Equivalent Ratios - Worksheet | Teach Starter - Free Printable

Problem: Solve the given ratios and rates problems.

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

1. 6 beetles out of 10 insects
- Ratio: \( \frac{6}{10} \)
- Simplify by dividing numerator and denominator by their greatest common divisor (GCD), which is 2:
\[
\frac{6 \div 2}{10 \div 2} = \frac{3}{5}
\]
- Answer: \( \frac{3}{5} \)

2. 15 dimes to 20 dimes
- Ratio: \( \frac{15}{20} \)
- Simplify by dividing numerator and denominator by their GCD, which is 5:
\[
\frac{15 \div 5}{20 \div 5} = \frac{3}{4}
\]
- Answer: \( \frac{3}{4} \)

3. 12 quarts to 30 quarts
- Ratio: \( \frac{12}{30} \)
- Simplify by dividing numerator and denominator by their GCD, which is 6:
\[
\frac{12 \div 6}{30 \div 6} = \frac{2}{5}
\]
- Answer: \( \frac{2}{5} \)

4. 42 blue cars out of 84 cars
- Ratio: \( \frac{42}{84} \)
- Simplify by dividing numerator and denominator by their GCD, which is 42:
\[
\frac{42 \div 42}{84 \div 42} = \frac{1}{2}
\]
- Answer: \( \frac{1}{2} \)

5. 48 gallons to 54 gallons
- Ratio: \( \frac{48}{54} \)
- Simplify by dividing numerator and denominator by their GCD, which is 6:
\[
\frac{48 \div 6}{54 \div 6} = \frac{8}{9}
\]
- Answer: \( \frac{8}{9} \)

6. 49 pennies to 84 pennies
- Ratio: \( \frac{49}{84} \)
- Simplify by dividing numerator and denominator by their GCD, which is 7:
\[
\frac{49 \div 7}{84 \div 7} = \frac{7}{12}
\]
- Answer: \( \frac{7}{12} \)

7. 4 cups to 20 cups
- Ratio: \( \frac{4}{20} \)
- Simplify by dividing numerator and denominator by their GCD, which is 4:
\[
\frac{4 \div 4}{20 \div 4} = \frac{1}{5}
\]
- Answer: \( \frac{1}{5} \)

8. 12 miles out of 15 miles
- Ratio: \( \frac{12}{15} \)
- Simplify by dividing numerator and denominator by their GCD, which is 3:
\[
\frac{12 \div 3}{15 \div 3} = \frac{4}{5}
\]
- Answer: \( \frac{4}{5} \)

---

#### Part 2: Express each phrase as a rate and unit rate. (Round your answer to the nearest hundredth.)

9. 9 pencils for 11 dollars
- Rate: \( \frac{9 \text{ pencils}}{11 \text{ dollars}} \)
- Unit Rate: Pencils per dollar:
\[
\frac{9}{11} \approx 0.82 \text{ pencils per dollar}
\]
- Answer: Rate: \( \frac{9}{11} \), Unit Rate: \( 0.82 \) pencils per dollar

10. 2 inches of snow in 9 hours
- Rate: \( \frac{2 \text{ inches}}{9 \text{ hours}} \)
- Unit Rate: Inches per hour:
\[
\frac{2}{9} \approx 0.22 \text{ inches per hour}
\]
- Answer: Rate: \( \frac{2}{9} \), Unit Rate: \( 0.22 \) inches per hour

11. 140 miles on 8 gallons of gas
- Rate: \( \frac{140 \text{ miles}}{8 \text{ gallons}} \)
- Unit Rate: Miles per gallon:
\[
\frac{140}{8} = 17.5 \text{ miles per gallon}
\]
- Answer: Rate: \( \frac{140}{8} \), Unit Rate: \( 17.5 \) miles per gallon

12. 11 batteries cost $16 dollars
- Rate: \( \frac{11 \text{ batteries}}{16 \text{ dollars}} \)
- Unit Rate: Batteries per dollar:
\[
\frac{11}{16} \approx 0.69 \text{ batteries per dollar}
\]
- Answer: Rate: \( \frac{11}{16} \), Unit Rate: \( 0.69 \) batteries per dollar

13. 20 dollars for 6 books
- Rate: \( \frac{20 \text{ dollars}}{6 \text{ books}} \)
- Unit Rate: Dollars per book:
\[
\frac{20}{6} \approx 3.33 \text{ dollars per book}
\]
- Answer: Rate: \( \frac{20}{6} \), Unit Rate: \( 3.33 \) dollars per book

14. 15 chocolate bars cost 10 dollars
- Rate: \( \frac{15 \text{ chocolate bars}}{10 \text{ dollars}} \)
- Unit Rate: Chocolate bars per dollar:
\[
\frac{15}{10} = 1.5 \text{ chocolate bars per dollar}
\]
- Answer: Rate: \( \frac{15}{10} \), Unit Rate: \( 1.5 \) chocolate bars per dollar

15. 5 dollars for 4 cans of tuna
- Rate: \( \frac{5 \text{ dollars}}{4 \text{ cans}} \)
- Unit Rate: Dollars per can:
\[
\frac{5}{4} = 1.25 \text{ dollars per can}
\]
- Answer: Rate: \( \frac{5}{4} \), Unit Rate: \( 1.25 \) dollars per can

16. 5 calculators cost 155.00
- Rate: \( \frac{5 \text{ calculators}}{155 \text{ dollars}} \)
- Unit Rate: Calculators per dollar:
\[
\frac{5}{155} \approx 0.03 \text{ calculators per dollar}
\]
- Answer: Rate: \( \frac{5}{155} \), Unit Rate: \( 0.03 \) calculators per dollar

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
1. & \frac{3}{5} \\
2. & \frac{3}{4} \\
3. & \frac{2}{5} \\
4. & \frac{1}{2} \\
5. & \frac{8}{9} \\
6. & \frac{7}{12} \\
7. & \frac{1}{5} \\
8. & \frac{4}{5} \\
9. & \text{Rate: } \frac{9}{11}, \text{ Unit Rate: } 0.82 \text{ pencils per dollar} \\
10. & \text{Rate: } \frac{2}{9}, \text{ Unit Rate: } 0.22 \text{ inches per hour} \\
11. & \text{Rate: } \frac{140}{8}, \text{ Unit Rate: } 17.5 \text{ miles per gallon} \\
12. & \text{Rate: } \frac{11}{16}, \text{ Unit Rate: } 0.69 \text{ batteries per dollar} \\
13. & \text{Rate: } \frac{20}{6}, \text{ Unit Rate: } 3.33 \text{ dollars per book} \\
14. & \text{Rate: } \frac{15}{10}, \text{ Unit Rate: } 1.5 \text{ chocolate bars per dollar} \\
15. & \text{Rate: } \frac{5}{4}, \text{ Unit Rate: } 1.25 \text{ dollars per can} \\
16. & \text{Rate: } \frac{5}{155}, \text{ Unit Rate: } 0.03 \text{ calculators per dollar} \\
\end{array}
}
\]