There Are 8 Brooms And 6 Mops In A Janitor's Closet. What Is The Ratio Of The Number Of Mops To The Number Of Brooms?A. $\frac{3}{4}$ B. $\frac{4}{3}$ C. $\frac{7}{3}$ D. $\frac{3}{7}$

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In mathematics, a ratio is a way to compare two numbers by division. It is a fraction that shows the relationship between two quantities. In this article, we will explore how to find the ratio of the number of mops to the number of brooms in a janitor's closet.

The Problem

There are 8 brooms and 6 mops in a janitor's closet. We need to find the ratio of the number of mops to the number of brooms.

What is a Ratio?

A ratio is a comparison of two numbers by division. It is a fraction that shows the relationship between two quantities. In this case, we want to find the ratio of the number of mops to the number of brooms.

Finding the Ratio

To find the ratio of the number of mops to the number of brooms, we need to divide the number of mops by the number of brooms.

Number of mops = 6 Number of brooms = 8

Ratio = Number of mops / Number of brooms = 6 / 8 = 3 / 4

Simplifying the Ratio

The ratio 3/4 is already in its simplest form. However, we can simplify it further by dividing both the numerator and the denominator by their greatest common divisor (GCD).

GCD of 3 and 4 = 1

Since the GCD is 1, the ratio 3/4 is already in its simplest form.

Conclusion

The ratio of the number of mops to the number of brooms in a janitor's closet is 3/4. This means that for every 4 brooms, there are 3 mops.

Answer

The correct answer is A. 3/4.

Real-World Applications

Ratios are used in many real-world applications, such as:

  • Cooking: Recipes often require a ratio of ingredients to produce a desired dish.
  • Building: Architects use ratios to design buildings and ensure that they are proportional.
  • Finance: Investors use ratios to evaluate the performance of stocks and bonds.

Tips and Tricks

  • Use a calculator: When finding ratios, use a calculator to simplify the fraction.
  • Check for common factors: Before simplifying a ratio, check if the numerator and denominator have any common factors.
  • Use real-world examples: Use real-world examples to help illustrate the concept of ratios.

Common Mistakes

  • Forgetting to simplify: Failing to simplify a ratio can lead to incorrect answers.
  • Not checking for common factors: Failing to check for common factors can lead to incorrect simplifications.
  • Using the wrong operation: Using the wrong operation (e.g., addition instead of division) can lead to incorrect answers.

Conclusion

In this article, we will answer some frequently asked questions about ratios to help you better understand this concept.

Q: What is a ratio?

A: A ratio is a way to compare two numbers by division. It is a fraction that shows the relationship between two quantities.

Q: How do I find the ratio of two numbers?

A: To find the ratio of two numbers, you need to divide the first number by the second number. For example, if you want to find the ratio of 6 to 8, you would divide 6 by 8.

Q: What is the difference between a ratio and a proportion?

A: A ratio is a comparison of two numbers by division, while a proportion is a statement that two ratios are equal. For example, 2:3 is a ratio, while 2/3 = 4/6 is a proportion.

Q: How do I simplify a ratio?

A: To simplify a ratio, you need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD. For example, if you have the ratio 6/8, the GCD is 2, so you would divide both numbers by 2 to get 3/4.

Q: What is the ratio of 12 to 16?

A: To find the ratio of 12 to 16, you need to divide 12 by 16. This can be simplified to 3/4.

Q: What is the ratio of 20 to 25?

A: To find the ratio of 20 to 25, you need to divide 20 by 25. This can be simplified to 4/5.

Q: How do I use ratios in real-world applications?

A: Ratios are used in many real-world applications, such as:

  • Cooking: Recipes often require a ratio of ingredients to produce a desired dish.
  • Building: Architects use ratios to design buildings and ensure that they are proportional.
  • Finance: Investors use ratios to evaluate the performance of stocks and bonds.

Q: What are some common mistakes to avoid when working with ratios?

A: Some common mistakes to avoid when working with ratios include:

  • Forgetting to simplify: Failing to simplify a ratio can lead to incorrect answers.
  • Not checking for common factors: Failing to check for common factors can lead to incorrect simplifications.
  • Using the wrong operation: Using the wrong operation (e.g., addition instead of division) can lead to incorrect answers.

Q: How do I know if a ratio is in its simplest form?

A: A ratio is in its simplest form if the numerator and the denominator have no common factors other than 1. You can check this by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both numbers by the GCD.

Conclusion

In conclusion, ratios are an essential concept in mathematics that allows us to compare two numbers by division. By understanding how to find and simplify ratios, we can apply this concept to real-world problems and make informed decisions.