(1/2+1/3+1/6)^2011 :(4/12)^2=?

Mar 9, 2025 by ADMIN 32 views

Solving the Math Puzzle: (1/2+1/3+1/6)^2011 :(4/12)^2=?

Math puzzles and brain teasers are an excellent way to challenge our problem-solving skills and keep our minds sharp. In this article, we will delve into a fascinating math puzzle that involves simplifying complex expressions and applying mathematical concepts to arrive at the solution. The puzzle is as follows: (1/2+1/3+1/6)^2011 :(4/12)^2=? Let's break it down step by step and explore the solution.

Understanding the Puzzle

The given puzzle involves two main expressions: (1/2+1/3+1/6)^2011 and (4/12)^2. To solve this puzzle, we need to simplify each expression separately and then compare the results.

Simplifying the First Expression

The first expression is (1/2+1/3+1/6)^2011. To simplify this expression, we need to find a common denominator for the fractions 1/2, 1/3, and 1/6. The least common multiple (LCM) of 2, 3, and 6 is 6. Therefore, we can rewrite the fractions with a common denominator of 6:

1/2 = 3/6 1/3 = 2/6 1/6 = 1/6

Now, we can add the fractions:

(3/6 + 2/6 + 1/6) = 6/6 = 1

So, the simplified expression is (1)^2011. Since any number raised to the power of 0 is 1, and any number raised to the power of 1 is itself, we can conclude that (1)^2011 = 1.

Simplifying the Second Expression

The second expression is (4/12)^2. To simplify this expression, we need to find the square of the fraction 4/12. We can do this by multiplying the numerator and denominator by the same number:

(4/12)^2 = (44)/(1212) = 16/144

We can simplify the fraction 16/144 by dividing both the numerator and denominator by their greatest common divisor, which is 16:

16/144 = 1/9

Comparing the Results

Now that we have simplified both expressions, we can compare the results. The first expression is (1)^2011 = 1, and the second expression is 1/9. Since 1 is not equal to 1/9, the puzzle is not asking for a direct comparison between the two expressions. Instead, it is asking us to evaluate the expressions separately and then provide the result.

In conclusion, the solution to the math puzzle (1/2+1/3+1/6)^2011 :(4/12)^2=? is 1 and 1/9, respectively. The puzzle requires us to simplify complex expressions and apply mathematical concepts to arrive at the solution. By following the steps outlined in this article, we can confidently solve the puzzle and understand the underlying mathematical concepts.

Additional Tips and Tricks

Here are some additional tips and tricks to help you solve math puzzles like this one:

Simplify complex expressions: When faced with complex expressions, try to simplify them by finding a common denominator or using other mathematical techniques.
Apply mathematical concepts: Math puzzles often require the application of mathematical concepts, such as algebra, geometry, or trigonometry. Make sure to use the relevant concepts to arrive at the solution.
Check your work: Always check your work to ensure that you have arrived at the correct solution. This will help you avoid mistakes and build confidence in your problem-solving skills.

Math puzzles and brain teasers are an excellent way to challenge our problem-solving skills and keep our minds sharp. By following the steps outlined in this article, we can confidently solve the puzzle and understand the underlying mathematical concepts. Remember to simplify complex expressions, apply mathematical concepts, and check your work to arrive at the solution. With practice and patience, you can become a math puzzle master and tackle even the most challenging puzzles with ease.
Q&A: (1/2+1/3+1/6)^2011 :(4/12)^2=?

In our previous article, we solved the math puzzle (1/2+1/3+1/6)^2011 :(4/12)^2=? and arrived at the solution. However, we received many questions from readers who wanted to know more about the puzzle and its solution. In this article, we will answer some of the most frequently asked questions about the puzzle.

Q: What is the common denominator for the fractions 1/2, 1/3, and 1/6?

A: The least common multiple (LCM) of 2, 3, and 6 is 6. Therefore, we can rewrite the fractions with a common denominator of 6:

1/2 = 3/6 1/3 = 2/6 1/6 = 1/6

Q: Why did we add the fractions (3/6 + 2/6 + 1/6) = 6/6 = 1?

A: We added the fractions because we wanted to simplify the expression (1/2+1/3+1/6)^2011. By adding the fractions, we were able to find a common denominator and simplify the expression.

Q: What is the significance of the exponent 2011 in the expression (1)^2011?

A: The exponent 2011 is significant because it tells us how many times to multiply the base number 1 by itself. Since any number raised to the power of 0 is 1, and any number raised to the power of 1 is itself, we can conclude that (1)^2011 = 1.

Q: Why did we simplify the fraction (4/12)^2 by dividing both the numerator and denominator by their greatest common divisor, which is 16?

A: We simplified the fraction (4/12)^2 by dividing both the numerator and denominator by their greatest common divisor, which is 16, to make the fraction easier to work with. This is a common technique used in mathematics to simplify fractions.

Q: What is the final answer to the puzzle (1/2+1/3+1/6)^2011 :(4/12)^2=?

A: The final answer to the puzzle is 1 and 1/9, respectively.

Q: Can you provide more examples of math puzzles like this one?

A: Yes, we can provide more examples of math puzzles like this one. Here are a few examples:

(1/4+1/8+1/16)^3 :(9/16)^2
(2/3+1/6+1/9)^2 :(3/4)^3
(1/2+1/4+1/8)^4 :(3/8)^2

In conclusion, we hope this Q&A article has provided you with a better understanding of the math puzzle (1/2+1/3+1/6)^2011 :(4/12)^2=? and its solution. If you have any more questions or need further clarification, please don't hesitate to ask. We are always here to help.

Here are some additional resources that you may find helpful:

Math textbooks: If you want to learn more about mathematics, consider purchasing a math textbook that covers the topics you are interested in.
Online math resources: There are many online resources available that can help you learn mathematics, including video tutorials, online courses, and practice problems.
Math communities: Joining a math community can be a great way to connect with other math enthusiasts and get help with math problems.