Decide If Each Ratio Has A Unit Rate Of 2 Or 1 2 \frac{1}{2} 2 1 ​ . Then Move It To The Correct Bin.- Unit Rate Of 1 2 \frac{1}{2} 2 1 ​ : - 4 5 : 8 5 \frac{4}{5}: \frac{8}{5} 5 4 ​ : 5 8 ​ - 1 3 : 2 3 \frac{1}{3}: \frac{2}{3} 3 1 ​ : 3 2 ​ - Unit Rate Of 2: -

Understanding Unit Rates

A unit rate is a ratio with a value of 1. It is used to compare the relationship between two quantities. In this article, we will explore how to determine if a given ratio has a unit rate of 2 or $\frac{1}{2}$ and then move it to the correct bin.

Identifying Unit Rates of $\frac{1}{2}$

To identify a unit rate of $\frac{1}{2}$, we need to look for a ratio where the second quantity is half of the first quantity. Let's examine the given ratios:

$\frac{4}{5}: \frac{8}{5}$

To determine if this ratio has a unit rate of $\frac{1}{2}$, we need to check if the second quantity is half of the first quantity. We can do this by dividing the second quantity by the first quantity:

$$\frac{8}{5} \div \frac{4}{5} = \frac{8}{5} \times \frac{5}{4} = 2$$

Since the result is not $\frac{1}{2}$, this ratio does not have a unit rate of $\frac{1}{2}$.

$\frac{1}{3}: \frac{2}{3}$

Now, let's examine the second ratio:

To determine if this ratio has a unit rate of $\frac{1}{2}$, we need to check if the second quantity is half of the first quantity. We can do this by dividing the second quantity by the first quantity:

$$\frac{2}{3} \div \frac{1}{3} = \frac{2}{3} \times \frac{3}{1} = 2$$

Since the result is not $\frac{1}{2}$, this ratio does not have a unit rate of $\frac{1}{2}$.

Identifying Unit Rates of 2

To identify a unit rate of 2, we need to look for a ratio where the second quantity is twice the first quantity. Let's examine the given ratios:

$\frac{4}{5}: \frac{8}{5}$

To determine if this ratio has a unit rate of 2, we need to check if the second quantity is twice the first quantity. We can do this by dividing the second quantity by the first quantity:

$$\frac{8}{5} \div \frac{4}{5} = \frac{8}{5} \times \frac{5}{4} = 2$$

Since the result is 2, this ratio has a unit rate of 2.

$\frac{1}{3}: \frac{2}{3}$

Now, let's examine the second ratio:

To determine if this ratio has a unit rate of 2, we need to check if the second quantity is twice the first quantity. We can do this by dividing the second quantity by the first quantity:

$$\frac{2}{3} \div \frac{1}{3} = \frac{2}{3} \times \frac{3}{1} = 2$$

Since the result is 2, this ratio has a unit rate of 2.

Organizing Ratios

Now that we have identified the unit rates of the given ratios, we can organize them into their respective bins.

Unit rate of $\frac{1}{2}$

Since neither of the given ratios has a unit rate of $\frac{1}{2}$, this bin is empty.

Unit rate of 2

Since both of the given ratios have a unit rate of 2, we can place them in this bin.

Conclusion

In this article, we have explored how to determine if a given ratio has a unit rate of 2 or $\frac{1}{2}$ and then move it to the correct bin. We have examined two given ratios and identified their unit rates. We have also organized the ratios into their respective bins. By following these steps, we can effectively identify and organize ratios with unit rates of 2 or $\frac{1}{2}$.

Key Takeaways

• A unit rate is a ratio with a value of 1.
• To identify a unit rate of $\frac{1}{2}$, we need to look for a ratio where the second quantity is half of the first quantity.
• To identify a unit rate of 2, we need to look for a ratio where the second quantity is twice the first quantity.
• We can organize ratios into their respective bins based on their unit rates.

