What Is The Quotient Of The Following Division?$\[ -\frac{4}{5} \div 2 \\]A. \[$-1 \frac{3}{5}\$\]B. \[$-\frac{2}{5}\$\]C. \[$\frac{1}{2}\$\]D. \[$1 \frac{3}{5}\$\]

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Introduction

In mathematics, division is a fundamental operation that involves sharing a certain quantity into equal parts or groups. When we divide a number by another number, we are essentially finding out how many times the divisor fits into the dividend. In this article, we will explore the concept of division and how to find the quotient of a given division problem.

What is the Quotient of a Division?

The quotient of a division is the result of dividing one number by another. It represents the number of times the divisor fits into the dividend. For example, if we divide 12 by 3, the quotient is 4, because 3 fits into 12 four times.

The Division Problem

The division problem we are given is:

βˆ’45Γ·2{ -\frac{4}{5} \div 2 }

To find the quotient of this division, we need to follow the order of operations (PEMDAS):

  1. Divide the numerator (-4) by the denominator (5): -4 Γ· 5 = -\frac{4}{5}
  2. Divide the result by 2: -\frac{4}{5} Γ· 2

Solving the Division Problem

To solve the division problem, we can use the following steps:

  1. Multiply the numerator and denominator by 2 to get rid of the fraction: -\frac{4}{5} Γ— \frac{2}{2} = -\frac{8}{10}
  2. Simplify the fraction: -\frac{8}{10} = -\frac{4}{5}
  3. Divide the numerator and denominator by 2: -\frac{4}{5} Γ· 2 = -\frac{2}{5} Γ· 2
  4. Multiply the numerator and denominator by 2 to get rid of the fraction: -\frac{2}{5} Γ— \frac{2}{2} = -\frac{4}{10}
  5. Simplify the fraction: -\frac{4}{10} = -\frac{2}{5}

The Final Answer

Therefore, the quotient of the division problem is:

βˆ’25{ -\frac{2}{5} }

Conclusion

In conclusion, the quotient of a division is the result of dividing one number by another. To find the quotient of a given division problem, we need to follow the order of operations and simplify the fraction. In this article, we explored the concept of division and how to find the quotient of a given division problem.

Common Mistakes to Avoid

When solving division problems, it's essential to avoid common mistakes such as:

  • Not following the order of operations
  • Not simplifying the fraction
  • Not multiplying the numerator and denominator by the same number

Tips and Tricks

Here are some tips and tricks to help you solve division problems:

  • Use the order of operations to guide your calculations
  • Simplify the fraction as soon as possible
  • Multiply the numerator and denominator by the same number to get rid of the fraction

Practice Problems

Here are some practice problems to help you reinforce your understanding of division:

  1. 34Γ·2{ \frac{3}{4} \div 2 }
  2. βˆ’23Γ·3{ -\frac{2}{3} \div 3 }
  3. 56Γ·2{ \frac{5}{6} \div 2 }

Answer Key

Here are the answers to the practice problems:

  1. 38{ \frac{3}{8} }
  2. βˆ’29{ -\frac{2}{9} }
  3. 512{ \frac{5}{12} }

Conclusion

Introduction

In our previous article, we explored the concept of division and how to find the quotient of a given division problem. In this article, we will answer some frequently asked questions about the quotient of a division.

Q: What is the quotient of a division?

A: The quotient of a division is the result of dividing one number by another. It represents the number of times the divisor fits into the dividend.

Q: How do I find the quotient of a division?

A: To find the quotient of a division, you need to follow the order of operations (PEMDAS) and simplify the fraction. Here are the steps:

  1. Divide the numerator by the denominator
  2. Simplify the fraction
  3. Divide the numerator and denominator by the same number to get rid of the fraction

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

A: The quotient is the result of dividing one number by another, while the remainder is the amount left over after the division. For example, if you divide 12 by 3, the quotient is 4 and the remainder is 0.

Q: Can the quotient be a negative number?

A: Yes, the quotient can be a negative number. For example, if you divide -4 by 2, the quotient is -2.

Q: Can the quotient be a fraction?

A: Yes, the quotient can be a fraction. For example, if you divide 1/2 by 3, the quotient is 1/6.

Q: How do I handle division by zero?

A: Division by zero is undefined. If you try to divide a number by zero, you will get an error message or an undefined result.

Q: Can I use a calculator to find the quotient of a division?

A: Yes, you can use a calculator to find the quotient of a division. However, make sure to follow the order of operations and simplify the fraction to get the correct result.

Q: What are some common mistakes to avoid when finding the quotient of a division?

A: Some common mistakes to avoid when finding the quotient of a division include:

  • Not following the order of operations
  • Not simplifying the fraction
  • Not multiplying the numerator and denominator by the same number to get rid of the fraction

Q: How can I practice finding the quotient of a division?

A: You can practice finding the quotient of a division by using online resources, such as math websites and apps, or by working on practice problems. You can also try dividing different numbers and fractions to get a feel for how the quotient works.

Conclusion

In conclusion, the quotient of a division is the result of dividing one number by another. By following the order of operations and simplifying the fraction, you can find the quotient of a division. Remember to avoid common mistakes and practice finding the quotient of a division to become proficient.

Additional Resources

Here are some additional resources to help you learn more about the quotient of a division:

  • Khan Academy: Division
  • Mathway: Division
  • IXL: Division

Practice Problems

Here are some practice problems to help you reinforce your understanding of the quotient of a division:

  1. 34Γ·2{ \frac{3}{4} \div 2 }
  2. βˆ’23Γ·3{ -\frac{2}{3} \div 3 }
  3. 56Γ·2{ \frac{5}{6} \div 2 }

Answer Key

Here are the answers to the practice problems:

  1. 38{ \frac{3}{8} }
  2. βˆ’29{ -\frac{2}{9} }
  3. 512{ \frac{5}{12} }

Conclusion

In conclusion, the quotient of a division is an essential concept in mathematics. By following the order of operations and simplifying the fraction, you can find the quotient of a division. Remember to practice finding the quotient of a division to become proficient.