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Chapter 2: Problem 2

Find each quotient. $$-20 \div(-5)$$

Short Answer

Expert verified
The quotient is 4.

Step by step solution

01

Identify the Components

In the expression \(-20 \div (-5)\), we have a negative dividend \(-20\) and a negative divisor \(-5\). Identifying the components helps in determining the result.
02

Simplify the Absolute Values

Calculate the division of the absolute values: \(\frac{20}{5} = 4\). We ignore the negative signs for now and focus on the division of the absolute values.
03

Determine the Sign of the Quotient

Since we are dividing two numbers with the same sign (negative and negative), the quotient will be positive. Therefore, the quotient of \(-20 \div (-5)\) will be\(+4\).

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Key Concepts

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

Understanding Absolute Value
When dealing with division, you'll often come across the term "absolute value." This concept is quite simple but important. The absolute value of a number is its distance from zero on the number line, without considering its sign. Simply put, it is always a non-negative number.
For instance:
  • The absolute value of \(-7\) is \(7\)
  • The absolute value of \(5\) is \(5\)
  • The absolute value of zero is \(0\)
To find the absolute value, you simply remove any negative signs. This is important in mathematical operations like division, where simplifying to absolute values first can make calculations easier to handle.
Working with Negative Numbers
Negative numbers can seem tricky at first, but once you understand their rules, they're quite manageable. A negative number is any number that is less than zero, and it's represented with a minus sign (\(-\)). Some simple rules can help guide you:
  • When you multiply or divide two negative numbers, the result is a positive number.
  • If one number is negative and the other is positive, your result will be negative.
In the example \(-20 \/ -5\), both the numbers are negative. According to the rules, dividing two negatives results in a positive. So, \(-20 \/ -5 = +4\). Understanding these interactions helps you predict the signs of your answers easily.
What is a Quotient?
The term "quotient" refers to the result of dividing one number by another. In other words, it is what you get after performing the division operation. Understanding the concept of a quotient can help in many math problems.
  • When \((-20) \/ (-5)\), the quotient is \(+4\).
  • The division of two numbers with like signs (both positive or both negative) yields a positive quotient.
  • Conversely, dividing two numbers with different signs (one negative and one positive) will result in a negative quotient.
Remember, the process involves dividing the absolute values first, then determining the sign based on the rules for negative numbers.

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