Find The Quotient. 90 − 10 = ? \frac{90}{-10} = \, ? − 10 90 ​ = ?

Introduction

When it comes to dividing numbers, it's essential to understand the concept of quotients and how to calculate them. In this article, we will delve into the world of division and explore the process of finding the quotient. We will also examine a specific problem, $\frac{90}{-10} = \, ?$, and provide a step-by-step solution to help you understand the concept better.

What is a Quotient?

A quotient is the result of dividing one number by another. It represents the number of times the divisor (the number by which we are dividing) fits into the dividend (the number being divided). In other words, it's the answer to a division problem.

The Order of Operations

When dealing with division, it's crucial to follow the order of operations (PEMDAS):

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

The Problem: $\frac{90}{-10} = \, ?$

Now, let's tackle the problem at hand: $\frac{90}{-10} = \, ?$. To find the quotient, we need to divide 90 by -10.

Step 1: Divide 90 by 10

First, we'll divide 90 by 10 to get the quotient. 90 ÷ 10 = 9.

Step 2: Determine the Sign of the Quotient

Since we are dividing by a negative number (-10), the quotient will be negative. Therefore, the quotient is -9.

Conclusion

In conclusion, the quotient of $\frac{90}{-10}$ is -9. By following the order of operations and understanding the concept of quotients, we can easily solve division problems like this one.

Real-World Applications

Understanding quotients is essential in various real-world applications, such as:

• Finance: When calculating interest rates or investment returns, quotients are used to determine the amount of money earned or lost.
• Science: In physics and chemistry, quotients are used to calculate rates of change, such as velocity or concentration.
• Everyday Life: When shopping or cooking, quotients are used to determine the number of items or ingredients needed.

Tips and Tricks

Here are some tips and tricks to help you master division and find quotients:

• Use visual aids: Draw diagrams or use number lines to help you visualize the division process.
• Break down problems: Break down complex division problems into simpler ones to make them more manageable.
• Practice, practice, practice: The more you practice dividing numbers, the more comfortable you'll become with finding quotients.

Common Mistakes to Avoid

When finding quotients, it's essential to avoid common mistakes, such as:

• Forgetting to change the sign: When dividing by a negative number, remember to change the sign of the quotient.
• Not following the order of operations: Make sure to follow the order of operations (PEMDAS) to ensure accurate results.
• Rounding errors: Be careful when rounding numbers to avoid errors in your calculations.

Conclusion

In conclusion, finding quotients is a fundamental concept in mathematics that has numerous real-world applications. By understanding the concept of quotients and following the order of operations, you can easily solve division problems like $\frac{90}{-10} = \, ?$. Remember to practice regularly and avoid common mistakes to become proficient in finding quotients.

Introduction

In our previous article, we explored the concept of quotients and how to calculate them. We also examined a specific problem, $\frac{90}{-10} = \, ?$, and provided a step-by-step solution to help you understand the concept better. In this article, we will address some frequently asked questions (FAQs) related to finding quotients.

Q&A

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

A: A quotient is the result of dividing one number by another, while a remainder is the amount left over after the division. For example, if we divide 17 by 5, the quotient is 3 and the remainder is 2.

Q: How do I handle negative numbers when finding quotients?

A: When dividing by a negative number, the quotient will be negative. For example, $\frac{-10}{2} = -5$. When dividing a negative number by a positive number, the quotient will be negative. For example, $\frac{-10}{2} = -5$. When dividing a positive number by a negative number, the quotient will be positive. For example, $\frac{10}{-2} = -5$.

Q: What is the order of operations when finding quotients?

A: The order of operations when finding quotients is:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I handle decimals when finding quotients?

A: When dividing decimals, you can use long division or a calculator to find the quotient. For example, $\frac{0.5}{0.2} = 2.5$.

Q: What is the difference between a quotient and a fraction?

A: A quotient is the result of dividing one number by another, while a fraction is a way of representing a quotient as a ratio of two numbers. For example, $\frac{1}{2}$ is a fraction that represents the quotient of 1 divided by 2.

Q: How do I simplify fractions when finding quotients?

A: To simplify a fraction, you can divide both the numerator and the denominator by their greatest common divisor (GCD). For example, $\frac{6}{8}$ can be simplified by dividing both 6 and 8 by 2, resulting in $\frac{3}{4}$.

Q: What is the difference between a quotient and a product?

A: A quotient is the result of dividing one number by another, while a product is the result of multiplying two or more numbers together. For example, $3 \times 4 = 12$ is a product, while $\frac{12}{3} = 4$ is a quotient.

Conclusion

In conclusion, finding quotients is a fundamental concept in mathematics that has numerous real-world applications. By understanding the concept of quotients and following the order of operations, you can easily solve division problems. We hope this Q&A article has helped address some of the frequently asked questions related to finding quotients.

Additional Resources

• Math textbooks: Check out your local library or online resources for math textbooks that cover division and quotients.
• Online tutorials: Websites like Khan Academy, Mathway, and IXL offer interactive tutorials and practice exercises to help you improve your math skills.
• Math apps: Download math apps like Photomath, Math Tricks, or Math Tricks Pro to practice division and quotients on the go.

Final Tips

• Practice regularly: The more you practice dividing numbers, the more comfortable you'll become with finding quotients.
• Use visual aids: Draw diagrams or use number lines to help you visualize the division process.
• Break down problems: Break down complex division problems into simpler ones to make them more manageable.

By following these tips and practicing regularly, you'll become proficient in finding quotients and solving division problems with ease.