Write Two Expressions Where The Solution Is 28

Two Expressions That Equal 28: Exploring Mathematical Creativity

This article delves into the fascinating world of mathematical expressions, specifically focusing on crafting two distinct expressions that both evaluate to 28. While seemingly simple, this exercise opens the door to exploring various mathematical operations, showcasing the versatility and beauty of numbers. We'll explore different approaches, focusing on clarity and step-by-step explanations to make the concepts accessible to a wide range of readers, from beginners to those seeking a more challenging mathematical puzzle. We'll also touch upon the broader implications of such exercises in enhancing mathematical understanding and problem-solving skills.

Expression 1: A Blend of Basic Operations

Our first expression will utilize fundamental arithmetic operations: addition, subtraction, multiplication, and division. The key to creating interesting expressions lies in combining these operations strategically to achieve the desired result.

Let's break down the expression:

(15 + 13) * 1

This expression, while seemingly straightforward, demonstrates a core principle: the order of operations. Parentheses dictate that we perform the addition within them first:

15 + 13 = 28

Then, we multiply the result by 1:

28 * 1 = 28

Therefore, the complete expression (15 + 13) * 1 evaluates to 28.

Understanding Order of Operations (PEMDAS/BODMAS)

The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) is crucial to understanding the order in which mathematical operations are carried out. Without adhering to these rules, we risk arriving at incorrect results. This expression highlights the importance of using parentheses to clearly define the sequence of operations.

Expression 2: Exploring Exponents and Roots

Our second expression will introduce exponents and potentially roots, adding another layer of complexity and showcasing the richness of mathematical operations. This expression will not only demonstrate that 28 can be achieved through multiple methods, but also illustrate the powerful capabilities of exponents in manipulating numerical values.

Let's construct the expression:

(√676) + 30 - 24/3 - 2

This expression involves several steps:

1. Square Root: We begin by calculating the square root of 676. The square root of a number is a value that, when multiplied by itself, equals the original number. In this case:

   √676 = 26

2. Division: Next, we handle the division operation:

   24/3 = 8

3. Addition and Subtraction: Finally, we combine the results through addition and subtraction, following the order of operations:

   26 + 30 - 8 - 2 = 46

This expression, unlike the previous one, uses a variety of operations, demonstrating how multiple mathematical concepts can be combined to achieve a specific numerical target. While it currently doesn't reach 28, let's explore modifications to obtain the correct result. Our goal now is to find a modification to achieve 28. Let's attempt the following expression:

*(√(4*7^2) ) + (7!/(6!5!)) + 10/2 - 4

This expression involves:

1. Parentheses and Exponents: Let's address the operations inside the first set of parentheses. We have:

4 * 7^2 = 4 * 49 = 196

√196 = 14

2. Factorial: Next, we deal with the factorial operation:

7!/(6!5!) = (7654321) / ((654321) * (54321)) = 7/(54321) = 7/120 = Incorrect.

Let's rework the factorial part to make this expression solvable:

7!/6! = 7, therefore:

14 + 7 + 5 -4 = 22. This doesn't work. Let's try something else. This example demonstrates the iterative nature of problem-solving. We may need to try a different approach. Let's make this easier:

(√(676) - 12 + 16/2)

1. Square Root: √676 = 26

2. Division: 16/2 = 8

3. Addition and Subtraction: 26 - 12 + 8 = 22. Still incorrect.

Let's try a completely different approach for a simpler expression:

7 * 4

This expression directly multiplies 7 and 4, resulting in:

7 * 4 = 28

This simpler expression achieves our goal effectively, highlighting that multiple solutions exist for the same mathematical problem.

The Importance of Mathematical Expression Practice

The exercises of creating expressions that equal a specific number are more than just mathematical puzzles. They provide numerous benefits:

• Enhanced Problem-Solving Skills: Finding different ways to express the same numerical value sharpens problem-solving abilities. It encourages thinking outside the box and exploring various mathematical strategies.

• Strengthened Number Sense: Practicing such exercises improves familiarity with numbers and their relationships, enhancing intuition and mental calculation skills.

• Improved Understanding of Operations: Manipulating numbers and operations reinforces understanding of fundamental mathematical concepts such as order of operations, exponents, roots, and factorials.

Expanding the Challenge: Beyond 28

Once comfortable with creating expressions that equal 28, you can expand the challenge by:

• Targeting Different Numbers: Try creating expressions that equal different numbers, gradually increasing the complexity.

• Introducing More Operations: Incorporate logarithmic functions, trigonometric functions, and other advanced operations.

• Setting Constraints: Add constraints such as limiting the number of operations or the types of numbers allowed.

Conclusion: A Journey of Mathematical Discovery

Creating expressions that evaluate to a specific number, like 28 in our case, is an engaging exercise that enhances mathematical understanding and problem-solving skills. It showcases the versatility and elegance of mathematical operations, allowing for creativity and exploration within the constraints of numerical rules. By continuously challenging yourself with similar problems, you can significantly improve your mathematical aptitude and develop a deeper appreciation for the beauty of numbers. Remember to experiment, try different combinations, and don't be afraid to make mistakes – they are essential stepping stones on the path to mathematical mastery.