • If you divide a negative number by a positive number, the result is negative.
  • If you divide a positive number by a negative number, the result is negative.
  • If you divide a negative number by another negative number, the result is positive.
In the exercise, you divided -9.1 by -3. Following the rule that a negative divided by a negative yields a positive result, the answer was positive. Hence, \(-9.1 \div -3 = 3.0333...\). Always remember these rules, and you will be able to handle any division problem involving negative numbers confidently.

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Most popular questions from this chapter

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