Which Is The Best Estimate Of $\frac{90}{7} + 1 \frac{3}{4}$?A. 2 B. 6 C. 12 D. 24

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Introduction

In mathematics, estimation is a crucial skill that helps us approximate the value of a mathematical expression. It is an essential tool for problem-solving, as it enables us to make educated guesses about the solution to a problem. In this article, we will explore the concept of estimation and apply it to a specific mathematical expression: $\frac{90}{7} + 1 \frac{3}{4}$.

Understanding the Expression

The given expression is a combination of a fraction and a mixed number. To estimate the value of this expression, we need to understand the individual components. The fraction $\frac{90}{7}$ represents the division of 90 by 7, while the mixed number $1 \frac{3}{4}$ represents the sum of 1 and $\frac{3}{4}$.

Estimating the Fraction

To estimate the value of $\frac{90}{7}$, we can use the concept of rounding. We can round 90 to the nearest multiple of 7, which is 98. This gives us an estimate of $\frac{98}{7}$, which is approximately 14.

Estimating the Mixed Number

To estimate the value of $1 \frac{3}{4}$, we can convert the mixed number to an improper fraction. This gives us $\frac{7}{4}$, which is approximately 1.75.

Combining the Estimates

Now that we have estimated the values of the individual components, we can combine them to estimate the value of the entire expression. We can add the estimates of the fraction and the mixed number: $14 + 1.75 = 15.75$.

Comparing the Estimates

The estimated value of the expression is 15.75. Now, let's compare this estimate to the given options:

  • A. 2
  • B. 6
  • C. 12
  • D. 24

Based on our estimate, we can see that option C (12) is the closest to our estimated value.

Conclusion

In conclusion, estimating the value of a mathematical expression is an essential skill that helps us make educated guesses about the solution to a problem. By applying the concept of estimation to the given expression, we were able to approximate the value of $\frac{90}{7} + 1 \frac{3}{4}$ and determine that the best estimate is option C (12).

Why Estimation is Important

Estimation is an important skill in mathematics because it helps us:

  • Make educated guesses about the solution to a problem
  • Approximate the value of a mathematical expression
  • Develop problem-solving skills
  • Improve our understanding of mathematical concepts

Real-World Applications of Estimation

Estimation has many real-world applications, including:

  • Finance: Estimating the value of investments or financial transactions
  • Science: Estimating the value of physical quantities, such as distance or time
  • Engineering: Estimating the value of complex systems or structures
  • Business: Estimating the value of products or services

Tips for Improving Estimation Skills

To improve your estimation skills, try the following:

  • Practice estimating the value of mathematical expressions
  • Use real-world examples to practice estimation
  • Develop your problem-solving skills
  • Improve your understanding of mathematical concepts

Common Estimation Mistakes

When estimating the value of a mathematical expression, it's common to make mistakes. Some common mistakes include:

  • Rounding errors
  • Incorrect conversion of units
  • Failure to consider significant figures
  • Insufficient practice or experience

Conclusion

Q&A: Estimation in Mathematics

Q: What is estimation in mathematics?

A: Estimation is the process of approximating the value of a mathematical expression or a physical quantity. It involves making educated guesses about the solution to a problem, often using rough calculations or mental math.

Q: Why is estimation important in mathematics?

A: Estimation is important in mathematics because it helps us:

  • Make educated guesses about the solution to a problem
  • Approximate the value of a mathematical expression
  • Develop problem-solving skills
  • Improve our understanding of mathematical concepts

Q: How do I estimate the value of a mathematical expression?

A: To estimate the value of a mathematical expression, follow these steps:

  1. Identify the key components of the expression
  2. Use rough calculations or mental math to approximate the value of each component
  3. Combine the approximations to estimate the value of the entire expression

Q: What are some common estimation mistakes?

A: Some common estimation mistakes include:

  • Rounding errors
  • Incorrect conversion of units
  • Failure to consider significant figures
  • Insufficient practice or experience

Q: How can I improve my estimation skills?

A: To improve your estimation skills, try the following:

  • Practice estimating the value of mathematical expressions
  • Use real-world examples to practice estimation
  • Develop your problem-solving skills
  • Improve your understanding of mathematical concepts

Q: What are some real-world applications of estimation?

A: Estimation has many real-world applications, including:

  • Finance: Estimating the value of investments or financial transactions
  • Science: Estimating the value of physical quantities, such as distance or time
  • Engineering: Estimating the value of complex systems or structures
  • Business: Estimating the value of products or services

Q: Can estimation be used in everyday life?

A: Yes, estimation can be used in everyday life. For example, you can use estimation to:

  • Estimate the cost of a meal at a restaurant
  • Estimate the time it will take to complete a task
  • Estimate the amount of money you will need for a project

Q: How can I use estimation to solve problems?

A: To use estimation to solve problems, follow these steps:

  1. Identify the key components of the problem
  2. Use rough calculations or mental math to approximate the value of each component
  3. Combine the approximations to estimate the solution to the problem

Q: What are some tips for using estimation in problem-solving?

A: Some tips for using estimation in problem-solving include:

  • Use rough calculations or mental math to approximate the value of each component
  • Consider the context of the problem and the units involved
  • Use estimation to check your answers and make sure they are reasonable

Conclusion

In conclusion, estimation is an essential skill in mathematics that helps us make educated guesses about the solution to a problem. By applying the concept of estimation to real-world problems, we can develop our problem-solving skills and improve our understanding of mathematical concepts. With practice and experience, you can become a more confident problem-solver and use estimation to tackle a wide range of challenges.