Applying the Division Algorithm

Oct 13, 2025 by thesweetdesigns.com 100 views

Select the Best Answer for the Question: 3.7 ÷ 1.1 = ?

Understanding the Problem

When faced with a division problem, we need to find the quotient of two numbers. In this case, we are asked to find the result of 3.7 divided by 1.1. To solve this problem, we will use the standard division algorithm, which involves dividing the dividend (3.7) by the divisor (1.1).

The Division Algorithm

The division algorithm states that for any two numbers, a and b, where b is not equal to zero, there exist unique integers q and r such that:

a = bq + r

where q is the quotient and r is the remainder.

Applying the Division Algorithm

In this case, we have:

a = 3.7 b = 1.1

We need to find the quotient (q) and the remainder (r).

Performing the Division

To perform the division, we can use long division or a calculator. Let's use a calculator to find the result.

Using a calculator, we get:

3.7 ÷ 1.1 = 3.363636...

Rounding to the Nearest Hundredth

Since we are asked to round the result to the nearest hundredth, we need to look at the thousandth place, which is 3 in this case. Since 3 is less than 5, we round down to 3.36.

Selecting the Best Answer

Now that we have the result, we can select the best answer from the options provided.

A. 4.8 B. 0.297 C. 3.36 D. 4.07

Based on our calculation, the correct answer is:

C. 3.36

Conclusion

In this problem, we used the division algorithm to find the result of 3.7 divided by 1.1. We then rounded the result to the nearest hundredth and selected the best answer from the options provided. The correct answer is C. 3.36.

Key Takeaways

The division algorithm states that for any two numbers, a and b, where b is not equal to zero, there exist unique integers q and r such that a = bq + r.
To perform division, we can use long division or a calculator.
When rounding a result to the nearest hundredth, we look at the thousandth place and round up or down accordingly.

Practice Problems

Try solving the following problems:

2.5 ÷ 0.5 = ?
4.2 ÷ 1.2 = ?
1.8 ÷ 0.3 = ?

Answer Key

5
3.5
6
Frequently Asked Questions (FAQs) about Division

Q: What is division?

A: Division is a mathematical operation that involves finding the quotient of two numbers. It is the inverse operation of multiplication.

Q: How do I perform division?

A: To perform division, you can use long division or a calculator. Long division involves dividing the dividend by the divisor, while a calculator can quickly give you the result.

Q: What is the difference between division and multiplication?

A: Division and multiplication are inverse operations. While multiplication involves finding the product of two numbers, division involves finding the quotient of two numbers.

Q: Can I divide by zero?

A: No, you cannot divide by zero. Division by zero is undefined and will result in an error.

Q: How do I round a result to the nearest hundredth?

A: To round a result to the nearest hundredth, you need to look at the thousandth place. If the thousandth place is less than 5, you round down. If the thousandth place is 5 or greater, you round up.

Q: What is the remainder in division?

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

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 decimal numbers in division?

A: When dividing decimal numbers, you need to line up the decimal points and perform the division as usual. The result will also be a decimal number.

Q: Can I divide a negative number by a positive number?

A: Yes, you can divide a negative number by a positive number. The result will be a negative number.

Q: Can I divide a positive number by a negative number?

A: Yes, you can divide a positive number by a negative number. The result will be a negative number.

Q: What is the order of operations in division?

A: The order of operations in division is:

Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)

Q: Can I use a calculator to perform division?

A: Yes, you can use a calculator to perform division. Calculators can quickly give you the result of a division problem.

Q: How do I check my division answer?

A: To check your division answer, you can multiply the quotient by the divisor and add the remainder. If the result is equal to the dividend, then your answer is correct.

Conclusion

Division is a fundamental mathematical operation that involves finding the quotient of two numbers. It is the inverse operation of multiplication and is used in a wide range of applications. By understanding the basics of division, you can perform division problems with confidence and accuracy.

Practice Problems

Try solving the following problems:

4.2 ÷ 1.2 = ?
2.5 ÷ 0.5 = ?
1.8 ÷ 0.3 = ?

Answer Key