Which Ratios Have A Unit Rate Of 4? Choose ALL That Apply.A. 4 Cups : 1 1 4 1 \frac{1}{4} 1 4 1 ​ Cups B. 7 8 \frac{7}{8} 8 7 ​ Cup : 3 1 2 3 \frac{1}{2} 3 2 1 ​ Cups C. 2 1 2 2 \frac{1}{2} 2 2 1 ​ Cups : 5 8 \frac{5}{8} 8 5 ​ Cup D. 2 Cups :

In mathematics, a unit rate is a ratio in which the second term is equal to 1. It is a way to express a comparison between two quantities in a simplified form. When we have a ratio with a unit rate, it means that the second term is a single unit, making it easier to understand and compare the quantities. In this article, we will explore which ratios have a unit rate of 4.

What is a Unit Rate?

A unit rate is a ratio in which the second term is equal to 1. It is a way to express a comparison between two quantities in a simplified form. For example, if we have a ratio of 4 cups to 1 cup, the unit rate is 4. This means that for every 1 cup, we have 4 cups.

Choosing the Correct Ratios

Now that we understand what a unit rate is, let's look at the given ratios and determine which ones have a unit rate of 4.

A. 4 cups : $1 \frac{1}{4}$ cups

To determine if this ratio has a unit rate of 4, we need to simplify the second term. $1 \frac{1}{4}$ cups can be converted to an improper fraction: $\frac{5}{4}$ cups. Now, we can divide both terms by the second term to get the unit rate: $\frac{4}{\frac{5}{4}} = \frac{16}{5}$. This is not equal to 4, so this ratio does not have a unit rate of 4.

B. $\frac{7}{8}$ cup : $3 \frac{1}{2}$ cups

To determine if this ratio has a unit rate of 4, we need to simplify the second term. $3 \frac{1}{2}$ cups can be converted to an improper fraction: $\frac{7}{2}$ cups. Now, we can divide both terms by the second term to get the unit rate: $\frac{\frac{7}{8}}{\frac{7}{2}} = \frac{7}{8} \times \frac{2}{7} = \frac{1}{4}$. This is not equal to 4, so this ratio does not have a unit rate of 4.

C. $2 \frac{1}{2}$ cups : $\frac{5}{8}$ cup

To determine if this ratio has a unit rate of 4, we need to simplify the second term. $\frac{5}{8}$ cup is already in its simplest form. Now, we can divide both terms by the second term to get the unit rate: $\frac{2 \frac{1}{2}}{\frac{5}{8}} = \frac{\frac{5}{2}}{\frac{5}{8}} = \frac{5}{2} \times \frac{8}{5} = 4$. This ratio has a unit rate of 4.

D. 2 cups : 1 cup

To determine if this ratio has a unit rate of 4, we can simply divide both terms by the second term: $\frac{2}{1} = 2$. This is not equal to 4, so this ratio does not have a unit rate of 4.

Conclusion

In conclusion, only one of the given ratios has a unit rate of 4: C. $2 \frac{1}{2}$ cups : $\frac{5}{8}$ cup. This ratio has a unit rate of 4, making it the correct answer.

Additional Tips and Tricks

When working with ratios and unit rates, it's essential to simplify the second term to get the correct unit rate. This can be done by converting mixed numbers to improper fractions and then dividing both terms by the second term. Additionally, make sure to check if the second term is equal to 1, as this is the definition of a unit rate.

Common Mistakes to Avoid

When working with ratios and unit rates, it's easy to make mistakes. Here are some common mistakes to avoid:

• Not simplifying the second term before calculating the unit rate
• Not checking if the second term is equal to 1
• Not using the correct division method to calculate the unit rate

By avoiding these common mistakes, you can ensure that you get the correct unit rate and make accurate comparisons between quantities.

Real-World Applications

Understanding unit rates is essential in real-world applications, such as:

• Cooking: When a recipe calls for a certain amount of ingredients, you need to understand the unit rate to adjust the quantities accordingly.
• Finance: When comparing prices of different products, you need to understand the unit rate to make informed decisions.
• Science: When working with measurements, you need to understand the unit rate to make accurate calculations.

By understanding unit rates, you can make informed decisions and make accurate calculations in various real-world applications.

Conclusion

In this article, we will answer some frequently asked questions about unit rates.

Q: What is a unit rate?

A: A unit rate is a ratio in which the second term is equal to 1. It is a way to express a comparison between two quantities in a simplified form.

Q: How do I calculate a unit rate?

A: To calculate a unit rate, you need to simplify the second term and then divide both terms by the second term. For example, if you have a ratio of 4 cups to 1 cup, you can calculate the unit rate by dividing both terms by the second term: $\frac{4}{1} = 4$.

Q: What is the difference between a ratio and a unit rate?

A: A ratio is a comparison between two quantities, while a unit rate is a ratio in which the second term is equal to 1. For example, the ratio 4 cups to 1 cup is equal to the unit rate 4.

Q: Can a unit rate be greater than 1?

A: Yes, a unit rate can be greater than 1. For example, the ratio 8 cups to 1 cup has a unit rate of 8.

Q: Can a unit rate be less than 1?

A: Yes, a unit rate can be less than 1. For example, the ratio 1 cup to 8 cups has a unit rate of $\frac{1}{8}$.

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

A: Unit rates are used in various real-world applications, such as cooking, finance, and science. For example, when a recipe calls for a certain amount of ingredients, you need to understand the unit rate to adjust the quantities accordingly.

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

A: Some common mistakes to avoid when working with unit rates include:

• Not simplifying the second term before calculating the unit rate
• Not checking if the second term is equal to 1
• Not using the correct division method to calculate the unit rate

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and then add the numerator. For example, the mixed number 2 $\frac{1}{2}$ can be converted to an improper fraction by multiplying the whole number by the denominator and then adding the numerator: $2 \times 2 + 1 = 5$. The improper fraction is then $\frac{5}{2}$.

Q: How do I convert an improper fraction to a mixed number?

A: To convert an improper fraction to a mixed number, you need to divide the numerator by the denominator and then write the remainder as the new numerator. For example, the improper fraction $\frac{5}{2}$ can be converted to a mixed number by dividing the numerator by the denominator and then writing the remainder as the new numerator: $5 \div 2 = 2$ with a remainder of 1. The mixed number is then 2 $\frac{1}{2}$.

Q: What are some real-world examples of unit rates?

A: Some real-world examples of unit rates include:

• Cooking: When a recipe calls for a certain amount of ingredients, you need to understand the unit rate to adjust the quantities accordingly.
• Finance: When comparing prices of different products, you need to understand the unit rate to make informed decisions.
• Science: When working with measurements, you need to understand the unit rate to make accurate calculations.

Conclusion

In conclusion, unit rates are an essential concept in mathematics and real-world applications. By understanding how to calculate and use unit rates, you can make informed decisions and make accurate calculations in various situations. Remember to avoid common mistakes and use the correct division method to calculate the unit rate. With practice and patience, you can become proficient in working with unit rates.