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Chapter 10: Problem 8

Divide, if possible. Check each answer. $$ -72 \div(-9) $$

Short Answer

Expert verified
The answer is 8.

Step by step solution

01

- Identify the problem

We need to divide $$ -72 \text{ by } -9 $$.
02

- Perform the division

To divide two negative numbers, divide the absolute values and the result will be positive. So, $$ \frac{72}{9} = 8 $$.
03

- Determine the sign

Since both numbers are negative, the result is positive. Therefore, $$ -72 \text{ divided by } -9 = 8 $$.
04

- Check the answer

To verify, multiply the result by the divisor: $$ 8 \text{ times } -9 \text{ should equal } -72 $$. Check: $$ 8 \times (-9) = -72 $$, which confirms our answer is correct.

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Key Concepts

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

Absolute Value
When working with division of negative numbers, it's important to understand the concept of absolute value. The absolute value of a number is its distance from zero, regardless of direction on the number line. For example, the absolute value of \( -72 \) is \( 72 \), and the absolute value of \( -9 \) is \( 9 \). We can represent this as \( \mid -72 \mid = 72 \) and \( \mid -9 \mid = 9 \). By focusing on the absolute values, we simplify the division problem without worrying about the signs initially.
Multiplication Check
After performing division, it's always a good idea to check your work using multiplication. This step ensures the accuracy of your division. For instance, after solving the problem \( -72 \) divided by \( -9 \) and getting \( 8 \), we can check by multiplying:
- \( 9 \) (our original divisor) times \( 8 \) (our result) should equal \( -72 \) (our original dividend).
Indeed, \( 8 \times -9 = -72 \), confirming the division is correct. This step can prevent mistakes and give you confidence in your solution.
Positive and Negative Numbers
Understanding how to handle positive and negative numbers is crucial. There are some key rules:
  • Dividing two positive numbers gives a positive result. For example, \( 72 \) divided by \( 9 \) is \( 8 \).
  • Dividing two negative numbers also gives a positive result. This is because the negatives cancel out, so \( -72 \) divided by \(-9 \) results in \(8 \).
  • Dividing a positive number by a negative gives a negative result. For instance, \( 72 \) divided by \( -9 \) is \(-8 \).
  • Similarly, dividing a negative number by a positive gives a negative result. For example, \( -72 \) divided by \( 9 \) is \( -8 \).
Remembering these rules will help you handle division problems with negative numbers accurately.

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