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Chapter 10: Problem 1

Divide, if possible. Check each answer. $$ 36 \div(-6) $$

Short Answer

Expert verified
-6

Step by step solution

01

- Understand the Division

Determine what the division is asking for. The problem is asking to divide 36 by -6.
02

- Calculate the Division

Perform the division: \[ 36 \times \frac{1}{-6} = -6 \]
03

- Verify the Result

To verify, multiply the result by the divisor: \( -6 \times -6 \). The multiplication should give the original number.\[ -6 \times -6 = 36 \]. This confirms the result.

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Key Concepts

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

Division of Integers
In mathematics, division is one of the fundamental operations. When we talk about dividing integers, we're referring to taking one integer and determining how many times it can be evenly divided by another integer. This involves two main parts: the dividend (the number being divided) and the divisor (the number you are dividing by).

For example, in the exercise 36 梅 (-6), 36 is the dividend, and -6 is the divisor. The way we express this mathematically is: \( 36 \div (-6) \).

When performing this operation, you might encounter two situations for the sign of the numbers:
  • Both numbers are positive or both are negative: The result will be positive.
  • One number is positive and the other is negative: The result will be negative.
This is a crucial point to remember for correctly solving such problems.
Negative Numbers
Negative numbers can sometimes confuse students because they seem contrary to the intuition developed with positive numbers. The main idea is that negative numbers represent values less than zero, often visualized as being 'to the left of zero' on a number line.

In division and multiplication involving negative numbers, the rules for determining the sign of the result are:
  • Negative 脳 Negative = Positive: For example, \(-6 \times -6 = 36\).
  • Positive 脳 Negative = Negative: For example, \(36 \div (-6) = -6\).

Applying this to our example, since we are dividing a positive number (36) by a negative number (-6), the result is negative, so \ 36 \div -6 = -6 \.
Verification of Results
Verification is vital in mathematics to ensure that your solutions are correct. One efficient way to verify a division result is through multiplication. Essentially, if you divide a number by another number, you should be able to reverse this operation by multiplying the result by the divisor to get back to the original number.

This method can be seen in our exercise for confirming the division of 36 by -6:
  • First, divide: \( 36 \div -6 = -6 \).
  • Next, verify by multiplication: \( -6 \times -6 = -36 \).
  • This resulting product should be equal to the original dividend, 36. Since it matches, we confirm that our division result \( 36 \div -6 = -6 \) is correct.

This double-checking process helps catch any errors and reinforces the correct understanding of the division operation.

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