Ratios and Rates Worksheets - Math Monks - Free Printable

Let's solve each problem step by step. For each question, we need to:

1. Find the ratio — this is the comparison of two quantities (e.g., apples to dollars).
2. Find the unit rate — this is the rate per one unit of the second quantity (e.g., cost per apple).

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1) 20 apples for $4

- Ratio: 20 apples : $4 → $4 / 20 apples = 4:20 or simplified: 1:5
- But typically, ratios are written as apples to dollars or dollars to apples, depending on context.
- Here, since it's "20 apples for $4", the ratio is 20:4 or simplified: 5:1 (apples to dollars)
- Unit rate: Cost per apple = $4 ÷ 20 = $0.20/apple

✔ Answer:
- Ratio: 5:1 (apples:dollars)
- Rate: $0.20 /apple

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2) 228 balls in 12 bags

- Ratio: 228 balls : 12 bags → 228:12 → simplify: divide both by 12 → 19:1
- Unit rate: 228 ÷ 12 = 19 balls/bag

✔ Answer:
- Ratio: 19:1 (balls:bags)
- Rate: 19 /bag

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3) $20 for 5 movie tickets

- Ratio: $20 : 5 tickets → 20:5 → simplify: 4:1 (dollars:tickets)
- Unit rate: $20 ÷ 5 = $4/ticket

✔ Answer:
- Ratio: 4:1 (dollars:tickets)
- Rate: $4 /ticket

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4) 35 girls in 7 batches

- Ratio: 35 girls : 7 batches → 35:7 → simplify: 5:1
- Unit rate: 35 ÷ 7 = 5 girls/batch

✔ Answer:
- Ratio: 5:1 (girls:batches)
- Rate: 5 /batch

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5) 40 customers in 8 hours

- Ratio: 40 customers : 8 hours → 40:8 → simplify: 5:1
- Unit rate: 40 ÷ 8 = 5 customers/hour

✔ Answer:
- Ratio: 5:1 (customers:hours)
- Rate: 5 /hour

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6) 12 trains in 6 minutes

- Ratio: 12 trains : 6 minutes → 12:6 → simplify: 2:1
- Unit rate: 12 ÷ 6 = 2 trains/minute

✔ Answer:
- Ratio: 2:1 (trains:minutes)
- Rate: 2 /minute

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7) 720 miles in 10 hours

- Ratio: 720 miles : 10 hours → 720:10 → simplify: 72:1
- Unit rate: 720 ÷ 10 = 72 miles/hour

✔ Answer:
- Ratio: 72:1 (miles:hours)
- Rate: 72 /hour

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8) 4675 toys among 11 girls

- Ratio: 4675 toys : 11 girls → 4675:11
- Unit rate: 4675 ÷ 11 = ?

Let’s calculate:
- 11 × 425 = 4675 → yes! So, 425 toys/girl

✔ Answer:
- Ratio: 4675:11 (or simplified: 425:1)
- Rate: 425 /girl

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9) 52,074 kg of goods in 99 trucks

- Ratio: 52,074 kg : 99 trucks → 52074:99
- Unit rate: 52,074 ÷ 99

Let’s divide:
- 99 × 526 = ?
- 100 × 526 = 52,600
- Subtract 1×526 = 526 → 52,600 − 526 = 52,074 → YES!
- So, 52,074 ÷ 99 = 526 kg/truck

✔ Answer:
- Ratio: 52074:99 (or simplified: 526:1)
- Rate: 526 /truck

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10) 220 houses in 20 km

- Ratio: 220 houses : 20 km → 220:20 → simplify: 11:1
- Unit rate: 220 ÷ 20 = 11 houses/km

✔ Answer:
- Ratio: 11:1 (houses:km)
- Rate: 11 /km

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✔ Final Answers Table:

| # | Ratio | Rate |
|---|--------------|-------------------|
| 1 | 5:1 | $0.20 /apple |
| 2 | 19:1 | 19 /bag |
| 3 | 4:1 | $4 /ticket |
| 4 | 5:1 | 5 /batch |
| 5 | 5:1 | 5 /hour |
| 6 | 2:1 | 2 /minute |
| 7 | 72:1 | 72 /hour |
| 8 | 425:1 | 425 /girl |
| 9 | 526:1 | 526 /truck |
|10 | 11:1 | 11 /km |

> 🔍 Note: The ratio is often written in simplest form (like 5:1), and the unit rate is the value per one unit of the second quantity.

Let me know if you'd like a printable version or explanation for any specific step!