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Chapter 3: Problem 229

In the following exercises, divide. $$-180 \div 15$$

Short Answer

Expert verified
-12

Step by step solution

01

Determine the Sign of the Result

A positive number divided by a negative number results in a negative number. Since we are dividing -180 by 15, the result will be negative.
02

Perform the Division

Ignore the signs for now and just divide the absolute values. Calculate 180 梅 15.
03

Calculate 180 梅 15

Divide 180 by 15: 180 梅 15 = 12.
04

Apply the Sign

Since the original problem has a negative dividend and a positive divisor, the answer is negative. Therefore, -180 梅 15 = -12.

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Key Concepts

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

division of integers
Division of integers is a foundational concept in prealgebra. When dividing two integers, it is important to consider both the magnitude and the sign of the numbers involved. Here's a simple process to follow:
  • Identify the signs of the dividend (number being divided) and the divisor (number you are dividing by).
  • Determine whether the result will be positive or negative based on the signs.
  • Divide the absolute values of the integers to find the magnitude of the result.
  • Apply the determined sign to the result.
For example, in the given exercise -180 梅 15, we identify that the dividend (-180) is negative and the divisor (15) is positive. As dividing a negative by a positive yields a negative result, we know the result will be negative. We then divide the absolute values: 180 梅 15 = 12. Applying the sign, the final answer is -12.
negative and positive numbers
Understanding how to handle negative and positive numbers is crucial in division.
  • If both numbers are positive, the result is positive.
  • If both numbers are negative, the result is positive since two negatives cancel each other out.
  • If one number is positive and the other is negative, the result is negative.
This rule simplifies the process because it means we can focus on the absolute values and just apply the sign rules. For instance, in our problem, we have a negative dividend (-180) and a positive divisor (15). Since they have different signs, the result must be negative. Always verify the signs first to avoid mistakes in your calculations.
absolute values in division
Absolute values play a key role in division. The absolute value of a number is its distance from zero, regardless of direction. This means we can temporarily ignore the signs and work with the pure numerical values.
  • Find the absolute value of the dividend and the divisor.
  • Perform the division operation with these absolute values.
  • Reapply the determined sign from earlier steps to the result.
In our example -180 梅 15, the absolute values are 180 and 15. Dividing these gives 180 梅 15 = 12. Since we've already noted the negative sign based on the rule for signs, we end up with -12. Using absolute values makes division straightforward and helps prevent errors resulting from misinterpreted signs.

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