finding rate Worksheets - Free Printable

The image you've uploaded is a math worksheet titled *"Finding Ratios and Unit Rate"*, with problems that require students to find both the ratio (as a comparison of two quantities) and the unit rate (the rate per one unit). The worksheet includes an answer key on the right side.

Let’s go through the concept, then analyze each problem step by step, explaining how to solve them.

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🔍 Understanding the Concepts

1. Ratio: A comparison of two numbers, written as `a:b` or `a/b`.
Example: 10 hours to drive 710 miles → ratio is 710:10

2. Unit Rate: A rate where the second quantity is 1. It tells "how much per one unit".
To find the unit rate, divide the first number by the second.
Example: 710 miles ÷ 10 hours = 71 miles per hour

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✔ Step-by-Step Solutions

We'll go through each problem, showing:
- The ratio
- The unit rate

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#### Example (Ex): 14 copies in 2 minutes
- Ratio: 14:2
- Unit rate: 14 ÷ 2 = 7 copies per minute

✔ Answer: 14:2, 7

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#### 1) 10 hours to drive 710 miles
- Ratio: 710:10
- Unit rate: 710 ÷ 10 = 71 miles per hour

✔ Answer: 710:10, 71

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#### 2) 3 boxes can hold 12 books
- Ratio: 12:3
- Unit rate: 12 ÷ 3 = 4 books per box

✔ Answer: 12:3, 4

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#### 3) 111 dollars for 37 TV channels
- Ratio: 111:37
- Unit rate: 111 ÷ 37 = 3 dollars per channel

✔ Answer: 111:37, 3

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#### 4) 48 customers over 2 days
- Ratio: 48:2
- Unit rate: 48 ÷ 2 = 24 customers per day

✔ Answer: 48:2, 24

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#### 5) 8 classrooms with 136 students
- Ratio: 136:8
- Unit rate: 136 ÷ 8 = 17 students per class

✔ Answer: 136:8, 17

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#### 6) 174 cherry pieces in 6 bags of candy
- Ratio: 174:6
- Unit rate: 174 ÷ 6 = 29 pieces per bag

✔ Answer: 174:6, 29

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#### 7) 54 dollars for mowing 2 lawns
- Ratio: 54:2
- Unit rate: 54 ÷ 2 = 27 dollars per lawn

✔ Answer: 54:2, 27

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#### 8) 2 mail trucks had 26 bags of letters
- Ratio: 26:2
- Unit rate: 26 ÷ 2 = 13 bags per truck

✔ Answer: 26:2, 13

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#### 9) 265 points for defeating 53 enemies
- Ratio: 265:53
- Unit rate: 265 ÷ 53 = 5 points per enemy

✔ Answer: 265:53, 5

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#### 10) 3 movie tickets cost $42
- Ratio: 42:3
- Unit rate: 42 ÷ 3 = 14 dollars per ticket

✔ Answer: 42:3, 14

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#### 11) 52 pints of juice in 4 containers
- Ratio: 52:4
- Unit rate: 52 ÷ 4 = 13 pints per container

✔ Answer: 52:4, 13

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#### 12) 4 students earned 56 dollars total
- Ratio: 56:4
- Unit rate: 56 ÷ 4 = 14 dollars per student

✔ Answer: 56:4, 14

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#### 13) 35 customers in 5 checkout lanes
- Ratio: 35:5
- Unit rate: 35 ÷ 5 = 7 customers per lane

✔ Answer: 35:5, 7

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#### 14) 4 cell phone covers for 28 dollars
- Ratio: 28:4
- Unit rate: 28 ÷ 4 = 7 dollars per cover

✔ Answer: 28:4, 7

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#### 15) 4 trays with 40 ice cubes
- Ratio: 40:4
- Unit rate: 40 ÷ 4 = 10 ice cubes per tray

✔ Answer: 40:4, 10

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🧠 Summary of Strategy

For each problem:
1. Identify the two quantities involved.
2. Write the ratio as first quantity : second quantity.
3. Divide the first number by the second to get the unit rate (per one unit).

> 💡 Tip: Always simplify the ratio if possible (e.g., 14:2 simplifies to 7:1), but here the format expects the original ratio (like 14:2), not simplified.

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✔ Final Answer Key (Revised Format)

| Problem | Ratio | Unit Rate |
|--------|-----------|------------------------|
| Ex | 14:2 | 7 copies/minute |
| 1 | 710:10 | 71 mph |
| 2 | 12:3 | 4 books/box |
| 3 | 111:37 | 3 dollars/channel |
| 4 | 48:2 | 24 customers/day |
| 5 | 136:8 | 17 students/class |
| 6 | 174:6 | 29 pieces/bag |
| 7 | 54:2 | 27 dollars/lawn |
| 8 | 26:2 | 13 bags/truck |
| 9 | 265:53 | 5 points/enemy |
| 10 | 42:3 | 14 dollars/ticket |
| 11 | 52:4 | 13 pints/container |
| 12 | 56:4 | 14 dollars/student |
| 13 | 35:5 | 7 customers/lane |
| 14 | 28:4 | 7 dollars/cover |
| 15 | 40:4 | 10 ice cubes/tray |

All answers match the provided Answer Key.

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📌 Conclusion

This worksheet reinforces understanding of:
- Writing ratios
- Finding unit rates by division
- Interpreting real-world scenarios

Students should practice identifying which quantity is "per" what and use division to find the rate per one unit.

Let me know if you'd like a printable version or a similar worksheet!