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Chapter 1: Problem 41

Find each quotient. $$ \frac{96}{-16} $$

Short Answer

Expert verified
-6

Step by step solution

01

Understand the problem

The goal is to find the quotient of the division \( \frac{96}{-16} \).
02

Compute the quotient

Divide the numerator (96) by the denominator (-16): \( 96 \div -16 = -6 \).
03

Write the final answer

The quotient of \( \frac{96}{-16} \) is \( -6 \).

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Key Concepts

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

quotient
The quotient is the result of dividing one number by another. In our example, the quotient is what we get when we divide 96 by -16.
  • First, identify the numbers to be divided: 96 (the numerator) and -16 (the denominator).
  • Next, perform the division: 96 divided by -16 equals -6.
So, the quotient of 96 and -16 is -6. Understanding quotients is essential in algebra as it helps in simplifying expressions and solving equations.
numerator
The numerator is the number above the division line in a fraction. It represents how many parts of the whole we have. In our problem, the numerator is 96.
  • The numerator is the term being divided.
  • In the fraction \( \frac{96}{-16} \), 96 is the numerator.
When computing a quotient, the numerator is divided by the denominator. Here, 96 is divided by -16 to find the quotient -6.
denominator
The denominator is the number below the division line in a fraction. It indicates how many equal parts the whole is divided into. In our problem, the denominator is -16.
  • The denominator tells us the size of each part.
  • In the fraction \( \frac{96}{-16} \), -16 is the denominator.
We divide the numerator by the denominator to find the quotient. Here, 96 divided by -16 yields -6.
negative numbers
Negative numbers are numbers less than zero, represented by a minus sign (-). They appear frequently in algebra and arithmetic.
  • In our example, the denominator -16 is a negative number.
  • When dividing a positive number by a negative number, the quotient will be negative.
  • Therefore, \( \frac{96}{-16} \) equals -6 because dividing a positive by a negative yields a negative result.
Understanding negative numbers is crucial for correctly performing operations like division and for solving algebraic problems.

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