Problem 59 - Elementary and Intermediate Algebra

Question

Divide, if possible, and check. If a quotient is undefined, state this. $$ -100 \div(-11) $$

Step-by-Step Solution

Answer

9.09

Step 1 - Identify the Division Operation

Recognize that the problem requires dividing -100 by -11. This can be written as \(-100 \div (-11)\)

Step 2 - Apply Division Rules

Use the rule that dividing two negative numbers results in a positive quotient. Thus, \(-100 \div (-11) = 100 \div 11\).

Step 3 - Perform the Division

Calculate \(100 \div 11\). This yields approximately 9.0909, which can be rounded to 9.09.

Step 4 - State the Result

The final quotient is approximately 9.09.

Step 5 - Check the Division

Verify by multiplying the quotient by the divisor to see if you get back the original number: \(9.09 \times (-11) \approx -100\).

Key Concepts

division rules

In mathematics, understanding division rules is crucial for solving problems effectively. When dividing numbers, there are a few key principles to remember:

• Dividing two positive numbers results in a positive quotient.
• Dividing a positive number by a negative number results in a negative quotient.
• Dividing two negative numbers results in a positive quotient.
• Dividing a negative number by a positive number results in a negative quotient.

In the given problem, \(-100 \div (-11)\), because both numbers are negative, the quotient will be positive.

negative numbers

Negative numbers can be tricky when not understood properly. They appear often in real-life contexts such as temperature, finance, and altitude. Understanding their behavior in mathematical operations is essential. Here are some simple rules when dealing with negative numbers:

• Adding a negative number is the same as subtracting the corresponding positive number.
• Subtracting a negative number is the same as adding the corresponding positive number.
• Multiplying or dividing two negative numbers always yields a positive result.

Applying this knowledge, let’s understand how -100 divided by -11 transforms to a positive result:
When you perform the division, the two negative signs 'cancel out' each other, resulting in a positive quotient. So, \(-100 \div (-11) = 9.09\), approximately.

checking division results

To ensure that the result of your division is correct, it’s important to check your work. Here’s a simple verification process:

• Multiply the quotient by the divisor.
• The product should equal the original dividend.

For our problem, \(-100 \div (-11) = 9.09\), approximately. To verify:

1. Multiply the quotient by the original divisor: \(9.09 \times (-11) = -99.99\), which can be rounded to \-100\.

2. Since \(-100 \approx -100\), our solution is confirmed to be correct.

By consistently performing this check, you can confidently ensure the accuracy of your division results.