Problem 41 - Beginning and Intermediate Algebra

Question

Find each quotient. \(\frac{96}{-16}\)

Step-by-Step Solution

Answer

-6

Step 1: Identify the dividend and divisor

The given problem is to find the quotient of \(\frac{96}{-16}\). Here, the dividend is 96 and the divisor is -16.

Step 2: Divide the absolute values

Calculate \(\frac{|96|}{|16|}\). Since \(|96| = 96\) and \(|16| = 16\), divide 96 by 16 to get 6.

Step 3: Determine the sign of the quotient

Since the dividend is positive and the divisor is negative, the quotient will be negative. Therefore, the quotient of \(\frac{96}{-16}\) is -6.

Key Concepts

absolute value

Absolute value is a fundamental concept in mathematics that describes the magnitude of a number without considering its sign.
To find the absolute value, you simply look at how far the number is from zero on the number line.
For example:

• The absolute value of 96 is written as \( |96| = 96 \)
• The absolute value of -16 is written as \( |-16| = 16 \)

In our step-by-step solution, finding the absolute values of both the dividend (96) and the divisor (-16) helps us simplify the division process by removing the consideration of their signs.
This makes it easier to perform the actual division because we only deal with positive numbers at this stage.

positive and negative numbers

Understanding positive and negative numbers is crucial for solving division problems with integers.
Positive numbers are greater than zero and negative numbers are less than zero.
When dividing these numbers, the following rules apply:

• Positive ÷ Positive = Positive (\(96 ÷ 16 = 6\))
• Negative ÷ Negative = Positive (\( -96 ÷ -16 = 6\))
• Positive ÷ Negative = Negative (\( 96 ÷ -16 = -6\))
• Negative ÷ Positive = Negative (\( -96 ÷ 16 = -6\))

In our provided example, we divide a positive number (96) by a negative number (-16). According to the rule mentioned above, the result is negative, which is why our final quotient is -6.

quotient

The quotient is the result of a division problem.
In mathematical terms, if you divide a number called the dividend by another number called the divisor, the result you get is the quotient.
For example, in the problem at hand: \(\frac{96}{-16} = -6\), the quotient is -6.
The steps to find the quotient are:

• Identify the dividend and the divisor.
• Calculate the absolute value of both the dividend and the divisor.
• Perform the division using the absolute values.
• Determine the sign of the quotient based on the signs of the original numbers.

By following these steps, you ensure that you correctly determine both the magnitude and the sign of the quotient.