Perform The Following Divisions:1. $8.1 \div 1.782$2. $0.4 \div 3.124$3. $0.9 \div 0.45$4. $3.2 \div 1.28$

In mathematics, division is a fundamental operation that involves splitting a number into equal parts or groups. It is an essential concept in arithmetic and algebra, and it plays a crucial role in various mathematical operations. In this article, we will perform four divisions using the given numbers: $8.1 \div 1.782$, $0.4 \div 3.124$, $0.9 \div 0.45$, and $3.2 \div 1.28$.

Division 1: $8.1 \div 1.782$

To perform the division $8.1 \div 1.782$, we need to follow the order of operations (PEMDAS):

1. Understand the problem: We are asked to divide $8.1$ by $1.782$.
2. Check for any simplifications: There are no simplifications that can be made to the numbers.
3. Perform the division: To perform the division, we need to divide $8.1$ by $1.782$. We can do this by using long division or a calculator.

Using a calculator, we get:

$8.1 \div 1.782 = 4.54$

Therefore, the result of the division $8.1 \div 1.782$ is $4.54$.

Division 2: $0.4 \div 3.124$

To perform the division $0.4 \div 3.124$, we need to follow the order of operations (PEMDAS):

1. Understand the problem: We are asked to divide $0.4$ by $3.124$.
2. Check for any simplifications: There are no simplifications that can be made to the numbers.
3. Perform the division: To perform the division, we need to divide $0.4$ by $3.124$. We can do this by using long division or a calculator.

Using a calculator, we get:

$0.4 \div 3.124 = 0.128$

Therefore, the result of the division $0.4 \div 3.124$ is $0.128$.

Division 3: $0.9 \div 0.45$

To perform the division $0.9 \div 0.45$, we need to follow the order of operations (PEMDAS):

1. Understand the problem: We are asked to divide $0.9$ by $0.45$.
2. Check for any simplifications: There are no simplifications that can be made to the numbers.
3. Perform the division: To perform the division, we need to divide $0.9$ by $0.45$. We can do this by using long division or a calculator.

Using a calculator, we get:

$0.9 \div 0.45 = 2$

Therefore, the result of the division $0.9 \div 0.45$ is $2$.

Division 4: $3.2 \div 1.28$

To perform the division $3.2 \div 1.28$, we need to follow the order of operations (PEMDAS):

1. Understand the problem: We are asked to divide $3.2$ by $1.28$.
2. Check for any simplifications: There are no simplifications that can be made to the numbers.
3. Perform the division: To perform the division, we need to divide $3.2$ by $1.28$. We can do this by using long division or a calculator.

Using a calculator, we get:

$3.2 \div 1.28 = 2.5$

Therefore, the result of the division $3.2 \div 1.28$ is $2.5$.

Conclusion

In this article, we performed four divisions using the given numbers: $8.1 \div 1.782$, $0.4 \div 3.124$, $0.9 \div 0.45$, and $3.2 \div 1.28$. We used the order of operations (PEMDAS) to perform the divisions and obtained the results: $4.54$, $0.128$, $2$, and $2.5$ respectively. These results demonstrate the importance of following the order of operations and using the correct mathematical techniques to perform divisions.

Key Takeaways

• Division is a fundamental operation in mathematics that involves splitting a number into equal parts or groups.
• To perform a division, we need to follow the order of operations (PEMDAS).
• We can use long division or a calculator to perform divisions.
• The results of the divisions demonstrate the importance of following the order of operations and using the correct mathematical techniques.

Frequently Asked Questions

• What is the order of operations (PEMDAS)?
  • The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed.
  • The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.
• How do I perform a division using long division?
  • To perform a division using long division, we need to follow these steps:
    • Write the dividend (the number being divided) on top of a line.
    • Write the divisor (the number by which we are dividing) below the line.
    • Divide the first digit of the dividend by the divisor and write the result below the line.
    • Multiply the result by the divisor and subtract the product from the dividend.
    • Bring down the next digit of the dividend and repeat the process.
    • Continue this process until we have divided all the digits of the dividend.
• How do I perform a division using a calculator?
  • To perform a division using a calculator, we need to follow these steps:
    • Enter the dividend (the number being divided) into the calculator.
    • Enter the divisor (the number by which we are dividing) into the calculator.
    • Press the division button (usually denoted by a slash or a ÷ symbol).
    • The calculator will display the result of the division.
      Division Q&A: Frequently Asked Questions and Answers =====================================================

In this article, we will answer some of the most frequently asked questions about division. Whether you are a student, a teacher, or simply someone who wants to learn more about division, this article is for you.

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed. The acronym PEMDAS stands for Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction.

Q: How do I perform a division using long division?

A: To perform a division using long division, you need to follow these steps:

1. Write the dividend (the number being divided) on top of a line.
2. Write the divisor (the number by which we are dividing) below the line.
3. Divide the first digit of the dividend by the divisor and write the result below the line.
4. Multiply the result by the divisor and subtract the product from the dividend.
5. Bring down the next digit of the dividend and repeat the process.
6. Continue this process until you have divided all the digits of the dividend.

Q: How do I perform a division using a calculator?

A: To perform a division using a calculator, you need to follow these steps:

1. Enter the dividend (the number being divided) into the calculator.
2. Enter the divisor (the number by which we are dividing) into the calculator.
3. Press the division button (usually denoted by a slash or a ÷ symbol).
4. The calculator will display the result of the division.

Q: What is the difference between division and multiplication?

A: Division and multiplication are two different mathematical operations. Division involves splitting a number into equal parts or groups, while multiplication involves combining numbers to get a product.

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

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

Q: Can I divide a fraction by a fraction?

A: Yes, you can divide a fraction by a fraction. To do this, you need to invert the second fraction (i.e., flip the numerator and denominator) and then multiply the two fractions.

Q: What is the result of dividing zero by a number?

A: The result of dividing zero by a number is zero.

Q: What is the result of dividing a number by zero?

A: The result of dividing a number by zero is undefined.

Q: Can I divide a decimal number by a decimal number?

A: Yes, you can divide a decimal number by a decimal number. To do this, you need to follow the same steps as dividing a whole number by a whole number.

Q: Can I divide a mixed number by a mixed number?

A: Yes, you can divide a mixed number by a mixed number. To do this, you need to convert the mixed numbers to improper fractions and then follow the same steps as dividing a fraction by a fraction.

Conclusion

In this article, we have answered some of the most frequently asked questions about division. Whether you are a student, a teacher, or simply someone who wants to learn more about division, we hope that this article has been helpful to you.

Key Takeaways

• Division is a fundamental operation in mathematics that involves splitting a number into equal parts or groups.
• To perform a division, you need to follow the order of operations (PEMDAS).
• You can use long division or a calculator to perform divisions.
• The results of divisions can be positive, negative, or zero, depending on the numbers being divided.

Frequently Asked Questions

• What is the order of operations (PEMDAS)?
• How do I perform a division using long division?
• How do I perform a division using a calculator?
• What is the difference between division and multiplication?
• Can I divide a negative number by a negative number?
• Can I divide a fraction by a fraction?
• What is the result of dividing zero by a number?
• What is the result of dividing a number by zero?
• Can I divide a decimal number by a decimal number?
• Can I divide a mixed number by a mixed number?