Find Unit Rates Worksheets [PDF] (7.RP.A.1): 7th Grade Math - Free Printable

Problem: Solve the unit rate problems and explain the solution.

#### Problem 1:
Harry rented an ATV to drive up a mountain. He drove \(4 \frac{1}{5}\) miles in \(3 \frac{1}{4}\) hours. If he travels at a constant rate, how many miles will he drive in 1 hour?

Solution:
1. Convert the mixed numbers to improper fractions:
- \(4 \frac{1}{5} = \frac{21}{5}\)
- \(3 \frac{1}{4} = \frac{13}{4}\)

2. To find the unit rate (miles per hour), divide the distance by the time:
\[
\text{Unit rate} = \frac{\text{Distance}}{\text{Time}} = \frac{\frac{21}{5}}{\frac{13}{4}}
\]

3. Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
\frac{\frac{21}{5}}{\frac{13}{4}} = \frac{21}{5} \times \frac{4}{13} = \frac{21 \times 4}{5 \times 13} = \frac{84}{65}
\]

4. Simplify the fraction if possible. Here, \(\frac{84}{65}\) is already in simplest form.

5. Convert the improper fraction to a mixed number:
\[
\frac{84}{65} = 1 \frac{19}{65}
\]

Answer:
\[
\boxed{1 \frac{19}{65}}
\]

---

#### Problem 2:
At the Olympics, a long-distance swimmer swam 18 miles in \(1 \frac{3}{5}\) hours. What was the speed of the swimmer in miles per hour?

Solution:
1. Convert the mixed number to an improper fraction:
- \(1 \frac{3}{5} = \frac{8}{5}\)

2. To find the unit rate (speed in miles per hour), divide the distance by the time:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{18}{\frac{8}{5}}
\]

3. Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
\frac{18}{\frac{8}{5}} = 18 \times \frac{5}{8} = \frac{18 \times 5}{8} = \frac{90}{8}
\]

4. Simplify the fraction:
\[
\frac{90}{8} = \frac{45}{4}
\]

5. Convert the improper fraction to a mixed number:
\[
\frac{45}{4} = 11 \frac{1}{4}
\]

Answer:
\[
\boxed{11 \frac{1}{4}}
\]

---

#### Problem 3:
Carmen is making some bread dough. Her grandma’s recipe requires \(2 \frac{1}{4}\) cups of flour and \(3 \frac{3}{8}\) teaspoons of salt. Using the same recipe, how much salt will she need for 1 cup of flour?

Solution:
1. Convert the mixed numbers to improper fractions:
- \(2 \frac{1}{4} = \frac{9}{4}\)
- \(3 \frac{3}{8} = \frac{27}{8}\)

2. To find the amount of salt needed for 1 cup of flour, set up a proportion:
\[
\text{Salt per cup of flour} = \frac{\text{Total salt}}{\text{Total flour}} = \frac{\frac{27}{8}}{\frac{9}{4}}
\]

3. Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
\frac{\frac{27}{8}}{\frac{9}{4}} = \frac{27}{8} \times \frac{4}{9} = \frac{27 \times 4}{8 \times 9} = \frac{108}{72}
\]

4. Simplify the fraction:
\[
\frac{108}{72} = \frac{3}{2}
\]

5. Convert the improper fraction to a mixed number:
\[
\frac{3}{2} = 1 \frac{1}{2}
\]

Answer:
\[
\boxed{1 \frac{1}{2}}
\]

---

#### Problem 4:
A recycling plant processes \(\frac{1}{4}\) ton of paper every 3 minutes. If the plant operates at a constant rate, how many tons of paper does the recycling plant process in 1 hour?

Solution:
1. First, determine the rate of processing in tons per minute:
\[
\text{Rate} = \frac{\frac{1}{4} \text{ ton}}{3 \text{ minutes}} = \frac{1}{4} \div 3 = \frac{1}{4} \times \frac{1}{3} = \frac{1}{12} \text{ tons per minute}
\]

2. There are 60 minutes in 1 hour. Multiply the rate by 60 to find the total tons processed in 1 hour:
\[
\text{Tons in 1 hour} = \frac{1}{12} \times 60 = 5 \text{ tons}
\]

Answer:
\[
\boxed{5}
\]

---

#### Problem 5:
Andrew is making sun tea on his back porch. He put a thermometer in the pitcher and found that the temperature of the tea is increasing 2.3 degrees every 4 minutes. If the temperature of the tea increases at a constant rate, how much will the temperature increase in 1 hour?

Solution:
1. First, determine the rate of temperature increase per minute:
\[
\text{Rate} = \frac{2.3 \text{ degrees}}{4 \text{ minutes}} = 0.575 \text{ degrees per minute}
\]

2. There are 60 minutes in 1 hour. Multiply the rate by 60 to find the total temperature increase in 1 hour:
\[
\text{Temperature increase in 1 hour} = 0.575 \times 60 = 34.5 \text{ degrees}
\]

Answer:
\[
\boxed{34.5}
\]

---

Final Answers:

1. \(\boxed{1 \frac{19}{65}}\)
2. \(\boxed{11 \frac{1}{4}}\)
3. \(\boxed{1 \frac{1}{2}}\)
4. \(\boxed{5}\)
5. \(\boxed{34.5}\)