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Chapter 10: Problem 6

Divide, if possible. Check each answer. $$ -18 \div(-2) $$

Short Answer

Expert verified
The result of -18 梅 -2 is 9.

Step by step solution

01

- Identify the Numbers

First, identify the numbers involved in the division. The two numbers here are -18 and -2.
02

- Understand Division with Negatives

Division involving two negative numbers results in a positive number. This is because a negative divided by a negative equals a positive.
03

- Divide the Absolute Values

Now, ignore the negative signs and divide the absolute values of the numbers. 18 梅 2 = 9
04

- Determine the Final Sign

Since a negative divided by a negative is positive, the result of -18 梅 -2 is positive. Thus, -18 梅 -2 = 9.
05

- Check the Answer

To check the accuracy, multiply the quotient (result) by the divisor. If the product equals the dividend, the answer is correct. 9 脳 -2 = -18, which matches the original dividend. Therefore, the answer is correct.

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero and are symbolized by a minus sign (-). When dealing with negative numbers in division, it is important to remember some rules:
  • Positive divided by positive = positive
  • Negative divided by negative = positive
  • Positive divided by negative = negative
  • Negative divided by positive = negative
In our example, \(-18 \div -2\), we are dividing two negative numbers. As per the rules, the result is positive. Thus, -18 梅 -2 = 9.
Absolute Values
Absolute value refers to the distance a number is from zero on the number line, regardless of direction. For instance, the absolute value of both 18 and -18 is 18. Absolute values are always non-negative.

When dividing with negative numbers, it is often helpful to first consider the absolute values. By ignoring the negative signs, you can perform the division as with positive numbers. For \(-18 \div -2\), we first consider 18 梅 2, which gives us 9. After obtaining the result, we apply the appropriate sign based on the rules for negative numbers.
Mathematics Checking Methods
Verifying your division result is essential in mathematics to ensure accuracy. One common method to check a division result is multiplication. Multiply the quotient (result) by the divisor to see if you get back the dividend.

For our example, \(-18 \div -2 \), we found the result to be 9. To check this, we multiply 9 (quotient) by -2 (divisor). The product is -18, which matches our original dividend, confirming the correctness of our answer.

Another method to check division is using estimation. Approximate the numbers involved and perform the division to see if the result is close to your original calculation.

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