Finding The Equivalent Expression To 6+(2+3) Times 5

In the realm of mathematics, evaluating expressions accurately hinges on adhering to the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This article delves into the process of simplifying the expression $6+(2+3) \times 5$ and meticulously examines the provided options to pinpoint the equivalent expression. Understanding the order of operations is paramount not only for academic pursuits but also for various real-world applications involving calculations and problem-solving.

Deciphering the Original Expression: $6+(2+3) \times 5$

Let's embark on a step-by-step journey to unravel the expression $6+(2+3) \times 5$. This will serve as our benchmark against which we'll evaluate the given options. To accurately decipher this mathematical puzzle, we must rigorously adhere to the order of operations, a fundamental principle in mathematics. The acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) provides a roadmap for navigating the intricacies of mathematical expressions. First and foremost, we address the parentheses. Within the parentheses, we encounter the sum of 2 and 3, a straightforward calculation that yields 5. This initial step simplifies our expression to $6 + 5 \times 5$.

Next, the order of operations dictates that we tackle multiplication before venturing into addition. We observe the product of 5 and 5, which confidently presents us with 25. Our expression now elegantly transforms into $6 + 25$. With the multiplication hurdle cleared, we arrive at the final act: addition. Adding 6 to 25, we arrive at the conclusive result of 31. Therefore, the expression $6 + (2 + 3) \times 5$ unequivocally evaluates to 31. This meticulous breakdown not only unveils the solution but also underscores the paramount importance of adhering to the order of operations. In the mathematical landscape, precision is key, and the order of operations serves as our guiding star, ensuring that we navigate complex expressions with accuracy and confidence. By methodically dissecting the expression, we have established a solid foundation for comparing and contrasting it with the options presented, setting the stage for our quest to identify the equivalent expression.

Evaluating Option A: $5+4 \times(5-6)$

Now, let's turn our attention to Option A: $5+4 \times (5-6)$. Our mission is to meticulously evaluate this expression, ensuring that we faithfully adhere to the prescribed order of operations. Much like our approach with the original expression, we will dissect this mathematical puzzle step by step, leaving no room for ambiguity. The first task at hand is to conquer the parentheses. Within the parentheses, we encounter the subtraction of 6 from 5. This seemingly simple operation yields a result of -1. Thus, our expression undergoes a transformation, morphing into $5 + 4 \times (-1)$.

With the parentheses successfully navigated, we now shift our focus to the realm of multiplication. We observe the product of 4 and -1, a calculation that confidently presents us with -4. Our expression now elegantly evolves into $5 + (-4)$. The stage is set for the final act: addition. Adding 5 to -4, we arrive at the conclusive result of 1. Therefore, Option A, $5 + 4 \times (5 - 6)$, unequivocally evaluates to 1. Comparing this result with the value we obtained for the original expression, which was 31, a stark contrast emerges. It becomes clear that Option A does not align with our target value. This meticulous evaluation serves as a crucial step in our quest to identify the expression that mirrors the original. By methodically dissecting each option, we inch closer to unveiling the equivalent expression, ensuring that our final selection is grounded in precision and mathematical accuracy.

Evaluating Option B: $1+10 \times 3$

Our exploration now leads us to Option B: $1+10 \times 3$. In the pursuit of mathematical clarity, we shall meticulously dissect this expression, adhering steadfastly to the revered order of operations. Our approach mirrors the precision we employed in evaluating the original expression and Option A. First and foremost, we turn our attention to the realm of multiplication. Within the expression, we encounter the product of 10 and 3, a straightforward calculation that confidently yields 30. This initial step transforms our expression into $1 + 30$.

With the multiplication hurdle cleared, we arrive at the final act: addition. Adding 1 to 30, we arrive at the conclusive result of 31. Therefore, Option B, $1 + 10 \times 3$, unequivocally evaluates to 31. A moment of mathematical revelation dawns upon us as we compare this result with the value we obtained for the original expression, which also stood at 31. A resounding alignment emerges, signaling that Option B holds the key to our quest. Option B mirrors the value of the original expression, marking it as a prime candidate for the equivalent expression. This meticulous evaluation underscores the power of methodical dissection and the unwavering adherence to the order of operations. As we continue our exploration, the significance of Option B's alignment with the original expression resonates, guiding our path toward the definitive answer.

