Alonso conducted a scientific experiment. For a certain time, the temperature of a compound rose 2, one third2 
3
1
​
  degrees in start fraction, 1, divided by, 20, end fraction 
20
1
​
  of an hour. What was the rate, in degrees per hour, that the temperature of the compound rose?

On the double number line below, fill in the given values, then 

To determine the rate at which the temperature of the compound rose in degrees per hour, we need to use the information given and perform the necessary calculations.

Given:
- Temperature rise: \( 2 \frac{1}{3} \) degrees
- Time: \( \frac{1}{20} \) hour

First, convert the mixed fraction \( 2 \frac{1}{3} \) to an improper fraction:

\[ 2 \frac{1}{3} = 2 + \frac{1}{3} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3} \]

Next, use the formula for the rate:

\[ \text{Rate} = \frac{\text{Temperature rise}}{\text{Time}} = \frac{\frac{7}{3} \text{ degrees}}{\frac{1}{20} \text{ hour}} \]

To divide by a fraction, multiply by its reciprocal:

\[ \frac{7}{3} \div \frac{1}{20} = \frac{7}{3} \times \frac{20}{1} = \frac{7 \times 20}{3} = \frac{140}{3} \]

Thus, the rate at which the temperature of the compound rose is:

\[ \frac{140}{3} \text{ degrees per hour} \]

Simplified, this is:

\[ \frac{140}{3} \approx 46.67 \text{ degrees per hour} \]

### Double Number Line

To fill in the double number line, follow these steps:

1. Mark the time interval \( \frac{1}{20} \) hour and the corresponding temperature rise \( 2 \frac{1}{3} \) degrees.
2. Mark the 1-hour mark, and above it, write \( 46.67 \) degrees to show the calculated rate.

### Do you want details or have any questions?

### Relative Questions:

1. How do you convert a mixed number to an improper fraction?
2. What is the reciprocal of a fraction?
3. How do you multiply two fractions?
4. Why do we multiply by the reciprocal when dividing by a fraction?
5. What is the significance of using the rate in scientific experiments?
6. How would you describe the relationship between time and temperature rise in this context?
7. Can you explain the steps to plot values on a double number line?
8. What are some practical applications of calculating rates in scientific experiments?

### Tip:

When dealing with fractions, always simplify them first for easier calculations and to avoid errors.

Discover how to calculate the rate at which the temperature of a compound rose during Alonso's scientific experiment. Includes step-by-step solution using fractions and rates. Suitable for Grades 6-8.

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