Which Is The Best Estimate Of $-14 \frac{1}{9}\left(-2 \frac{9}{10}\right$\]?A. $-42$ B. $-28$ C. 28 D. 42

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When it comes to multiplying negative numbers and fractions, it's essential to understand the rules and procedures to arrive at the correct answer. In this article, we will delve into the world of negative numbers and fractions, exploring the best estimate of the product of −1419(−2910)-14 \frac{1}{9}\left(-2 \frac{9}{10}\right).

Understanding Negative Numbers and Fractions

Before we dive into the multiplication, let's briefly review the concepts of negative numbers and fractions.

  • Negative Numbers: A negative number is a number that is less than zero. It is denoted by a minus sign (-) preceding the number. For example, -3 is a negative number.
  • Fractions: A fraction is a way of expressing a part of a whole. It consists of two parts: the numerator (the top number) and the denominator (the bottom number). For example, 3/4 is a fraction.

Multiplying Negative Numbers and Fractions

Now that we have a basic understanding of negative numbers and fractions, let's move on to multiplying them.

When multiplying two negative numbers, the result is always positive. This is because the negative signs cancel each other out.

On the other hand, when multiplying a negative number and a positive number, the result is always negative.

When multiplying two fractions, we multiply the numerators (the top numbers) and the denominators (the bottom numbers) separately.

Step-by-Step Solution

Now that we have a solid understanding of the rules, let's apply them to the given problem.

Step 1: Convert the Mixed Numbers to Improper Fractions

To multiply the mixed numbers, we need to convert them to improper fractions.

  • −1419-14 \frac{1}{9} can be converted to an improper fraction as follows:

    −1419=−14×9+19=−126+19=−1259-14 \frac{1}{9} = \frac{-14 \times 9 + 1}{9} = \frac{-126 + 1}{9} = \frac{-125}{9}

  • −2910-2 \frac{9}{10} can be converted to an improper fraction as follows:

    −2910=−2×10+910=−20+910=−1110-2 \frac{9}{10} = \frac{-2 \times 10 + 9}{10} = \frac{-20 + 9}{10} = \frac{-11}{10}

Step 2: Multiply the Numerators and Denominators

Now that we have the improper fractions, let's multiply the numerators and denominators.

  • Numerator: −125×−11=1375-125 \times -11 = 1375
  • Denominator: 9×10=909 \times 10 = 90

Step 3: Simplify the Result

Now that we have the product of the numerators and denominators, let's simplify the result.

  • 137590=152590=15518\frac{1375}{90} = 15 \frac{25}{90} = 15 \frac{5}{18}

Step 4: Estimate the Answer

Now that we have the simplified result, let's estimate the answer.

  • The numerator is 15, and the denominator is 18. This means that the result is slightly less than 1.

Conclusion

In conclusion, the best estimate of the product of −1419(−2910)-14 \frac{1}{9}\left(-2 \frac{9}{10}\right) is −28-28.

Answer Key

  • A. −42-42
  • B. −28-28
  • C. 28
  • D. 42

In the previous article, we explored the concept of multiplying negative numbers and fractions. However, we understand that there may be some questions and doubts that still linger. In this article, we will address some of the most frequently asked questions related to multiplying negative numbers and fractions.

Q: What is the rule for multiplying negative numbers?

A: When multiplying two negative numbers, the result is always positive. This is because the negative signs cancel each other out.

Q: What is the rule for multiplying a negative number and a positive number?

A: When multiplying a negative number and a positive number, the result is always negative.

Q: How do I multiply fractions?

A: To multiply fractions, you multiply the numerators (the top numbers) and the denominators (the bottom numbers) separately.

Q: What is the difference between multiplying mixed numbers and improper fractions?

A: When multiplying mixed numbers, you need to convert them to improper fractions first. This is because mixed numbers are a combination of a whole number and a fraction, while improper fractions are a single fraction with a numerator greater than the denominator.

Q: Can I simplify the result of multiplying fractions?

A: Yes, you can simplify the result of multiplying fractions by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both numbers by the GCD.

Q: How do I estimate the answer when multiplying fractions?

A: To estimate the answer when multiplying fractions, you can look at the numerator and denominator separately. If the numerator is larger than the denominator, the result will be greater than 1. If the numerator is smaller than the denominator, the result will be less than 1.

Q: What is the best way to approach multiplying negative numbers and fractions?

A: The best way to approach multiplying negative numbers and fractions is to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate any expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I use a calculator to multiply negative numbers and fractions?

A: Yes, you can use a calculator to multiply negative numbers and fractions. However, it's essential to understand the underlying math concepts to ensure that you are using the calculator correctly.

Conclusion

In conclusion, multiplying negative numbers and fractions can be a challenging task, but with the right approach and understanding of the underlying math concepts, it can be done with ease. We hope that this article has addressed some of the most frequently asked questions related to multiplying negative numbers and fractions and has provided you with a better understanding of this important math concept.

Additional Resources

If you are looking for additional resources to help you understand multiplying negative numbers and fractions, here are a few suggestions:

  • Khan Academy: Khan Academy offers a comprehensive math course that covers multiplying negative numbers and fractions.
  • Mathway: Mathway is an online math problem solver that can help you solve math problems, including multiplying negative numbers and fractions.
  • IXL: IXL is an online math practice platform that offers interactive math lessons and exercises to help you practice multiplying negative numbers and fractions.

We hope that this article has been helpful in addressing your questions and doubts related to multiplying negative numbers and fractions. If you have any further questions or concerns, please don't hesitate to reach out.