Ratio Worksheets | Ratio Worksheets for Teachers - Free Printable

Let's solve each problem step by step.

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Part 1: Express each ratio as a fraction in the simplest form

We simplify each ratio by dividing both numbers by their greatest common divisor (GCD).

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1) 6 beetles out of 10 insects
$$
\frac{6}{10} = \frac{3}{5}
$$

✔ Answer: $ \frac{3}{5} $

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2) 15 dimes to 20 dimes
$$
\frac{15}{20} = \frac{3}{4}
$$

✔ Answer: $ \frac{3}{4} $

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3) 12 quarts to 30 quarts
$$
\frac{12}{30} = \frac{2}{5}
$$

✔ Answer: $ \frac{2}{5} $

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4) 42 blue cars out of 84 cars
$$
\frac{42}{84} = \frac{1}{2}
$$

✔ Answer: $ \frac{1}{2} $

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5) 48 gallons to 54 gallons
$$
\frac{48}{54} = \frac{8}{9}
$$

✔ Answer: $ \frac{8}{9} $

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6) 49 pennies to 84 pennies
$$
\frac{49}{84} = \frac{7}{12}
$$
(GCD of 49 and 84 is 7)

✔ Answer: $ \frac{7}{12} $

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7) 4 cups to 20 cups
$$
\frac{4}{20} = \frac{1}{5}
$$

✔ Answer: $ \frac{1}{5} $

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8) 12 miles out of 15 miles
$$
\frac{12}{15} = \frac{4}{5}
$$

✔ Answer: $ \frac{4}{5} $

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✔ Part 1 Answers:

1. $ \frac{3}{5} $
2. $ \frac{3}{4} $
3. $ \frac{2}{5} $
4. $ \frac{1}{2} $
5. $ \frac{8}{9} $
6. $ \frac{7}{12} $
7. $ \frac{1}{5} $
8. $ \frac{4}{5} $

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Part 2: Express each phrase as a rate and unit rate

Rate: A comparison of two quantities with different units.
Unit Rate: The rate per one unit (e.g., dollars per pencil, miles per gallon).
Round to nearest hundredth.

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9) 9 pencils for 11 dollars

- Rate: $ \frac{11 \text{ dollars}}{9 \text{ pencils}} $
- Unit Rate: $ \frac{11}{9} \approx 1.22 $ dollars per pencil

✔ Rate: $ \frac{11}{9} $ dollars/pencil
✔ Unit Rate: $ 1.22 $ dollars/pencil

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10) 2 inches of snow in 9 hours

- Rate: $ \frac{2 \text{ inches}}{9 \text{ hours}} $
- Unit Rate: $ \frac{2}{9} \approx 0.22 $ inches/hour

✔ Rate: $ \frac{2}{9} $ inches/hour
✔ Unit Rate: $ 0.22 $ inches/hour

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11) 140 miles on 8 gallons of gas

- Rate: $ \frac{140 \text{ miles}}{8 \text{ gallons}} $
- Unit Rate: $ \frac{140}{8} = 17.5 $ miles/gallon

✔ Rate: $ \frac{140}{8} $ miles/gallon
✔ Unit Rate: $ 17.50 $ miles/gallon

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12) 11 batteries cost $16 dollars

- Rate: $ \frac{16 \text{ dollars}}{11 \text{ batteries}} $
- Unit Rate: $ \frac{16}{11} \approx 1.45 $ dollars/battery

✔ Rate: $ \frac{16}{11} $ dollars/battery
✔ Unit Rate: $ 1.45 $ dollars/battery

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13) 20 dollars for 6 books

- Rate: $ \frac{20 \text{ dollars}}{6 \text{ books}} $
- Unit Rate: $ \frac{20}{6} \approx 3.33 $ dollars/book

✔ Rate: $ \frac{20}{6} $ dollars/book
✔ Unit Rate: $ 3.33 $ dollars/book

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14) 15 chocolate bars cost 10 dollars

- Rate: $ \frac{10 \text{ dollars}}{15 \text{ bars}} $
- Unit Rate: $ \frac{10}{15} = \frac{2}{3} \approx 0.67 $ dollars/bar

✔ Rate: $ \frac{10}{15} $ dollars/bar
✔ Unit Rate: $ 0.67 $ dollars/bar

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15) 5 dollars for 4 cans of tuna

- Rate: $ \frac{5 \text{ dollars}}{4 \text{ cans}} $
- Unit Rate: $ \frac{5}{4} = 1.25 $ dollars/can

✔ Rate: $ \frac{5}{4} $ dollars/can
✔ Unit Rate: $ 1.25 $ dollars/can

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16) 5 calculators cost $155.00

- Rate: $ \frac{155 \text{ dollars}}{5 \text{ calculators}} $
- Unit Rate: $ \frac{155}{5} = 31.00 $ dollars/calculator

✔ Rate: $ \frac{155}{5} $ dollars/calculator
✔ Unit Rate: $ 31.00 $ dollars/calculator

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✔ Part 2 Answers:

| Problem | Rate | Unit Rate |
|--------|------|-----------|
| 9 | $ \frac{11}{9} $ dollars/pencil | $ 1.22 $ dollars/pencil |
| 10 | $ \frac{2}{9} $ inches/hour | $ 0.22 $ inches/hour |
| 11 | $ \frac{140}{8} $ miles/gallon | $ 17.50 $ miles/gallon |
| 12 | $ \frac{16}{11} $ dollars/battery | $ 1.45 $ dollars/battery |
| 13 | $ \frac{20}{6} $ dollars/book | $ 3.33 $ dollars/book |
| 14 | $ \frac{10}{15} $ dollars/bar | $ 0.67 $ dollars/bar |
| 15 | $ \frac{5}{4} $ dollars/can | $ 1.25 $ dollars/can |
| 16 | $ \frac{155}{5} $ dollars/calculator | $ 31.00 $ dollars/calculator |

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✔ Final Answer Summary:

#### Part 1: Ratios as Simplest Fractions
1. $ \frac{3}{5} $
2. $ \frac{3}{4} $
3. $ \frac{2}{5} $
4. $ \frac{1}{2} $
5. $ \frac{8}{9} $
6. $ \frac{7}{12} $
7. $ \frac{1}{5} $
8. $ \frac{4}{5} $

#### Part 2: Rates and Unit Rates
9. Rate: $ \frac{11}{9} $, Unit Rate: $ 1.22 $
10. Rate: $ \frac{2}{9} $, Unit Rate: $ 0.22 $
11. Rate: $ \frac{140}{8} $, Unit Rate: $ 17.50 $
12. Rate: $ \frac{16}{11} $, Unit Rate: $ 1.45 $
13. Rate: $ \frac{20}{6} $, Unit Rate: $ 3.33 $
14. Rate: $ \frac{10}{15} $, Unit Rate: $ 0.67 $
15. Rate: $ \frac{5}{4} $, Unit Rate: $ 1.25 $
16. Rate: $ \frac{155}{5} $, Unit Rate: $ 31.00 $

All answers are simplified and rounded appropriately.

Let me know if you'd like this formatted as a printable worksheet!