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Chapter 1: Problem 19

Fill in the blanks. The quotient of two negative numbers is__________.

Short Answer

Expert verified
The quotient of two negative numbers is a positive number.

Step by step solution

01

Understand the Division Operation

Understand that quotient is the result you get when you divide one number by another. This involves knowing that you will be dividing one negative number by another negative number.
02

Understand the Negative Number Rule

Recall that when two negative numbers are divided, the result is a positive number. This is because the two negative signs (-/-) cancel each other out and give a positive output.
03

Apply the Negative Number Rule

Now, apply the negative number rule to determine the result of the division, remembering that the final result will be a positive number.

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Key Concepts

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

Quotient
When we talk about the quotient, we are referring to the result of a division operation. To put it simply, if you divide one number by another, the answer you get is called the quotient.
In mathematical terms, if you have two numbers, say \( a \) and \( b \), and you divide \( a \) by \( b \), the result is the quotient. In symbols, it is expressed as \( \frac{a}{b} = \text{quotient} \).
In the scenario of dividing two negative numbers, the quotient will be determined using the rules for dividing such numbers, which we鈥檒l explore next.
Negative Numbers
Negative numbers are those numbers that are less than zero. They are represented with a minus sign \((-\)). In division operations, dealing with negative numbers involves understanding some simple rules.
When dividing negative numbers, remember these points:
  • A negative number divided by a negative number results in a positive number.
  • This is because the two negative signs cancel each other out, which is similar to the rule of multiplying negatives.
Think of negative signs as flipping the direction of a number. When you flip the direction of a negative number twice, it ends up facing the positive direction which brings us to the next concept, a positive result.
Positive Result
A positive result is what you obtain when you perform certain arithmetic operations under specific conditions on numbers. In division, if both the divisor and the dividend are negative, their quotient will be positive.
Why is this? Here鈥檚 a simple breakdown:
  • Visualize each division as an operation that involves direction, like a two-way street.
  • Each negative sign flips the "direction" of the number. Flip twice, and you鈥檙e back to the original positive direction.
  • Hence, dividing two negative numbers, like \((-8) \div (-4)\), gives a positive result, \(2\). The negative signs cancel out.
This rule makes it easier to predict the outcome without having to calculate it each time, bringing about clarity and efficiency in math.

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