Noah Makes An Acai Bowl Using \[$\frac{1}{4}\$\] Cup Of Bananas For Every \[$\frac{1}{3}\$\] Cup Of Apple Juice. He Wants To Know:Which Ratio Of Cups Of Banana To Cups Of Apple Juice Is Equivalent To \[$\frac{1}{4} :

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Introduction

Noah, a health-conscious individual, is in the process of preparing an acai bowl. He has a specific recipe in mind, which involves a combination of bananas and apple juice. The recipe calls for a certain ratio of cups of banana to cups of apple juice. However, Noah is unsure about the equivalent ratio of cups of banana to cups of apple juice. In this article, we will delve into the mathematical world and explore the concept of equivalent ratios to help Noah resolve his conundrum.

Understanding Equivalent Ratios

Before we dive into the specifics of Noah's recipe, let's take a step back and understand the concept of equivalent ratios. Equivalent ratios are ratios that have the same value, but are expressed in different terms. For example, the ratio 2:3 is equivalent to the ratio 4:6, as both ratios have the same value, but are expressed in different terms.

Noah's Recipe: A Mathematical Representation

Noah's recipe involves a ratio of cups of banana to cups of apple juice. The recipe calls for {\frac{1}{4}$}$ cup of bananas for every {\frac{1}{3}$}$ cup of apple juice. We can represent this ratio mathematically as:

1413=34\frac{\frac{1}{4}}{\frac{1}{3}} = \frac{3}{4}

This ratio represents the number of cups of banana to cups of apple juice in Noah's recipe.

Finding Equivalent Ratios

Now that we have a mathematical representation of Noah's recipe, let's explore the concept of equivalent ratios. We want to find a ratio of cups of banana to cups of apple juice that is equivalent to [$\frac1}{4}\frac{1{3}$.

To find an equivalent ratio, we can multiply or divide both terms of the ratio by the same non-zero number. Let's multiply both terms of the ratio by 12:

14×12=3\frac{1}{4} \times 12 = 3

13×12=4\frac{1}{3} \times 12 = 4

This gives us a new ratio of 3:4, which is equivalent to the original ratio of [$\frac1}{4}\frac{1{3}$.

Conclusion

In conclusion, we have explored the concept of equivalent ratios and applied it to Noah's acai bowl recipe. We have found that the ratio of 3:4 is equivalent to the original ratio of [$\frac1}{4}\frac{1{3}$. This means that for every 3 cups of banana, Noah can use 4 cups of apple juice to achieve the same ratio.

Real-World Applications

The concept of equivalent ratios has numerous real-world applications. In cooking, equivalent ratios can be used to scale up or down a recipe. For example, if a recipe calls for a ratio of 2:3, but you want to make a larger batch, you can multiply both terms of the ratio by the same number to achieve the desired ratio.

In business, equivalent ratios can be used to compare different products or services. For example, if a company offers a product with a ratio of 3:4, but a competitor offers a similar product with a ratio of 2:3, the company can use equivalent ratios to compare the two products and determine which one is more cost-effective.

Final Thoughts

In conclusion, the concept of equivalent ratios is a powerful tool that can be applied to a wide range of situations. Whether you're a health-conscious individual like Noah, or a business owner looking to compare products, equivalent ratios can help you make informed decisions and achieve your goals.

Glossary of Terms

  • Equivalent ratios: Ratios that have the same value, but are expressed in different terms.
  • Ratio: A comparison of two or more numbers.
  • Scale up: To increase the size of a recipe or product.
  • Scale down: To decrease the size of a recipe or product.

References

About the Author

Q&A: Equivalent Ratios and Beyond

In our previous article, we explored the concept of equivalent ratios and applied it to Noah's acai bowl recipe. We found that the ratio of 3:4 is equivalent to the original ratio of [$\frac1}{4}\frac{1{3}$. In this article, we will continue to explore the concept of equivalent ratios and answer some frequently asked questions.

Q: What is the difference between equivalent ratios and proportional ratios?

A: Equivalent ratios and proportional ratios are often used interchangeably, but they have slightly different meanings. Equivalent ratios refer to ratios that have the same value, but are expressed in different terms. Proportional ratios, on the other hand, refer to ratios that have the same value and are expressed in the same terms.

Q: How do I find equivalent ratios?

A: To find equivalent ratios, you can multiply or divide both terms of the ratio by the same non-zero number. For example, if you have a ratio of 2:3, you can multiply both terms by 4 to get an equivalent ratio of 8:12.

Q: Can I use equivalent ratios to compare different products or services?

A: Yes, equivalent ratios can be used to compare different products or services. For example, if a company offers a product with a ratio of 3:4, but a competitor offers a similar product with a ratio of 2:3, you can use equivalent ratios to compare the two products and determine which one is more cost-effective.

Q: How do I scale up or down a recipe using equivalent ratios?

A: To scale up or down a recipe using equivalent ratios, you can multiply or divide both terms of the ratio by the same non-zero number. For example, if a recipe calls for a ratio of 2:3, but you want to make a larger batch, you can multiply both terms by 4 to get an equivalent ratio of 8:12.

Q: Can I use equivalent ratios in real-world applications beyond cooking and business?

A: Yes, equivalent ratios can be used in a wide range of real-world applications beyond cooking and business. For example, in science, equivalent ratios can be used to compare the concentrations of different substances. In engineering, equivalent ratios can be used to compare the dimensions of different structures.

Q: How do I determine if two ratios are equivalent?

A: To determine if two ratios are equivalent, you can multiply or divide both terms of each ratio by the same non-zero number. If the resulting ratios are the same, then the original ratios are equivalent.

Q: Can I use equivalent ratios to solve problems involving proportions?

A: Yes, equivalent ratios can be used to solve problems involving proportions. For example, if you have a ratio of 2:3 and you want to find the equivalent ratio when the first term is multiplied by 4, you can multiply both terms by 4 to get an equivalent ratio of 8:12.

Conclusion

In conclusion, equivalent ratios are a powerful tool that can be used in a wide range of situations. Whether you're a health-conscious individual like Noah, or a business owner looking to compare products, equivalent ratios can help you make informed decisions and achieve your goals.

Glossary of Terms

  • Equivalent ratios: Ratios that have the same value, but are expressed in different terms.
  • Proportional ratios: Ratios that have the same value and are expressed in the same terms.
  • Scale up: To increase the size of a recipe or product.
  • Scale down: To decrease the size of a recipe or product.

References

About the Author

The author is a mathematics enthusiast with a passion for explaining complex concepts in a simple and easy-to-understand manner. With a background in mathematics and education, the author is well-equipped to provide insightful and informative content on a wide range of mathematical topics.