Write $2 \frac{1}{4}$ Miles In $\frac{3}{4}$ Hour As A Unit Rate.Enter The Correct Answer In The Box. □ \square □ Miles Per Hour

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Understanding Unit Rates

A unit rate is a ratio that compares two quantities, where one of the quantities is 1. In other words, it's a rate that has a denominator of 1. Unit rates are often used to compare different rates or to express a rate in a more convenient form. In this article, we will learn how to convert a mixed number to a unit rate.

Converting Mixed Numbers to Fractions

Before we can convert a mixed number to a unit rate, we need to convert it to a fraction. A mixed number is a combination of a whole number and a fraction. For example, $2 \frac1}{4}$ is a mixed number that can be written as a fraction $\frac{9{4}$.

Converting Fractions to Unit Rates

Now that we have our mixed number in fraction form, we can convert it to a unit rate. To do this, we need to divide the numerator by the denominator. In this case, we have $\frac{9}{4}$, so we will divide 9 by 4.

Calculating the Unit Rate

To calculate the unit rate, we will divide the numerator by the denominator:

94=2.25\frac{9}{4} = 2.25

Converting the Unit Rate to a Mixed Number

Now that we have our unit rate as a decimal, we can convert it back to a mixed number. To do this, we will divide the decimal by 1 and write the result as a mixed number:

2.25=2142.25 = 2 \frac{1}{4}

Writing the Unit Rate as a Fraction

We can also write the unit rate as a fraction. To do this, we will divide the numerator by the denominator:

94=94\frac{9}{4} = \frac{9}{4}

Writing the Unit Rate as a Unit Rate

Finally, we can write the unit rate as a unit rate. To do this, we will divide the numerator by the denominator and write the result as a unit rate:

94=94 miles per hour\frac{9}{4} = \frac{9}{4} \text{ miles per hour}

Conclusion

In this article, we learned how to convert a mixed number to a unit rate. We started by converting the mixed number to a fraction, then we converted the fraction to a unit rate by dividing the numerator by the denominator. We also learned how to convert the unit rate back to a mixed number and how to write it as a fraction and a unit rate.

Example Problem

Write $2 \frac{1}{4}$ miles in $\frac{3}{4}$ hour as a unit rate.

Solution

To solve this problem, we will follow the steps we learned in this article. First, we will convert the mixed number to a fraction:

214=942 \frac{1}{4} = \frac{9}{4}

Next, we will convert the fraction to a unit rate by dividing the numerator by the denominator:

94=2.25\frac{9}{4} = 2.25

Finally, we will write the unit rate as a unit rate:

2.25=94 miles per hour2.25 = \frac{9}{4} \text{ miles per hour}

Answer

\frac{9}{4}$ miles per hour<br/> **Frequently Asked Questions (FAQs)** =====================================

Q: What is a unit rate?

A: A unit rate is a ratio that compares two quantities, where one of the quantities is 1. In other words, it's a rate that has a denominator of 1.

Q: Why do we need to convert mixed numbers to unit rates?

A: We need to convert mixed numbers to unit rates because unit rates are often used to compare different rates or to express a rate in a more convenient form.

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

A: To convert a mixed number to a fraction, you need to multiply the whole number by the denominator and then add the numerator. For example, $2 \frac{1}{4}$ can be written as $\frac{9}{4}$.

Q: How do I convert a fraction to a unit rate?

A: To convert a fraction to a unit rate, you need to divide the numerator by the denominator. For example, $\frac{9}{4}$ can be written as 2.25.

Q: How do I convert a unit rate to a mixed number?

A: To convert a unit rate to a mixed number, you need to divide the decimal by 1 and write the result as a mixed number. For example, 2.25 can be written as $2 \frac{1}{4}$.

Q: How do I write a unit rate as a fraction?

A: To write a unit rate as a fraction, you need to divide the numerator by the denominator. For example, 2.25 can be written as $\frac{9}{4}$.

Q: How do I write a unit rate as a unit rate?

A: To write a unit rate as a unit rate, you need to divide the numerator by the denominator and write the result as a unit rate. For example, $\frac{9}{4}$ can be written as $\frac{9}{4} \text{ miles per hour}$.

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

A: A unit rate is a ratio that compares two quantities, where one of the quantities is 1. A rate is a ratio that compares two quantities, where the denominator is not necessarily 1.

Q: Can I use a calculator to convert a mixed number to a unit rate?

A: Yes, you can use a calculator to convert a mixed number to a unit rate. However, it's always a good idea to understand the steps involved in the conversion process.

Q: Can I convert a unit rate to a mixed number using a calculator?

A: Yes, you can use a calculator to convert a unit rate to a mixed number. However, it's always a good idea to understand the steps involved in the conversion process.

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

A: Unit rates have many real-world applications, such as calculating speed, distance, and time. For example, if you're driving a car at a speed of 60 miles per hour, you can use a unit rate to calculate the distance you'll travel in a certain amount of time.

Q: Can I use unit rates to compare different rates?

A: Yes, you can use unit rates to compare different rates. For example, if you have two different rates, such as 2.25 miles per hour and 3.5 miles per hour, you can use a unit rate to compare them.

Q: Can I use unit rates to express a rate in a more convenient form?

A: Yes, you can use unit rates to express a rate in a more convenient form. For example, if you have a rate of 2.25 miles per hour, you can use a unit rate to express it as $\frac{9}{4}$ miles per hour.