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Chapter 2: Problem 62

Divide the real numbers, if possible. $$\frac{30}{-6}$$

Short Answer

Expert verified
-5

Step by step solution

01

Understand the Problem

We need to divide the given real numbers 30 and -6.
02

Perform the Division

To divide 30 by -6, simply perform the division operation: \ \ \(\frac{30}{-6} = -5\)
03

Verify the Result

Check by multiplying the quotient -5 by -6 to ensure it equals the numerator 30: \ \ \(-5 \times -6 = 30\)

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Key Concepts

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

Division of Integers
When we talk about dividing integers, we are essentially distributing one number (the dividend) by another (the divisor). In our exercise, we are dividing 30 by -6.

To divide these numbers, we perform the division operation: \[ \frac{30}{-6} = -5 \] The result of dividing any integer by another can result in a positive or negative quotient, depending on the signs of the numbers involved.

Here's a simple rule to remember:
  • If the two integers have the same sign (both positive or both negative), the quotient will be positive.
  • If the two integers have different signs (one positive and one negative), the quotient will be negative.
In our example, 30 is positive and -6 is negative. Hence, the result \(-5\) is negative.
Multiplication Verification
After performing division, it's important to verify the result. This is done by multiplying the quotient by the divisor to check if we get back the numerator. This verification helps in ensuring our division was correct.

In our given example, we divide 30 by -6 to get -5. To verify: \[-5 \times -6 = 30\]

A few points to remember:
  • Multiplying two negative numbers results in a positive number.
  • When verified, the product should match the original dividend.
Therefore, multiplying -5 by -6 gives us 30, which matches our original number, verifying our result as accurate.
Negative Numbers
Negative numbers can often be confusing, but they follow specific rules which make calculations straightforward when understood correctly.

Here's a quick guide:
  • A negative number is any number less than zero.
  • The product of two negative numbers is positive: \(-5 \times -6 = 30\)
  • The product of a positive and a negative number is negative: \(-5 \times 6 = -30\) or \(5 \times -6 = -30\)
  • The quotient from dividing a positive by a negative or a negative by a positive is always negative, as seen in our exercise: \(\frac{30}{-6} = -5\)
Understanding these rules helps in avoiding mistakes during calculations. Negative numbers are just as easy to work with as positive ones once you get the hang of these rules.

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Most popular questions from this chapter

One of the most famous blizzards in the United States was the blizzard of \(1888 .\) In one part of Nebraska, the temperature plunged from \(40^{\circ} \mathrm{F}\) to \(-25^{\circ} \mathrm{F}\) in \(5 \mathrm{hr}\). What was the average change in temperature during this time?

During a drought, the change in elevation for a retention pond was \(-9\) in. over a 1 -month period. At this rate, what will the change in elevation be after 5 months?

a. What number must be multiplied by \(-4\) to obtain \(-36 ?\) b. What number must be multiplied by \(-4\) to obtain \(36 ?\)

Divide the real numbers, if possible. $$\frac{-48}{-3}$$

Divide the real numbers, if possible. $$60 \div(-3)$$
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