What Is The Quotient Of The Following Division Problem $245 \div 17 = ?$A. 13 R 6 B. 15 R 7 C. 14 R 8 D. 14 R 7

What is the Quotient of the Division Problem $245 \div 17 = ?$

Understanding Division and Quotient

In mathematics, division is a fundamental operation that involves sharing a certain number of items into equal groups or finding the number of times a certain number is contained within another number. The result of a division operation is called the quotient, which represents the number of times the divisor is contained within the dividend. In this article, we will explore the concept of division and quotient, and we will solve the division problem $245 \div 17 = ?$ to determine the correct answer.

The Division Problem $245 \div 17 = ?$

To solve the division problem $245 \div 17 = ?$, we need to divide 245 by 17. This involves finding the number of times 17 is contained within 245. To do this, we can use long division or mental math.

Using Long Division to Solve the Problem

One way to solve the division problem $245 \div 17 = ?$ is to use long division. Long division is a method of dividing a number by another number by repeatedly subtracting the divisor from the dividend until the remainder is less than the divisor.

Here's how to use long division to solve the problem:

1. Write the dividend (245) on top of a line, and the divisor (17) below it.
2. Divide the first digit of the dividend (2) by the divisor (17). Since 2 is less than 17, we can't divide it evenly. So, we write 0 on top of the line.
3. Multiply the divisor (17) by the quotient (0) and subtract the result from the dividend (245). This gives us 245 - 0 = 245.
4. Bring down the next digit of the dividend (4) and add it to the remainder (245). This gives us 245 + 4 = 249.
5. Divide the result (249) by the divisor (17). Since 249 is greater than 17, we can divide it evenly. So, we write 14 on top of the line.
6. Multiply the divisor (17) by the quotient (14) and subtract the result from the dividend (249). This gives us 249 - 238 = 11.
7. Bring down the next digit of the dividend (5) and add it to the remainder (11). This gives us 11 + 5 = 16.
8. Divide the result (16) by the divisor (17). Since 16 is less than 17, we can't divide it evenly. So, we write 0 on top of the line.
9. Multiply the divisor (17) by the quotient (0) and subtract the result from the remainder (16). This gives us 16 - 0 = 16.
10. Since the remainder (16) is less than the divisor (17), we can stop the division process.

The Quotient and Remainder

Using long division, we find that the quotient of the division problem $245 \div 17 = ?$ is 14 with a remainder of 11. However, we need to consider the options provided in the problem.

Evaluating the Options

Let's evaluate the options provided in the problem:

A. 13 r 6 B. 15 r 7 C. 14 r 8 D. 14 r 7

We can see that option D, 14 r 7, matches the quotient and remainder we found using long division.

Conclusion

In conclusion, the quotient of the division problem $245 \div 17 = ?$ is 14 with a remainder of 7. This is option D in the problem. Therefore, the correct answer is:

The Final Answer is: D. 14 r 7

Understanding the Importance of Division and Quotient

Division and quotient are fundamental concepts in mathematics that have numerous real-world applications. In this article, we explored the concept of division and quotient, and we solved the division problem $245 \div 17 = ?$ to determine the correct answer. We used long division to find the quotient and remainder, and we evaluated the options provided in the problem to determine the correct answer.

Real-World Applications of Division and Quotient

Division and quotient have numerous real-world applications in fields such as finance, science, and engineering. For example, in finance, division is used to calculate interest rates and investment returns. In science, division is used to calculate the concentration of a solution or the number of particles in a sample. In engineering, division is used to calculate the size and shape of structures and machines.

Tips and Tricks for Solving Division Problems

Here are some tips and tricks for solving division problems:

• Use long division or mental math to solve division problems.
• Make sure to consider the remainder when solving division problems.
• Evaluate the options provided in the problem to determine the correct answer.
• Practice solving division problems to improve your skills and confidence.

Conclusion

In conclusion, division and quotient are fundamental concepts in mathematics that have numerous real-world applications. In this article, we explored the concept of division and quotient, and we solved the division problem $245 \div 17 = ?$ to determine the correct answer. We used long division to find the quotient and remainder, and we evaluated the options provided in the problem to determine the correct answer. We hope this article has provided you with a better understanding of division and quotient, and we encourage you to practice solving division problems to improve your skills and confidence.
Frequently Asked Questions (FAQs) About Division and Quotient

Q: What is division?

A: Division is a mathematical operation that involves sharing a certain number of items into equal groups or finding the number of times a certain number is contained within another number.

Q: What is the quotient?

A: The quotient is the result of a division operation, which represents the number of times the divisor is contained within the dividend.

Q: How do I solve a division problem?

A: To solve a division problem, you can use long division or mental math. Long division involves repeatedly subtracting the divisor from the dividend until the remainder is less than the divisor. Mental math involves using your knowledge of multiplication and division facts to solve the problem.

Q: What is the remainder?

A: The remainder is the amount left over after dividing a number by another number. It is the difference between the dividend and the product of the divisor and the quotient.

Q: Why is division important?

A: Division is an important mathematical operation because it has numerous real-world applications in fields such as finance, science, and engineering. It is used to calculate interest rates, investment returns, concentrations of solutions, and sizes and shapes of structures and machines.

Q: How do I evaluate the options provided in a division problem?

A: To evaluate the options provided in a division problem, you need to consider the quotient and remainder. You should look for the option that matches the quotient and remainder you found using long division or mental math.

Q: What are some common mistakes to avoid when solving division problems?

A: Some common mistakes to avoid when solving division problems include:

• Not considering the remainder
• Not evaluating the options provided in the problem
• Not using long division or mental math to solve the problem
• Not checking your work for errors

Q: How can I practice solving division problems?

A: You can practice solving division problems by using online resources, such as math websites and apps, or by working with a tutor or teacher. You can also practice solving division problems on your own by using worksheets or flashcards.

Q: What are some real-world applications of division?

A: Some real-world applications of division include:

• Calculating interest rates and investment returns in finance
• Calculating concentrations of solutions in science
• Calculating sizes and shapes of structures and machines in engineering
• Calculating the number of items in a group or the number of groups in a set

Q: How can I improve my skills and confidence when solving division problems?

A: You can improve your skills and confidence when solving division problems by:

• Practicing regularly
• Using online resources and worksheets
• Working with a tutor or teacher
• Checking your work for errors
• Evaluating the options provided in the problem

Q: What are some tips and tricks for solving division problems?

A: Some tips and tricks for solving division problems include:

• Using long division or mental math to solve the problem
• Considering the remainder
• Evaluating the options provided in the problem
• Practicing regularly
• Checking your work for errors

Conclusion

In conclusion, division and quotient are fundamental concepts in mathematics that have numerous real-world applications. In this article, we have answered some frequently asked questions about division and quotient, and we have provided tips and tricks for solving division problems. We hope this article has provided you with a better understanding of division and quotient, and we encourage you to practice solving division problems to improve your skills and confidence.