Solving Number Problems Addition And Place Value Explained

In this article, we will delve into a series of number-related problems, meticulously dissecting each question to provide a comprehensive understanding of the underlying mathematical principles. Our goal is to not only solve these specific problems but also to equip you with the knowledge and skills to tackle similar challenges with confidence. We'll cover concepts such as addition, place value, and problem-solving strategies, ensuring a thorough grasp of the fundamentals. So, let's embark on this mathematical journey and unlock the secrets behind these intriguing questions.

What Number Exceeds 36,987 by 7,548?

When we ask, "What number exceeds 36,987 by 7,548?", we are essentially looking for a number that is 7,548 greater than 36,987. This is a straightforward addition problem. The keyword "exceeds" indicates that we need to add the two numbers together. To solve this, we will perform the addition: 36,987 + 7,548. Understanding place value is crucial here. We add the digits in each place value column, starting from the ones place. If the sum in any column is greater than 9, we carry over the tens digit to the next column. So, let's break down the calculation:

• Starting with the ones place: 7 + 8 = 15. We write down 5 and carry over 1 to the tens place.
• In the tens place: 8 + 4 + 1 (carried over) = 13. We write down 3 and carry over 1 to the hundreds place.
• In the hundreds place: 9 + 5 + 1 (carried over) = 15. We write down 5 and carry over 1 to the thousands place.
• In the thousands place: 6 + 7 + 1 (carried over) = 14. We write down 4 and carry over 1 to the ten-thousands place.
• Finally, in the ten-thousands place: 3 + 1 (carried over) = 4.

Therefore, the result of the addition is 44,535. This means that the number which exceeds 36,987 by 7,548 is 44,535. This problem highlights the importance of understanding addition and place value in solving mathematical problems. We have methodically broken down the problem, showing each step of the calculation to ensure clarity and comprehension. By mastering these fundamental concepts, one can confidently approach more complex mathematical challenges.

Finding a Number 24,561 More Than 55,439

In this section, we tackle the problem: "A number is 24,561 more than 55,439. Find the number." This question, similar to the previous one, requires us to perform addition. The phrase "more than" clearly indicates that we need to add 24,561 to 55,439. This type of problem is common in mathematics and tests our ability to interpret word problems and translate them into mathematical operations. To find the number, we will add the two given numbers together. Let's break down the addition step by step, paying close attention to place values and carry-overs.

• Starting with the ones place: 9 + 1 = 10. We write down 0 and carry over 1 to the tens place.
• In the tens place: 3 + 6 + 1 (carried over) = 10. We write down 0 and carry over 1 to the hundreds place.
• In the hundreds place: 4 + 5 + 1 (carried over) = 10. We write down 0 and carry over 1 to the thousands place.
• In the thousands place: 5 + 4 + 1 (carried over) = 10. We write down 0 and carry over 1 to the ten-thousands place.
• Finally, in the ten-thousands place: 5 + 2 + 1 (carried over) = 8.

The sum we have calculated is 80,000. This means that the number which is 24,561 more than 55,439 is 80,000. This problem emphasizes the importance of recognizing keywords in word problems and translating them into mathematical operations. It also reinforces the understanding of addition and the concept of carrying over in place value. By practicing these types of problems, we can enhance our mathematical problem-solving skills and gain confidence in our ability to tackle more complex challenges.

Adding the Greatest 4-Digit Number to the Greatest 3-Digit Number

The next problem we will explore involves adding the greatest 4-digit number to the greatest 3-digit number. This question requires us to first identify the greatest 4-digit and 3-digit numbers and then perform addition. Understanding place value is crucial here. The greatest 4-digit number is the largest number that can be formed using four digits, which is 9,999. Similarly, the greatest 3-digit number is 999. Now that we have identified the two numbers, we need to add them together: 9,999 + 999. This addition will demonstrate our understanding of place value and the carrying-over process. Let's perform the addition step by step:

• Starting with the ones place: 9 + 9 = 18. We write down 8 and carry over 1 to the tens place.
• In the tens place: 9 + 9 + 1 (carried over) = 19. We write down 9 and carry over 1 to the hundreds place.
• In the hundreds place: 9 + 9 + 1 (carried over) = 19. We write down 9 and carry over 1 to the thousands place.
• Finally, in the thousands place: 9 + 1 (carried over) = 10. We write down 10.

Therefore, the sum of the greatest 4-digit number (9,999) and the greatest 3-digit number (999) is 10,998. This problem not only tests our ability to perform addition but also our understanding of place value and how to identify the greatest numbers within a given digit range. By breaking down the problem into smaller steps and focusing on each place value, we can confidently arrive at the correct solution. This type of problem reinforces the importance of fundamental mathematical concepts in problem-solving.

Shivani's Bank Account Balance After a Deposit

Our final problem involves a real-world scenario: "Shivani had ₹35,365 in her bank account. She deposited ₹36,360 more. What is the amount in her bank account?" This question requires us to calculate the total amount in Shivani's bank account after she made a deposit. The keyword "deposited" indicates that we need to add the amount she deposited to her initial balance. This problem demonstrates the practical application of addition in everyday situations, such as managing personal finances. To find the total amount, we will add ₹35,365 and ₹36,360 together. Let's break down the addition step by step, ensuring we align the place values correctly.

• Starting with the ones place: 5 + 0 = 5. We write down 5.
• In the tens place: 6 + 6 = 12. We write down 2 and carry over 1 to the hundreds place.
• In the hundreds place: 3 + 3 + 1 (carried over) = 7. We write down 7.
• In the thousands place: 5 + 6 = 11. We write down 1 and carry over 1 to the ten-thousands place.
• Finally, in the ten-thousands place: 3 + 3 + 1 (carried over) = 7. We write down 7.

Therefore, the total amount in Shivani's bank account after the deposit is ₹71,725. This problem highlights the importance of addition in practical, real-life scenarios. It also reinforces the concept of carrying over in addition and the significance of aligning place values correctly. By solving problems like this, we can appreciate the relevance of mathematics in our daily lives and develop our financial literacy skills.

Conclusion

In this article, we have explored a series of number-related problems, each requiring a different application of mathematical concepts. We have tackled questions involving addition, place value, and problem-solving strategies. By meticulously dissecting each problem and providing step-by-step solutions, we have aimed to enhance your understanding of these fundamental mathematical principles. We have seen how addition is used to solve problems involving exceeding numbers, finding amounts that are "more than" a given number, and calculating total amounts after deposits. We have also emphasized the importance of place value in performing addition and identifying the greatest numbers within a given digit range. Through these examples, we have demonstrated the practical relevance of mathematics in everyday situations.

By mastering these basic concepts and practicing problem-solving techniques, you can build a strong foundation in mathematics and confidently tackle more complex challenges. Remember, the key to success in mathematics lies in understanding the underlying principles and applying them consistently. We encourage you to continue exploring mathematical problems and seeking new challenges to further enhance your skills and knowledge.