Ratios and Rates Worksheets - Math Monks - Free Printable

Sure! Let’s solve each problem step by step. The goal is to find:

- Ratio: Usually written as “a : b” or “a to b”, showing the relationship between two quantities.
- Unit Rate: A rate with a denominator of 1 — meaning “how much per one unit” (e.g., cost per apple, balls per bag, etc.).

We’ll compute both for each question.

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1) 20 apples for $4

- Ratio: apples to dollars → 20 : 4
Simplify: divide both by 4 → 5 : 1

- Unit Rate: dollars per apple → $4 ÷ 20 = $0.20 /apple

✔ Answer: Ratio = 5:1, Rate = $0.20 /apple

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2) 228 balls in 12 bags

- Ratio: balls to bags → 228 : 12
Simplify: divide both by 12 → 19 : 1

- Unit Rate: balls per bag → 228 ÷ 12 = 19 /bag

✔ Answer: Ratio = 19:1, Rate = 19 /bag

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3) $20 for 5 movie tickets

- Ratio: dollars to tickets → 20 : 5
Simplify: divide both by 5 → 4 : 1

- Unit Rate: dollars per ticket → $20 ÷ 5 = $4 /ticket

✔ Answer: Ratio = 4:1, Rate = $4 /ticket

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4) 35 girls in 7 batches

- Ratio: girls to batches → 35 : 7
Simplify: divide both by 7 → 5 : 1

- Unit Rate: girls per batch → 35 ÷ 7 = 5 /batch

✔ Answer: Ratio = 5:1, Rate = 5 /batch

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5) 40 customers in 8 hours

- Ratio: customers to hours → 40 : 8
Simplify: divide both by 8 → 5 : 1

- Unit Rate: customers per hour → 40 ÷ 8 = 5 /hour

✔ Answer: Ratio = 5:1, Rate = 5 /hour

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6) 12 trains in 6 minutes

- Ratio: trains to minutes → 12 : 6
Simplify: divide both by 6 → 2 : 1

- Unit Rate: trains per minute → 12 ÷ 6 = 2 /minute

✔ Answer: Ratio = 2:1, Rate = 2 /minute

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7) 720 miles in 10 hours

- Ratio: miles to hours → 720 : 10
Simplify: divide both by 10 → 72 : 1

- Unit Rate: miles per hour → 720 ÷ 10 = 72 /hour

✔ Answer: Ratio = 72:1, Rate = 72 /hour

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8) 4675 toys among 11 girls

- Ratio: toys to girls → 4675 : 11
Simplify: divide both by 11 → 4675 ÷ 11 = 425 → 425 : 1

- Unit Rate: toys per girl → 4675 ÷ 11 = 425 /girl

✔ Answer: Ratio = 425:1, Rate = 425 /girl

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9) 52,074 kg of goods in 99 trucks

- Ratio: kg to trucks → 52074 : 99
Simplify: divide both by 99 → 52074 ÷ 99 = 526 → 526 : 1

- Unit Rate: kg per truck → 52074 ÷ 99 = 526 /truck

✔ Answer: Ratio = 526:1, Rate = 526 /truck

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10) 220 houses in 20 km

- Ratio: houses to km → 220 : 20
Simplify: divide both by 20 → 11 : 1

- Unit Rate: houses per km → 220 ÷ 20 = 11 /km

✔ Answer: Ratio = 11:1, Rate = 11 /km

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## ✔ Final Answers Summary:

| Question | Ratio | Unit 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 |

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💡 Key Tip: To find the unit rate, always divide the first quantity by the second. The ratio is usually simplified to its lowest terms, often showing "per 1" unit.

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