Evaluating Option C: $9 \times 5+10$

Our mathematical journey now guides us to Option C: $9 \times 5 + 10$. With the same unwavering commitment to precision, we embark on a meticulous evaluation of this expression, steadfastly upholding the principles of the order of operations. Our approach remains consistent: dissecting the expression step by step, ensuring that each operation is executed in its designated sequence. The initial focus of our attention rests upon the realm of multiplication. Within the expression, we encounter the product of 9 and 5, a calculation that confidently yields 45. This crucial step transforms our expression into $45 + 10$.

With the multiplication phase successfully navigated, we progress to the concluding act: addition. Adding 45 to 10, we arrive at the definitive result of 55. Therefore, Option C, $9 \times 5 + 10$, unequivocally evaluates to 55. A moment of comparison beckons as we juxtapose this result with the value we obtained for the original expression, which stood at 31. A clear divergence emerges, indicating that Option C does not share the same numerical essence as our target expression. This meticulous evaluation serves as a testament to the importance of thoroughness in mathematical analysis. By systematically dissecting each option, we gain clarity, enabling us to discern which expressions align with our objective and which veer away. The disparity between Option C's value and the original expression reinforces our pursuit of the true equivalent, driving us forward in our mathematical exploration.

Evaluating Option D: $(4 \times 5)+3$

Our quest for the equivalent expression now leads us to Option D: $(4 \times 5) + 3$. Maintaining our steadfast commitment to mathematical rigor, we embark on a meticulous evaluation of this expression, firmly guided by the principles of the order of operations. Our approach remains consistent: a step-by-step dissection, ensuring that each operation is executed with precision and accuracy. The initial focus of our attention rests upon the parentheses. Within the parentheses, we encounter the product of 4 and 5, a calculation that confidently yields 20. This crucial step transforms our expression into $20 + 3$.

With the operations within the parentheses successfully addressed, we progress to the concluding act: addition. Adding 20 to 3, we arrive at the definitive result of 23. Therefore, Option D, $(4 \times 5) + 3$, unequivocally evaluates to 23. A moment of comparison beckons as we juxtapose this result with the value we obtained for the original expression, which stood at 31. A clear divergence emerges, indicating that Option D does not share the same numerical essence as our target expression. This meticulous evaluation reinforces the importance of thoroughness in mathematical analysis. By systematically dissecting each option, we gain clarity, enabling us to discern which expressions align with our objective and which deviate. The disparity between Option D's value and the original expression underscores the need for precision in our quest for the equivalent, driving us forward in our mathematical exploration.

Conclusion: Identifying the Equivalent Expression

After a thorough evaluation of all the options, our meticulous journey culminates in the identification of the expression equivalent to $6+(2+3) \times 5$. We embarked on a step-by-step analysis of each option, ensuring that the sacred order of operations guided our every calculation. Our expedition revealed that Option B, $1+10 \times 3$, mirrors the value of the original expression, both proudly standing at 31. The other options, though intriguing in their own right, fell short of this alignment, each yielding a distinct numerical result. Option A presented us with 1, a stark contrast to our target. Option C soared to 55, while Option D settled at 23, neither resonating with the original expression's essence. In the realm of mathematics, precision reigns supreme, and our methodical approach has illuminated the path to the correct answer. Option B emerges as the undisputed champion, the expression that stands shoulder to shoulder with $6+(2+3) \times 5$ in numerical harmony. This conclusion underscores the power of meticulous evaluation and the unwavering adherence to mathematical principles. As we celebrate this triumph of analytical prowess, we carry forward the valuable lessons learned, ready to unravel future mathematical puzzles with confidence and clarity.

Therefore, the expression equivalent to $6+(2+3) \times 5$ is B. $1+10 \times 3$.