Which Quotient Is Correct? Use Multiplication And Addition To Help You.A. 107 ÷ 10 = 12 R 1 107 \div 10 = 12 \, R \, 1 107 ÷ 10 = 12 R 1 B. 107 ÷ 10 = 9 R 3 107 \div 10 = 9 \, R \, 3 107 ÷ 10 = 9 R 3 C. 107 ÷ 10 = 10 R 7 107 \div 10 = 10 \, R \, 7 107 ÷ 10 = 10 R 7 D. 107 ÷ 10 = 11 R 3 107 \div 10 = 11 \, R \, 3 107 ÷ 10 = 11 R 3

Which Quotient is Correct? Using Multiplication and Addition to Help You

Understanding Quotient and Remainder

In mathematics, when we divide one number by another, we get a quotient and a remainder. The quotient is the result of the division, while the remainder is what is left over after the division. For example, if we divide 17 by 5, we get a quotient of 3 and a remainder of 2, because 5 x 3 = 15 and 17 - 15 = 2.

Using Multiplication and Addition to Check Quotient and Remainder

To check if a quotient and remainder are correct, we can use multiplication and addition. We can multiply the quotient by the divisor and add the remainder to see if we get the original dividend. If we do, then the quotient and remainder are correct.

Checking Option A: $107 \div 10 = 12 \, r \, 1$

Let's check option A by multiplying the quotient by the divisor and adding the remainder. We get:

10 x 12 = 120 120 + 1 = 121

Since 121 is not equal to 107, option A is incorrect.

Checking Option B: $107 \div 10 = 9 \, r \, 3$

Let's check option B by multiplying the quotient by the divisor and adding the remainder. We get:

10 x 9 = 90 90 + 3 = 93

Since 93 is not equal to 107, option B is incorrect.

Checking Option C: $107 \div 10 = 10 \, r \, 7$

Let's check option C by multiplying the quotient by the divisor and adding the remainder. We get:

10 x 10 = 100 100 + 7 = 107

Since 107 is equal to 107, option C is correct.

Checking Option D: $107 \div 10 = 11 \, r \, 3$

Let's check option D by multiplying the quotient by the divisor and adding the remainder. We get:

10 x 11 = 110 110 + 3 = 113

Since 113 is not equal to 107, option D is incorrect.

Conclusion

In conclusion, the correct quotient is option C: $107 \div 10 = 10 \, r \, 7$. We can use multiplication and addition to check if a quotient and remainder are correct. By multiplying the quotient by the divisor and adding the remainder, we can see if we get the original dividend. If we do, then the quotient and remainder are correct.

Understanding the Importance of Quotient and Remainder

Quotient and remainder are important concepts in mathematics. They help us understand the relationship between numbers and how they can be divided. By understanding quotient and remainder, we can solve problems more easily and accurately.

Real-World Applications of Quotient and Remainder

Quotient and remainder have many real-world applications. For example, in cooking, we may need to divide a recipe into smaller portions. In this case, the quotient would be the number of portions and the remainder would be the amount of ingredients left over. In finance, we may need to divide a budget into smaller categories. In this case, the quotient would be the amount of money allocated to each category and the remainder would be the amount of money left over.

Common Mistakes When Working with Quotient and Remainder

When working with quotient and remainder, there are several common mistakes to avoid. One mistake is to confuse the quotient and remainder. For example, if we divide 17 by 5, the quotient is 3 and the remainder is 2, not the other way around. Another mistake is to forget to check if the quotient and remainder are correct. By using multiplication and addition, we can check if the quotient and remainder are correct and avoid making mistakes.

Tips for Working with Quotient and Remainder

Here are some tips for working with quotient and remainder:

• Always check if the quotient and remainder are correct by using multiplication and addition.
• Make sure to understand the relationship between the dividend, divisor, quotient, and remainder.
• Use real-world examples to help you understand quotient and remainder.
• Practice, practice, practice! The more you practice working with quotient and remainder, the more comfortable you will become with the concepts.

Conclusion

In conclusion, quotient and remainder are important concepts in mathematics. By understanding quotient and remainder, we can solve problems more easily and accurately. By using multiplication and addition, we can check if the quotient and remainder are correct and avoid making mistakes. With practice and patience, we can become proficient in working with quotient and remainder.
Quotient and Remainder Q&A

Frequently Asked Questions About Quotient and Remainder

Q: What is the quotient in a division problem?

A: The quotient is the result of the division, which is the number of times the divisor fits into the dividend.

Q: What is the remainder in a division problem?

A: The remainder is the amount left over after the division, which is the amount that the divisor does not fit into the dividend.

Q: How do I check if a quotient and remainder are correct?

A: You can check if a quotient and remainder are correct by multiplying the quotient by the divisor and adding the remainder. If the result is equal to the original dividend, then the quotient and remainder are correct.

Q: What is the difference between a quotient and a remainder?

A: The quotient is the result of the division, while the remainder is the amount left over after the division.

Q: Can a remainder be negative?

A: No, a remainder cannot be negative. The remainder is always a non-negative number.

Q: Can a quotient be negative?

A: Yes, a quotient can be negative. If the dividend is negative and the divisor is positive, then the quotient will be negative.

Q: How do I handle remainders when dividing fractions?

A: When dividing fractions, you can handle remainders by multiplying the dividend by the reciprocal of the divisor and then simplifying the result.

Q: Can I have a remainder of zero?

A: Yes, you can have a remainder of zero. This occurs when the dividend is exactly divisible by the divisor.

Q: How do I handle remainders when dividing decimals?

A: When dividing decimals, you can handle remainders by multiplying the dividend by the reciprocal of the divisor and then rounding the result to the desired number of decimal places.

Q: Can I have a quotient of zero?

A: Yes, you can have a quotient of zero. This occurs when the dividend is zero and the divisor is non-zero.

Q: How do I handle remainders when dividing mixed numbers?

A: When dividing mixed numbers, you can handle remainders by converting the mixed number to an improper fraction, dividing the fractions, and then converting the result back to a mixed number.

Q: Can I have a remainder that is greater than the divisor?

A: No, a remainder cannot be greater than the divisor. The remainder is always less than the divisor.

Q: How do I handle remainders when dividing negative numbers?

A: When dividing negative numbers, you can handle remainders by multiplying the dividend by the reciprocal of the divisor and then simplifying the result.

Conclusion

In conclusion, quotient and remainder are important concepts in mathematics. By understanding quotient and remainder, we can solve problems more easily and accurately. By using multiplication and addition, we can check if the quotient and remainder are correct and avoid making mistakes. With practice and patience, we can become proficient in working with quotient and remainder.

Additional Resources

• For more information on quotient and remainder, please visit the following websites:

• Khan Academy: Quotient and Remainder
• Mathway: Quotient and Remainder
• Wolfram Alpha: Quotient and Remainder

• For more practice problems on quotient and remainder, please visit the following websites:

• IXL: Quotient and Remainder
• Math Open Reference: Quotient and Remainder
• Purplemath: Quotient and Remainder