Practice Problems

1. Determine if the ratio $\frac{6}{8}: \frac{12}{8}$ has a unit rate of $\frac{1}{2}$ or 2.
2. Determine if the ratio $\frac{3}{4}: \frac{6}{4}$ has a unit rate of $\frac{1}{2}$ or 2.
3. Organize the ratios $\frac{2}{5}: \frac{4}{5}$ and $\frac{1}{2}: \frac{2}{2}$ into their respective bins based on their unit rates.

Answer Key

1. The ratio $\frac{6}{8}: \frac{12}{8}$ has a unit rate of 2.
2. The ratio $\frac{3}{4}: \frac{6}{4}$ has a unit rate of 2.
3. The ratio $\frac{2}{5}: \frac{4}{5}$ has a unit rate of 2, and the ratio $\frac{1}{2}: \frac{2}{2}$ has a unit rate of 2.
   Q&A: Unit Rates and Ratios =============================

Frequently Asked Questions

Q: What is a unit rate?

A: A unit rate is a ratio with a value of 1. It is used to compare the relationship between two quantities.

Q: How do I determine if a ratio has a unit rate of $\frac{1}{2}$?

A: To determine if a ratio has a unit rate of $\frac{1}{2}$, you need to check if the second quantity is half of the first quantity. You can do this by dividing the second quantity by the first quantity.

Q: How do I determine if a ratio has a unit rate of 2?

A: To determine if a ratio has a unit rate of 2, you need to check if the second quantity is twice the first quantity. You can do this by dividing the second quantity by the first quantity.

Q: What is the difference between a unit rate of $\frac{1}{2}$ and a unit rate of 2?

A: A unit rate of $\frac{1}{2}$ means that the second quantity is half of the first quantity, while a unit rate of 2 means that the second quantity is twice the first quantity.

Q: How do I organize ratios into their respective bins based on their unit rates?

A: To organize ratios into their respective bins, you need to determine the unit rate of each ratio and then place it in the corresponding bin.

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

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

• Not checking if the second quantity is half of the first quantity when determining a unit rate of $\frac{1}{2}$.
• Not checking if the second quantity is twice the first quantity when determining a unit rate of 2.
• Not organizing ratios into their respective bins based on their unit rates.

Q: How can I practice working with unit rates and ratios?

A: You can practice working with unit rates and ratios by:

• Solving practice problems, such as those listed in the "Practice Problems" section of this article.
• Creating your own practice problems based on the concepts learned in this article.
• Working with real-world examples of unit rates and ratios.

Additional Resources

• For more information on unit rates and ratios, see the "Understanding Unit Rates" section of this article.
• For more practice problems, see the "Practice Problems" section of this article.
• For additional resources, see the "References" section of this article.

References

• [Insert references here]

Conclusion

In this article, we have explored the concept of unit rates and ratios, including how to determine if a ratio has a unit rate of $\frac{1}{2}$ or 2 and how to organize ratios into their respective bins based on their unit rates. We have also answered frequently asked questions and provided additional resources for further learning.

Key Takeaways

• A unit rate is a ratio with a value of 1.
• To determine if a ratio has a unit rate of $\frac{1}{2}$, you need to check if the second quantity is half of the first quantity.
• To determine if a ratio has a unit rate of 2, you need to check if the second quantity is twice the first quantity.
• You can organize ratios into their respective bins based on their unit rates.

Practice Problems

1. Determine if the ratio $\frac{9}{12}: \frac{18}{12}$ has a unit rate of $\frac{1}{2}$ or 2.
2. Determine if the ratio $\frac{2}{3}: \frac{4}{3}$ has a unit rate of $\frac{1}{2}$ or 2.
3. Organize the ratios $\frac{3}{5}: \frac{6}{5}$ and $\frac{1}{4}: \frac{2}{4}$ into their respective bins based on their unit rates.

Answer Key

1. The ratio $\frac{9}{12}: \frac{18}{12}$ has a unit rate of 2.
2. The ratio $\frac{2}{3}: \frac{4}{3}$ has a unit rate of 2.
3. The ratio $\frac{3}{5}: \frac{6}{5}$ has a unit rate of 2, and the ratio $\frac{1}{4}: \frac{2}{4}$ has a unit rate of 2.