Subtract Quotient Of 15 Divided By 3 From Sum Of 33 And 7
This article provides a detailed explanation of how to solve the mathematical problem "Subtract the quotient of 15 ÷ 3 from the sum of 33 and 7." We will break down each step of the calculation, ensuring clarity and understanding. This is designed to help students and anyone interested in improving their arithmetic skills. Understanding the order of operations and how to apply them is crucial in mathematics. Let’s dive in and solve this problem together.
Understanding the Problem Statement
To effectively tackle this problem, we must first understand each component of the statement. The question asks us to perform two primary operations: division and subtraction, along with addition. The key is to follow the correct order of operations, commonly remembered by the acronym PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction). In our case, we have division, addition, and subtraction. We will address the division first, then the addition, and finally the subtraction to arrive at the correct answer.
Breaking Down the Components
- Quotient of 15 ÷ 3: This part requires us to divide 15 by 3. The quotient is the result of this division.
- Sum of 33 and 7: Here, we need to add 33 and 7 together. The sum is the result of this addition.
- Subtract the quotient from the sum: This is the final step where we subtract the result from step 1 (the quotient) from the result of step 2 (the sum).
By breaking down the problem into these smaller parts, we can approach it methodically and reduce the chances of error. Each step is straightforward, but understanding the relationships between them is essential for solving the problem correctly. Let's proceed to solve each part.
Step-by-Step Solution
Now that we understand the problem, let's solve it step by step. We'll begin by calculating the quotient of 15 ÷ 3, then find the sum of 33 and 7, and finally subtract the quotient from the sum. By meticulously following each step, we can ensure accuracy and clarity in our solution.
Step 1: Calculate the Quotient of 15 ÷ 3
The first part of the problem is to find the quotient of 15 ÷ 3. Division is one of the basic arithmetic operations, and in this case, it's quite straightforward. To find the quotient, we simply divide 15 by 3:
15 ÷ 3 = 5
So, the quotient of 15 divided by 3 is 5. This result will be used in the final subtraction step. Now that we have the quotient, let's move on to the next part of the problem, which involves finding the sum of 33 and 7.
Step 2: Find the Sum of 33 and 7
The next step in solving the problem is to determine the sum of 33 and 7. Addition is another fundamental arithmetic operation. To find the sum, we simply add the two numbers together:
33 + 7 = 40
Thus, the sum of 33 and 7 is 40. This result will be used along with the quotient we calculated earlier to complete the final subtraction. Now that we have both the quotient (5) and the sum (40), we can proceed to the final step.
Step 3: Subtract the Quotient from the Sum
The final step in solving the problem is to subtract the quotient we found in step 1 (which is 5) from the sum we found in step 2 (which is 40). Subtraction is the last operation we need to perform to arrive at the final answer.
We subtract 5 from 40 as follows:
40 - 5 = 35
Therefore, the result of subtracting the quotient of 15 ÷ 3 from the sum of 33 and 7 is 35. This completes the solution to the problem. Now, let's review the entire process to ensure we understand each step and the final answer.
Final Answer and Conclusion
After carefully following each step, we have arrived at the final answer. To recap, we first calculated the quotient of 15 ÷ 3, which was 5. Then, we found the sum of 33 and 7, which was 40. Finally, we subtracted the quotient (5) from the sum (40), resulting in 35. Therefore, the solution to the problem is 35.
The Correct Answer
The correct answer to the question "Subtract the quotient of 15 ÷ 3 from the sum of 33 and 7" is:
A. 35
Conclusion
In conclusion, this problem highlights the importance of understanding and following the correct order of operations. By breaking down the problem into smaller, manageable steps, we were able to solve it accurately. Each step, from finding the quotient to determining the sum and finally performing the subtraction, was crucial in reaching the correct answer. This approach not only helps in solving mathematical problems but also enhances problem-solving skills in general. Remember to always approach problems methodically, and you will find that even complex questions can be solved with ease.
Additional Practice Problems
To further enhance your understanding and skills, here are some additional practice problems similar to the one we just solved. These problems will help you reinforce your knowledge of arithmetic operations and the order in which they should be performed. Try solving them on your own, and you'll become more confident in your mathematical abilities. Practice is key to mastering these concepts.
Practice Problem 1
Subtract the quotient of 20 ÷ 4 from the sum of 42 and 8.
Practice Problem 2
What is the result of subtracting the quotient of 27 ÷ 3 from the sum of 55 and 10?
Practice Problem 3
Calculate the difference between the sum of 68 and 12 and the quotient of 36 ÷ 6.
Practice Problem 4
Subtract the quotient of 45 ÷ 5 from the sum of 71 and 9.
These practice problems provide an excellent opportunity to apply what you've learned. Remember to break each problem down into steps and follow the order of operations. Good luck, and happy solving!
Tips for Solving Similar Problems
To become proficient in solving problems like these, it's essential to develop a systematic approach. Here are some helpful tips that can guide you through similar mathematical challenges. These tips focus on understanding the problem, organizing your steps, and avoiding common pitfalls. By following these guidelines, you'll be better equipped to tackle arithmetic problems with confidence and accuracy.
1. Read and Understand the Problem Carefully
Before you start solving, make sure you fully understand what the problem is asking. Identify the key components and the operations you need to perform. Pay close attention to the wording and ensure you're clear on the sequence of steps. Misinterpreting the problem is a common mistake, so take your time to read and comprehend it thoroughly.
2. Break the Problem into Smaller Steps
Complex problems can be overwhelming if you try to solve them all at once. Instead, break the problem down into smaller, more manageable steps. This makes the problem less daunting and allows you to focus on one operation at a time. In the example we solved, we broke the problem into finding the quotient, finding the sum, and then subtracting.
3. Follow the Order of Operations (PEMDAS/BODMAS)
The order of operations is crucial in mathematics. PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) provides the correct sequence for performing operations. Always adhere to this order to avoid errors.
4. Show Your Work
Writing down each step of your solution is essential. It not only helps you keep track of your progress but also makes it easier to identify any mistakes you might have made. Showing your work also allows others to understand your thought process and provide assistance if needed.
5. Double-Check Your Calculations
After solving the problem, take a moment to review your calculations. Ensure that you haven't made any arithmetic errors. A simple mistake can lead to an incorrect answer, so double-checking is a critical step. You can also use estimation to see if your final answer is reasonable.
6. Practice Regularly
The key to mastering any skill, including problem-solving, is practice. The more you practice, the more comfortable and confident you'll become. Work through various problems and gradually increase the difficulty level. Consistent practice will help you develop a strong foundation in arithmetic.
7. Seek Help When Needed
If you're struggling with a problem, don't hesitate to seek help. Ask your teacher, classmates, or look for online resources. Understanding the concepts and techniques is more important than just getting the answer. Learning from your mistakes and getting clarification will help you improve your skills.
By following these tips, you'll be well-prepared to solve similar problems efficiently and accurately. Remember, problem-solving is a skill that improves with practice, so keep working at it, and you'll see progress over time.
