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Chapter 10: Problem 7

Divide, if possible. Check each answer. $$ \frac{-48}{-12} $$

Short Answer

Expert verified
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Step by step solution

01

Simplify the Division

To divide \( \frac{-48}{-12} \), simplify the negative signs first. When a negative number is divided by another negative number, the result is a positive number. Therefore, \( \frac{-48}{-12} = \frac{48}{12} \).
02

Divide Numerator by Denominator

Now, perform the division of the positive numbers: \( \frac{48}{12} = 4 \).
03

Verify the Answer

To verify the answer, multiply the quotient by the divisor. If the result equals the original numerator, the division is correct. So, multiply 4 (quotient) by -12 (original divisor): \( 4 \times -12 = -48 \). Since this matches the original numerator with the correct sign (negative), the answer is verified.

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Key Concepts

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

simplifying negative signs
When dealing with division involving negative numbers, the first step is to simplify the negative signs. This step is crucial because it makes the rest of the division easier and helps avoid mistakes. Remember, dividing two negative numbers results in a positive number.
To simplify, we can rewrite the division problem \(\frac{-48}{-12}\) as:\(\frac{48}{12}\). This is because a negative divided by a negative becomes positive. It's like saying two wrongs make a right in terms of math signs.
To emphasize, always remember:
  • Negative divided by negative equals positive.
  • Negative divided by positive equals negative.
  • Positive divided by negative equals negative.
This simplifies our next steps significantly.
positive quotient
After simplifying the negative signs, you're left with a positive division problem. This part is straightforward. For \(\frac{48}{12}\), just divide the numerator (48) by the denominator (12). Parts we need to follow:
1. Perform the division: 48 divided by 12 equals 4.
Thus, the quotient of \(\frac{48}{12}\) is 4.
It's essential to understand the result is positive because we simplified the negative signs earlier. By practicing more with various negative and positive divisions, this concept will become second nature.
verifying quotient
Verification is a final but important step in ensuring our answer is correct. You multiply the quotient obtained by the divisor and see if you get the original numerator.
In our example, the quotient is 4, and the divisor is -12. So, multiply 4 by -12:
\(4 \times -12 = -48\).
Check the result: Does -48 match the original numerator? Yes, it does.
This confirms our division was performed correctly. Verification helps ensure accuracy, making it a good habit, especially when learning new mathematical concepts. It's like double-checking your work to gain confidence in your answers.

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