Solving Math Expressions: A Step-by-Step Guide

In this article, we will break down and solve two mathematical expressions step by step. We will tackle the expressions $10 imes(48.5-13)+(9.1+0.9) imes 4$ and $B = 60 imes 12 imes 9-3.2$ . Whether you are a student looking to improve your math skills or just someone who enjoys problem-solving, this guide will help you understand the order of operations and how to approach complex calculations. Let’s dive in!

Understanding Order of Operations

Before we jump into the calculations, it’s crucial to understand the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This order dictates the sequence in which mathematical operations should be performed to ensure accurate results.

First, we handle Parentheses: Operations inside parentheses are always done first. This is essential because it groups terms together and ensures that the operations within are prioritized. Next, we deal with Exponents: This includes powers and roots. After exponents, we move on to Multiplication and Division: These operations are performed from left to right. It’s important to note that multiplication and division have equal priority, so the order in which they appear in the expression matters. Finally, we tackle Addition and Subtraction: Similar to multiplication and division, these operations are performed from left to right. Adhering to PEMDAS is the cornerstone of solving mathematical expressions accurately.

By following PEMDAS, we ensure that we tackle mathematical problems in a systematic way. This not only simplifies the process but also reduces the chances of making errors. Without a clear order, the same expression could yield different results, leading to confusion. Therefore, mastering and applying PEMDAS is a fundamental skill in mathematics. Now, let's put this into practice by solving our first expression.

Solving the First Expression: $10 imes(48.5-13)+(9.1+0.9) imes 4$

Let’s break down the first expression, $10 imes(48.5-13)+(9.1+0.9) imes 4$, step by step, applying the order of operations (PEMDAS) to ensure we arrive at the correct answer. Our initial expression is $10 imes(48.5-13)+(9.1+0.9) imes 4$. The first step in PEMDAS is to address the Parentheses. We have two sets of parentheses in this expression.

First, let’s calculate $(48.5-13)$. Subtracting 13 from 48.5 gives us 35.5. So, $(48.5-13) = 35.5$. Next, we’ll handle the second set of parentheses, $(9.1+0.9)$. Adding 9.1 and 0.9 results in 10. Therefore, $(9.1+0.9) = 10$. Now our expression looks like this: $10 imes 35.5 + 10 imes 4$. With the parentheses taken care of, we move on to Multiplication. We have two multiplication operations to perform.

First, we multiply 10 by 35.5, which equals 355. So, $10 imes 35.5 = 355$. Next, we multiply 10 by 4, which gives us 40. So, $10 imes 4 = 40$. Our expression is now simplified to: $355 + 40$. The final step is Addition. We add 355 and 40 together. Adding these two numbers gives us 395.

Therefore, the final result of the expression $10 imes(48.5-13)+(9.1+0.9) imes 4$ is 395. By meticulously following the order of operations, we were able to systematically solve this mathematical expression. Now, let's move on to the second expression.

Solving the Second Expression: $B = 60 imes 12 imes 9 - 3.2$

Now, let's tackle the second expression: $B = 60 imes 12 imes 9 - 3.2$. Again, we will follow the order of operations (PEMDAS) to ensure accuracy. In this expression, we have Multiplication and Subtraction. According to PEMDAS, Multiplication comes before Subtraction. However, we have a series of multiplications, $60 imes 12 imes 9$. We perform these operations from left to right.

First, let’s multiply 60 by 12. $60 imes 12$ equals 720. So, we now have $720 imes 9 - 3.2$. Next, we multiply 720 by 9. $720 imes 9$ gives us 6480. The expression is now $6480 - 3.2$. With the multiplication completed, we move on to Subtraction. We subtract 3.2 from 6480.

Subtracting 3.2 from 6480, we get 6476.8. Therefore, $6480 - 3.2 = 6476.8$. So, the final result for the expression $B = 60 imes 12 imes 9 - 3.2$ is 6476.8. By carefully applying the order of operations, we have successfully solved the second mathematical expression.

Conclusion

In this article, we have successfully solved two mathematical expressions by meticulously following the order of operations (PEMDAS). For the first expression, $10 imes(48.5-13)+(9.1+0.9) imes 4$, we found the solution to be 395. For the second expression, $B = 60 imes 12 imes 9 - 3.2$, the result was 6476.8. Understanding and applying PEMDAS is crucial for solving mathematical problems accurately and efficiently. This step-by-step approach not only helps in arriving at the correct answer but also enhances your problem-solving skills.

For further learning and practice on mathematical expressions and order of operations, you can visit reputable educational websites. Check out resources like Khan Academy's Arithmetic lessons for more in-depth explanations and practice problems.