Calculate The Following: ${ 167 \div 17 }$

by ADMIN 44 views

Introduction

Mathematical division is a fundamental operation in mathematics that involves splitting a number into equal parts or groups. It is an essential concept in various mathematical disciplines, including arithmetic, algebra, and geometry. In this article, we will delve into the concept of mathematical division, explore its significance, and calculate the result of 167 ÷ 17.

What is Mathematical Division?

Mathematical division is the process of finding the quotient of two numbers. It involves dividing a dividend (the number being divided) by a divisor (the number by which we are dividing) to obtain a quotient (the result of the division). The process of division can be represented as:

Dividend ÷ Divisor = Quotient

Types of Division

There are two main types of division: exact division and approximate division.

  • Exact Division: This type of division involves dividing a number by another number to obtain a whole number quotient. For example, 12 ÷ 3 = 4.
  • Approximate Division: This type of division involves dividing a number by another number to obtain a decimal quotient. For example, 12 ÷ 3 = 4.00.

Calculating 167 ÷ 17

To calculate 167 ÷ 17, we need to follow the steps of division.

  1. Write the dividend and divisor: Write the dividend (167) and divisor (17) in a vertical format, with the dividend on top and the divisor below.
  2. Divide the first digit: Divide the first digit of the dividend (1) by the divisor (17). Since 1 is less than 17, we write 0 as the first digit of the quotient.
  3. Bring down the next digit: Bring down the next digit of the dividend (6) and divide it by the divisor (17). The result is 36, which is greater than 17. So, we write 2 as the next digit of the quotient.
  4. Multiply and subtract: Multiply the divisor (17) by the next digit of the quotient (2) and subtract the result from the dividend (36). The result is 0.
  5. Bring down the next digit: Bring down the next digit of the dividend (7) and divide it by the divisor (17). The result is 41, which is greater than 17. So, we write 2 as the next digit of the quotient.
  6. Multiply and subtract: Multiply the divisor (17) by the next digit of the quotient (2) and subtract the result from the dividend (41). The result is 6.
  7. Bring down the next digit: Bring down the next digit of the dividend (1) and divide it by the divisor (17). The result is 0. So, we write 0 as the next digit of the quotient.

Result

The result of 167 ÷ 17 is 9.82.

Conclusion

Mathematical division is a fundamental operation in mathematics that involves splitting a number into equal parts or groups. It is an essential concept in various mathematical disciplines, including arithmetic, algebra, and geometry. In this article, we have explored the concept of mathematical division, its significance, and calculated the result of 167 ÷ 17. We have also discussed the types of division, including exact division and approximate division. By following the steps of division, we have obtained the result of 167 ÷ 17 as 9.82.

Real-World Applications

Mathematical division has numerous real-world applications in various fields, including:

  • Business: Division is used to calculate the cost per unit of a product, the profit per unit, and the return on investment.
  • Science: Division is used to calculate the concentration of a solution, the density of a substance, and the rate of a chemical reaction.
  • Engineering: Division is used to calculate the stress on a material, the strain on a structure, and the efficiency of a machine.

Practice Problems

To practice your division skills, try solving the following problems:

  • 432 ÷ 12 = ?
  • 945 ÷ 15 = ?
  • 1234 ÷ 17 = ?

References

  • "Mathematical Division" by Math Open Reference
  • "Division" by Khan Academy
  • "Mathematical Division" by Wikipedia

Glossary

  • Dividend: The number being divided.
  • Divisor: The number by which we are dividing.
  • Quotient: The result of the division.
  • Exact Division: Division that results in a whole number quotient.
  • Approximate Division: Division that results in a decimal quotient.
    Frequently Asked Questions (FAQs) About Mathematical Division ================================================================

Q: What is mathematical division?

A: Mathematical division is the process of finding the quotient of two numbers. It involves dividing a dividend (the number being divided) by a divisor (the number by which we are dividing) to obtain a quotient (the result of the division).

Q: What are the types of division?

A: There are two main types of division: exact division and approximate division.

  • Exact Division: This type of division involves dividing a number by another number to obtain a whole number quotient. For example, 12 ÷ 3 = 4.
  • Approximate Division: This type of division involves dividing a number by another number to obtain a decimal quotient. For example, 12 ÷ 3 = 4.00.

Q: How do I calculate 167 ÷ 17?

A: To calculate 167 ÷ 17, follow the steps of division:

  1. Write the dividend and divisor: Write the dividend (167) and divisor (17) in a vertical format, with the dividend on top and the divisor below.
  2. Divide the first digit: Divide the first digit of the dividend (1) by the divisor (17). Since 1 is less than 17, we write 0 as the first digit of the quotient.
  3. Bring down the next digit: Bring down the next digit of the dividend (6) and divide it by the divisor (17). The result is 36, which is greater than 17. So, we write 2 as the next digit of the quotient.
  4. Multiply and subtract: Multiply the divisor (17) by the next digit of the quotient (2) and subtract the result from the dividend (36). The result is 0.
  5. Bring down the next digit: Bring down the next digit of the dividend (7) and divide it by the divisor (17). The result is 41, which is greater than 17. So, we write 2 as the next digit of the quotient.
  6. Multiply and subtract: Multiply the divisor (17) by the next digit of the quotient (2) and subtract the result from the dividend (41). The result is 6.
  7. Bring down the next digit: Bring down the next digit of the dividend (1) and divide it by the divisor (17). The result is 0. So, we write 0 as the next digit of the quotient.

Q: What is the result of 167 ÷ 17?

A: The result of 167 ÷ 17 is 9.82.

Q: What are the real-world applications of mathematical division?

A: Mathematical division has numerous real-world applications in various fields, including:

  • Business: Division is used to calculate the cost per unit of a product, the profit per unit, and the return on investment.
  • Science: Division is used to calculate the concentration of a solution, the density of a substance, and the rate of a chemical reaction.
  • Engineering: Division is used to calculate the stress on a material, the strain on a structure, and the efficiency of a machine.

Q: How can I practice my division skills?

A: To practice your division skills, try solving the following problems:

  • 432 ÷ 12 = ?
  • 945 ÷ 15 = ?
  • 1234 ÷ 17 = ?

Q: What are some common mistakes to avoid when dividing numbers?

A: Some common mistakes to avoid when dividing numbers include:

  • Not following the order of operations: Make sure to follow the order of operations (PEMDAS) when dividing numbers.
  • Not using the correct divisor: Make sure to use the correct divisor when dividing numbers.
  • Not checking for exact division: Make sure to check if the division is exact or approximate.

Q: What are some resources for learning more about mathematical division?

A: Some resources for learning more about mathematical division include:

  • Math Open Reference: A comprehensive online reference for mathematical concepts, including division.
  • Khan Academy: A free online learning platform that offers video lessons and practice exercises on mathematical concepts, including division.
  • Wikipedia: A free online encyclopedia that offers articles on mathematical concepts, including division.