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Chapter 5: Problem 31

Divide. $$-19 \div(-6)$$

Short Answer

Expert verified
3.1667

Step by step solution

01

Understand the Sign Rules for Division

When dividing two numbers, if both numbers have the same sign, the quotient is positive. If the numbers have different signs, the quotient is negative.
02

Determine the Signs

In this problem, both numbers are negative: -19 (dividend) and -6 (divisor). Since both numbers have the same sign, the quotient will be positive.
03

Perform the Division

Divide the absolute values of the numbers: 19 divided by 6. This results in approximately 3.1667.

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Key Concepts

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

Sign Rules for Division
When dividing integers, understanding the sign rules is crucial. The rules are simple:
  • If the two numbers have the same sign (both positive or both negative), the result or quotient will be positive.
  • If the numbers have different signs (one positive and one negative), the result will be negative.
For example, if you divide -20 by -4, both numbers are negative, so the quotient is positive 5. Similarly, if you divide 20 by -4, the numbers have opposite signs, so the quotient is negative, resulting in -5. Keep these rules in mind, and you'll always know the sign of your division results.
Absolute Value
Before dividing numbers, it's essential to look at their absolute values. The absolute value of a number is its distance from 0 on the number line, regardless of direction. It's always a positive number.
For example, the absolute value of -7 is 7, written as \(|-7| = 7 \). Using absolute values can make calculations easier. You just have to apply the sign rules after dividing the absolute values. For instance, if dividing -19 by -6, you would first convert them to their absolute values, 19 and 6, which simplifies the division process.
Positive Quotient
After understanding signs and absolute values, knowing when your quotient is positive is easy. Apply the sign rules and compute using absolute values.
Let's consider the exercise problem: \(-19 \div (-6)\). Since both -19 and -6 are negative, their signs are the same, resulting in a positive quotient.
Now, calculate the absolute values: 19 divided by 6 gives approximately 3.1667. Therefore, the quotient of \(-19 \div -6\) is positive 3.1667.
Remember to first determine the sign, then calculate using absolute values. This will help you consistently get the correct positive or negative quotient.

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