Use Compatible Numbers To Estimate \[$-29\left(-\frac{2}{7}\right)\$\].Given That \[$-\frac{2}{7} \approx -\frac{2}{8} \approx -\frac{1}{4}\$\], Evaluate:A. \[$-7 \frac{1}{4}\$\] B. \[$-7\$\] C. \[$7
Introduction
Estimating negative fractions can be a challenging task, especially when dealing with complex expressions. However, by using compatible numbers, we can simplify the process and arrive at a more accurate estimate. In this article, we will explore the concept of compatible numbers and how to use them to estimate negative fractions.
What are Compatible Numbers?
Compatible numbers are rational numbers that are close to each other in value. They are often used in estimation problems to simplify complex calculations. In the context of negative fractions, compatible numbers can be used to estimate the value of an expression.
Given Expression
The given expression is {-29\left(-\frac{2}{7}\right)$}$. To estimate this expression, we need to find a compatible number for [-\frac{2}{7}$.
Finding Compatible Numbers
The given compatible numbers for [-\frac{2}{7}$ are [-\frac{2}{8}$ and [-\frac{1}{4}$. These numbers are close to [-\frac{2}{7}$ and can be used to estimate the expression.
Estimating the Expression
To estimate the expression, we can substitute the compatible numbers into the expression. Let's use [-\frac{2}{8}$ as the compatible number.
[$-29\left(-\frac{2}{7}\right) \approx -29\left(-\frac{2}{8}\right)$.
Simplifying the expression, we get:
[$\frac{29 \times 2}{8} = \frac{58}{8} = 7\frac{2}{8}$.
However, we are given that [-\frac{2}{7} \approx -\frac{1}{4}$. Let's use this compatible number to estimate the expression.
[$-29\left(-\frac{2}{7}\right) \approx -29\left(-\frac{1}{4}\right)$.
Simplifying the expression, we get:
[$\frac{29 \times 1}{4} = \frac{29}{4} = 7\frac{1}{4}$.
Conclusion
In conclusion, we have estimated the expression [$-29\left(-\frac{2}{7}\right)$ using compatible numbers. We found that the expression is approximately equal to [$7\frac{1}{4}$.
Discussion
The discussion category for this article is mathematics. The article explores the concept of compatible numbers and how to use them to estimate negative fractions.
Answer Key
The answer key for this article is:
A. [$-7 \frac{1}{4}$ is incorrect.
B. [$-7$ is incorrect.
C. [$7\frac{1}{4}$ is the correct answer.
Additional Resources
For more information on compatible numbers and estimation, please refer to the following resources:
FAQs
Q: What are compatible numbers? A: Compatible numbers are rational numbers that are close to each other in value.
Q: How do I use compatible numbers to estimate negative fractions? A: To estimate negative fractions, find a compatible number for the fraction and substitute it into the expression.
Q: What is the correct answer for the given expression? A: The correct answer is [$7\frac{1}{4}$.
Q: What are compatible numbers?
A: Compatible numbers are rational numbers that are close to each other in value. They are often used in estimation problems to simplify complex calculations.
Q: How do I find compatible numbers?
A: To find compatible numbers, look for rational numbers that are close to the given number. You can use a calculator or estimate the value of the number to find compatible numbers.
Q: What are some examples of compatible numbers?
A: Some examples of compatible numbers include:
- [-\frac{2}{7} \approx -\frac{2}{8} \approx -\frac{1}{4}$
- [\frac{3}{4} \approx \frac{4}{5} \approx \frac{5}{6}$
Q: How do I use compatible numbers to estimate negative fractions?
A: To estimate negative fractions, find a compatible number for the fraction and substitute it into the expression. For example, if you want to estimate [-\frac{2}{7}$, you can use [-\frac{2}{8}$ or [-\frac{1}{4}$ as a compatible number.
Q: What are some common mistakes to avoid when using compatible numbers?
A: Some common mistakes to avoid when using compatible numbers include:
- Using incompatible numbers that are too far apart in value
- Not checking the accuracy of the compatible numbers
- Not using the compatible numbers to estimate the expression correctly
Q: How do I check the accuracy of my compatible numbers?
A: To check the accuracy of your compatible numbers, compare the estimated value of the expression with the actual value. If the estimated value is close to the actual value, then the compatible numbers are accurate.
Q: What are some real-world applications of compatible numbers and estimation?
A: Some real-world applications of compatible numbers and estimation include:
- Estimating the cost of a project
- Estimating the time required to complete a task
- Estimating the value of a stock or investment
Q: How can I practice using compatible numbers and estimation?
A: You can practice using compatible numbers and estimation by working on estimation problems and checking your answers with a calculator or by using a different method.
Q: What are some resources for learning more about compatible numbers and estimation?
A: Some resources for learning more about compatible numbers and estimation include:
- Math Open Reference
- Khan Academy
- Mathway
- Online estimation calculators and tools
Q: Can I use compatible numbers to estimate decimals?
A: Yes, you can use compatible numbers to estimate decimals. For example, if you want to estimate [0.5$, you can use [0.4$ or [0.6$ as a compatible number.
Q: Can I use compatible numbers to estimate percents?
A: Yes, you can use compatible numbers to estimate percents. For example, if you want to estimate [25%$, you can use [20%$ or [30%$ as a compatible number.
Q: Can I use compatible numbers to estimate fractions with different denominators?
A: Yes, you can use compatible numbers to estimate fractions with different denominators. For example, if you want to estimate [\frac{1}{3}$, you can use [\frac{1}{4}$ or [\frac{2}{5}$ as a compatible number.
Q: Can I use compatible numbers to estimate mixed numbers?
A: Yes, you can use compatible numbers to estimate mixed numbers. For example, if you want to estimate [2\frac{1}{2}$, you can use [2\frac{1}{3}$ or [2\frac{2}{3}$ as a compatible number.