What Is The Quotient Of The Following Division Problem?$25489 \div 865 =?$A. 28 R 404 B. 29 R 404 C. 29 R 405 D. 30 R 403
What is the Quotient of the Division Problem 25489 ÷ 865?
Understanding the Division Problem
When we divide one number by another, we are essentially finding how many times the second number fits into the first number. In this case, we are trying to find the quotient of the division problem 25489 ÷ 865. The quotient is the result of the division operation, and it tells us how many times 865 fits into 25489.
The Division Algorithm
To solve this problem, we can use the division algorithm, which states that any integer can be expressed as the product of a quotient and a remainder. In other words, if we divide one number by another, we can always find a quotient and a remainder that satisfy the equation:
a = bq + r
where a is the dividend (the number being divided), b is the divisor (the number by which we are dividing), q is the quotient, and r is the remainder.
Applying the Division Algorithm
In this case, we want to find the quotient of 25489 ÷ 865. To do this, we can use the division algorithm and perform the division operation.
25489 ÷ 865 = ?
To find the quotient, we can start by dividing 25489 by 865. We can do this by repeatedly subtracting 865 from 25489 until we reach a number that is less than 865.
25489 - 865 = 24724 24724 - 865 = 23859 23859 - 865 = 22994 22994 - 865 = 22129 22129 - 865 = 21264 21264 - 865 = 20399 20399 - 865 = 19534 19534 - 865 = 18669 18669 - 865 = 17794 17794 - 865 = 16929 16929 - 865 = 16064 16064 - 865 = 15199 15199 - 865 = 14334 14334 - 865 = 13469 13469 - 865 = 12594 12594 - 865 = 11729 11729 - 865 = 10864 10864 - 865 = 9999 9999 - 865 = 9134 9134 - 865 = 8269 8269 - 865 = 7404 7404 - 865 = 6539 6539 - 865 = 5674 5674 - 865 = 4809 4809 - 865 = 3944 3944 - 865 = 3079 3079 - 865 = 2214 2214 - 865 = 1349 1349 - 865 = 484
Finding the Quotient and Remainder
Now that we have performed the division operation, we can find the quotient and remainder.
The quotient is the number of times 865 fits into 25489, which is 29.
The remainder is the number left over after we have divided 25489 by 865, which is 404.
Conclusion
Therefore, the quotient of the division problem 25489 ÷ 865 is 29 with a remainder of 404.
Answer
The correct answer is B. 29 r 404.
Discussion
This problem requires the use of the division algorithm and the ability to perform long division. It also requires an understanding of the concept of quotient and remainder.
Related Topics
- Division algorithm
- Quotient and remainder
- Long division
Key Terms
- Quotient: the result of a division operation
- Remainder: the number left over after a division operation
- Division algorithm: a method for finding the quotient and remainder of a division operation
Practice Problems
- 4321 ÷ 123 = ?
- 9876 ÷ 456 = ?
- 1111 ÷ 333 = ?
Solutions
- 4321 ÷ 123 = 35 r 22
- 9876 ÷ 456 = 21 r 384
- 1111 ÷ 333 = 3 r 134
Quotient and Remainder: Frequently Asked Questions
Understanding the Quotient and Remainder
In the previous article, we discussed the division problem 25489 ÷ 865 and found the quotient and remainder. In this article, we will answer some frequently asked questions about the quotient and remainder.
Q: What is the quotient?
A: The quotient is the result of a division operation. It is the number of times the divisor (the number by which we are dividing) fits into the dividend (the number being divided).
Q: What is the remainder?
A: The remainder is the number left over after a division operation. It is the amount that is left over after we have divided the dividend by the divisor.
Q: How do I find the quotient and remainder?
A: To find the quotient and remainder, you can use the division algorithm. This involves dividing the dividend by the divisor and finding the quotient and remainder.
Q: What is the difference between the quotient and remainder?
A: The quotient is the result of the division operation, while the remainder is the amount left over. For example, if we divide 25489 by 865, the quotient is 29 and the remainder is 404.
Q: Can the remainder be negative?
A: No, the remainder cannot be negative. The remainder is always a non-negative number.
Q: Can the quotient be negative?
A: Yes, the quotient can be negative. If the dividend is negative and the divisor is positive, the quotient will be negative.
Q: What is the relationship between the quotient and remainder?
A: The quotient and remainder are related by the equation:
a = bq + r
where a is the dividend, b is the divisor, q is the quotient, and r is the remainder.
Q: How do I use the quotient and remainder in real-life situations?
A: The quotient and remainder are used in many real-life situations, such as:
- Measuring ingredients for a recipe
- Calculating the cost of an item
- Determining the number of items in a set
Q: What are some common mistakes to avoid when working with the quotient and remainder?
A: Some common mistakes to avoid when working with the quotient and remainder include:
- Confusing the quotient and remainder
- Not checking for negative remainders
- Not using the correct equation to find the quotient and remainder
Conclusion
In this article, we have answered some frequently asked questions about the quotient and remainder. We have discussed the definition of the quotient and remainder, how to find them, and their relationship. We have also provided some examples of how to use the quotient and remainder in real-life situations and some common mistakes to avoid.
Related Topics
- Division algorithm
- Quotient and remainder
- Long division
Key Terms
- Quotient: the result of a division operation
- Remainder: the number left over after a division operation
- Division algorithm: a method for finding the quotient and remainder of a division operation
Practice Problems
- 4321 ÷ 123 = ?
- 9876 ÷ 456 = ?
- 1111 ÷ 333 = ?
Solutions
- 4321 ÷ 123 = 35 r 22
- 9876 ÷ 456 = 21 r 384
- 1111 ÷ 333 = 3 r 134
Additional Resources
- Division algorithm worksheet
- Quotient and remainder practice problems
- Long division tutorial