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

Understanding the Problem

When dealing with negative numbers and fractions, it's essential to understand the rules of multiplication. In this problem, we're asked to estimate the result of multiplying $-14 \frac{1}{9}$ by $-2 \frac{9}{10}$. To solve this, we need to follow the order of operations and apply the rules of multiplying negative numbers and fractions.

Breaking Down the Problem

To start, let's break down the given numbers into their decimal equivalents. $-14 \frac{1}{9}$ can be written as $-14.1111...$, and $-2 \frac{9}{10}$ can be written as $-2.9$. Now, we need to multiply these two numbers together.

Multiplying Negative Numbers

When multiplying two negative numbers, the result is always positive. This is because the negative signs cancel each other out. So, in this case, we can ignore the negative signs and focus on multiplying the absolute values of the numbers.

Multiplying Fractions

To multiply fractions, we need to multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom) separately. In this case, we have:

$-14.1111... \times -2.9 = 40.9999...$

Multiplying Decimals

To multiply decimals, we can simply multiply the numbers as if they were whole numbers and then count the number of decimal places in the factors. In this case, we have:

$-14.1111... \times -2.9 = -40.9999...$

Rounding the Result

Since we're asked to estimate the result, we can round the answer to the nearest whole number. In this case, we can round $-40.9999...$ to $-41$.

Conclusion

Based on our calculations, the best estimate of $-14 \frac{1}{9}\left(-2 \frac{9}{10}\right)$ is $-41$. This is the correct answer among the given options.

Why is this the Correct Answer?

The correct answer is $-41$ because when we multiply $-14.1111...$ by $-2.9$, we get $-40.9999...$, which rounds to $-41$. This is the only option that matches our calculation.

What if I Made a Mistake?

If you made a mistake in your calculation, you might get a different answer. However, the correct answer is $-41$, so if you're not getting this answer, you might want to double-check your work.

What if I Used a Calculator?

If you used a calculator to solve this problem, you might get a different answer. However, the correct answer is $-41$, so if you're not getting this answer, you might want to check your calculator settings.

What if I Used a Different Method?

If you used a different method to solve this problem, you might get a different answer. However, the correct answer is $-41$, so if you're not getting this answer, you might want to check your work.

Conclusion

In conclusion, the best estimate of $-14 \frac{1}{9}\left(-2 \frac{9}{10}\right)$ is $-41$. This is the correct answer among the given options.

Final Answer

The final answer is $-41$.

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: How do I multiply fractions?

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

Q: What is the difference between multiplying decimals and multiplying fractions?

A: When multiplying decimals, you can simply multiply the numbers as if they were whole numbers and then count the number of decimal places in the factors. When multiplying fractions, you need to multiply the numerators and denominators separately.

Q: Can I use a calculator to solve this problem?

A: Yes, you can use a calculator to solve this problem. However, make sure to check your calculator settings and double-check your work to ensure accuracy.

Q: What if I made a mistake in my calculation?

A: If you made a mistake in your calculation, you might get a different answer. However, the correct answer is $-41$, so if you're not getting this answer, you might want to double-check your work.

Q: Can I use a different method to solve this problem?

A: Yes, you can use a different method to solve this problem. However, the correct answer is $-41$, so if you're not getting this answer, you might want to check your work.

Q: Why is it important to follow the order of operations?

A: Following the order of operations is essential when solving mathematical problems. It ensures that you perform the operations in the correct order and avoid errors.

Q: Can I round my answer to the nearest whole number?

A: Yes, you can round your answer to the nearest whole number. However, make sure to check your work and ensure that your answer is accurate.

Q: What if I'm still unsure about the answer?

A: If you're still unsure about the answer, you might want to ask for help from a teacher or tutor. They can provide you with additional guidance and support to ensure that you understand the concept.

Q: Can I use a calculator to check my work?

A: Yes, you can use a calculator to check your work. This can help you ensure that your answer is accurate and avoid errors.

Q: What is the final answer to the problem?

A: The final answer to the problem is $-41$.

Conclusion

In conclusion, multiplying negative numbers and fractions can be a challenging concept, but with practice and patience, you can master it. Remember to follow the order of operations, multiply fractions correctly, and round your answer to the nearest whole number. If you're still unsure about the answer, don't hesitate to ask for help.

Final Answer

The final answer is $-41$.