Divide: $2.16 \div 0.27$

Apr 2, 2025 by ADMIN 27 views

$Divide: $2.16 \div 0.27$$

Introduction

Division is a fundamental operation in mathematics that involves finding the quotient of two numbers. It is an essential concept in various mathematical disciplines, including arithmetic, algebra, and geometry. In this article, we will focus on dividing a decimal number by another decimal number, specifically $2.16 \div 0.27$. We will explore the concept of division, the steps involved in performing division, and the solution to the given problem.

Understanding Division

Division is the inverse operation of multiplication. It involves finding the number of times one number can be divided by another number to produce a specified quotient. In other words, division is the process of finding the result of a multiplication operation when the product is known, and the multiplier is unknown.

For example, if we know that the product of 6 and a certain number is 18, we can find the quotient by dividing 18 by 6, which gives us 3. This means that 6 can be multiplied by 3 to produce 18.

Steps Involved in Division

To perform division, we need to follow a series of steps:

Write the problem: Write the division problem in the correct format, with the dividend (the number being divided) on top and the divisor (the number by which we are dividing) on the bottom.
Check for zeros: Check if the divisor is zero. If it is, the problem is undefined, and we cannot perform division.
Check for decimals: Check if the dividend or divisor is a decimal number. If it is, we need to perform decimal division.
Perform long division: Perform long division by dividing the dividend by the divisor, using the quotient and remainder to find the final answer.
Check the answer: Check the answer to ensure that it is correct.

Decimal Division

Decimal division involves dividing a decimal number by another decimal number. To perform decimal division, we need to follow the same steps as above, but with an additional step:

Convert to whole numbers: Convert the decimal numbers to whole numbers by multiplying both numbers by a power of 10 (e.g., 10, 100, 1000).
Perform long division: Perform long division using the whole numbers.
Convert back to decimals: Convert the whole number quotient back to a decimal number by dividing by the power of 10 used in step 1.

Solving the Problem

Now that we have understood the concept of division and the steps involved in performing division, let's solve the problem $2.16 \div 0.27$.

Step 1: Write the problem

2.16 \div 0.27

Step 2: Check for zeros

The divisor, 0.27, is not zero, so we can proceed with the problem.

Step 3: Check for decimals

Both the dividend, 2.16, and the divisor, 0.27, are decimal numbers, so we need to perform decimal division.

Step 4: Perform long division

To perform long division, we need to convert the decimal numbers to whole numbers by multiplying both numbers by a power of 10.

2.16 \times 10 = 21.6

0.27 \times10 = 2.7

Now, we can perform long division using the whole numbers:

21.6 \div 2.7 = 8

Step 5: Convert back to decimals

To convert the whole number quotient back to a decimal number, we need to divide by the power of 10 used in step 1.

8 \div 10 = 0.8

Therefore, the solution to the problem $2.16 \div 0.27$ is 0.8.

Conclusion

In this article, we have explored the concept of division, the steps involved in performing division, and the solution to the problem $2.16 \div 0.27$. We have learned that division is the inverse operation of multiplication and that it involves finding the number of times one number can be divided by another number to produce a specified quotient. We have also learned that decimal division involves converting decimal numbers to whole numbers, performing long division, and converting back to decimals. By following these steps, we can solve division problems involving decimal numbers.

Frequently Asked Questions

What is division? Division is the inverse operation of multiplication. It involves finding the number of times one number can be divided by another number to produce a specified quotient.
How do I perform division? To perform division, you need to follow a series of steps, including writing the problem, checking for zeros, checking for decimals, performing long division, and checking the answer.
What is decimal division? Decimal division involves dividing a decimal number by another decimal number. To perform decimal division, you need to convert the decimal numbers to whole numbers, perform long division, and convert back to decimals.
How do I solve a division problem involving decimal numbers? To solve a division problem involving decimal numbers, you need to follow the steps involved in decimal division, including converting the decimal numbers to whole numbers, performing long division, and converting back to decimals.

References

Introduction

Division is a fundamental operation in mathematics that involves finding the quotient of two numbers. It is an essential concept in various mathematical disciplines, including arithmetic, algebra, and geometry. In this article, we will answer some frequently asked questions (FAQs) on division, covering topics such as the concept of division, steps involved in performing division, and common mistakes to avoid.

Q&A on Division

Q1: What is division?

A1: Division is the inverse operation of multiplication. It involves finding the number of times one number can be divided by another number to produce a specified quotient.

Q2: How do I perform division?

A2: To perform division, you need to follow a series of steps, including writing the problem, checking for zeros, checking for decimals, performing long division, and checking the answer.

Q3: What is decimal division?

A3: Decimal division involves dividing a decimal number by another decimal number. To perform decimal division, you need to convert the decimal numbers to whole numbers, perform long division, and convert back to decimals.

Q4: How do I solve a division problem involving decimal numbers?

A4: To solve a division problem involving decimal numbers, you need to follow the steps involved in decimal division, including converting the decimal numbers to whole numbers, performing long division, and converting back to decimals.

Q5: What is the difference between division and multiplication?

A5: Division and multiplication are inverse operations. Division involves finding the number of times one number can be divided by another number to produce a specified quotient, while multiplication involves finding the product of two numbers.

Q6: How do I check if a division problem is undefined?

A6: A division problem is undefined if the divisor is zero. To check if a division problem is undefined, you need to check if the divisor is zero.

Q7: What is the quotient of a division problem?

A7: The quotient of a division problem is the result of the division operation. It is the number of times the dividend can be divided by the divisor to produce a specified quotient.

Q8: How do I perform long division?

A8: To perform long division, you need to follow a series of steps, including dividing the dividend by the divisor, using the quotient and remainder to find the final answer, and checking the answer.

Q9: What is the remainder of a division problem?

A9: The remainder of a division problem is the amount left over after the dividend has been divided by the divisor. It is the difference between the dividend and the product of the divisor and the quotient.

Q10: How do I check if a division problem is correct?

A10: To check if a division problem is correct, you need to follow a series of steps, including checking the quotient, checking the remainder, and checking the answer.

Common Mistakes to Avoid

Mistake 1: Not checking for zeros

Solution: Always check if the divisor is zero before performing division.
Example: If the divisor is zero, the problem is undefined, and you cannot perform division.

Mistake 2: Not checking for decimals

Solution: Always check if the dividend or divisor is a decimal number before performing division.
Example: If the dividend or divisor is a decimal number, you need to perform decimal division.

Mistake 3: Not performing long division correctly

Solution: Always follow the steps involved in performing long division, including dividing the dividend by the divisor, using the quotient and remainder to find the final answer, and checking the answer.
Example: If you do not perform long division correctly, you may get an incorrect quotient or remainder.

Mistake 4: Not checking the answer

Solution: Always check the answer to ensure that it is correct.
Example: If you do not check the answer, you may get an incorrect quotient or remainder.

Conclusion

Division is a fundamental operation in mathematics that involves finding the quotient of two numbers. It is an essential concept in various mathematical disciplines, including arithmetic, algebra, and geometry. In this article, we have answered some frequently asked questions (FAQs) on division, covering topics such as the concept of division, steps involved in performing division, and common mistakes to avoid. By following the steps involved in performing division and checking the answer, you can ensure that your division problems are correct.