Ratio Worksheets | Ratio Worksheets for Teachers - Free Printable
Educational worksheet: Ratio Worksheets | Ratio Worksheets for Teachers. Download and print for classroom or home learning activities.
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Step-by-step solution for: Ratio Worksheets | Ratio Worksheets for Teachers
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Show Answer Key & Explanations
Step-by-step solution for: Ratio Worksheets | Ratio Worksheets for Teachers
To solve the problem, we need to express each given ratio as a fraction in its simplest form. This involves finding the greatest common divisor (GCD) of the two numbers in the ratio and then dividing both the numerator and the denominator by this GCD.
Let's go through each problem step by step:
---
- Ratio: \( \frac{18}{22} \)
- GCD of 18 and 22 is 2.
- Simplify: \( \frac{18 \div 2}{22 \div 2} = \frac{9}{11} \)
Answer: \( \frac{9}{11} \)
---
- Ratio: \( \frac{12}{36} \)
- GCD of 12 and 36 is 12.
- Simplify: \( \frac{12 \div 12}{36 \div 12} = \frac{1}{3} \)
Answer: \( \frac{1}{3} \)
---
- Ratio: \( \frac{16}{18} \)
- GCD of 16 and 18 is 2.
- Simplify: \( \frac{16 \div 2}{18 \div 2} = \frac{8}{9} \)
Answer: \( \frac{8}{9} \)
---
- Ratio: \( \frac{25}{60} \)
- GCD of 25 and 60 is 5.
- Simplify: \( \frac{25 \div 5}{60 \div 5} = \frac{5}{12} \)
Answer: \( \frac{5}{12} \)
---
- Ratio: \( \frac{12}{24} \)
- GCD of 12 and 24 is 12.
- Simplify: \( \frac{12 \div 12}{24 \div 12} = \frac{1}{2} \)
Answer: \( \frac{1}{2} \)
---
- Ratio: \( \frac{9}{30} \)
- GCD of 9 and 30 is 3.
- Simplify: \( \frac{9 \div 3}{30 \div 3} = \frac{3}{10} \)
Answer: \( \frac{3}{10} \)
---
- Ratio: \( \frac{12}{48} \)
- GCD of 12 and 48 is 12.
- Simplify: \( \frac{12 \div 12}{48 \div 12} = \frac{1}{4} \)
Answer: \( \frac{1}{4} \)
---
- Ratio: \( \frac{32}{48} \)
- GCD of 32 and 48 is 16.
- Simplify: \( \frac{32 \div 16}{48 \div 16} = \frac{2}{3} \)
Answer: \( \frac{2}{3} \)
---
- Ratio: \( \frac{6}{42} \)
- GCD of 6 and 42 is 6.
- Simplify: \( \frac{6 \div 6}{42 \div 6} = \frac{1}{7} \)
Answer: \( \frac{1}{7} \)
---
- Ratio: \( \frac{30}{35} \)
- GCD of 30 and 35 is 5.
- Simplify: \( \frac{30 \div 5}{35 \div 5} = \frac{6}{7} \)
Answer: \( \frac{6}{7} \)
---
- Ratio: \( \frac{12}{21} \)
- GCD of 12 and 21 is 3.
- Simplify: \( \frac{12 \div 3}{21 \div 3} = \frac{4}{7} \)
Answer: \( \frac{4}{7} \)
---
- Ratio: \( \frac{21}{24} \)
- GCD of 21 and 24 is 3.
- Simplify: \( \frac{21 \div 3}{24 \div 3} = \frac{7}{8} \)
Answer: \( \frac{7}{8} \)
---
- Ratio: \( \frac{10}{35} \)
- GCD of 10 and 35 is 5.
- Simplify: \( \frac{10 \div 5}{35 \div 5} = \frac{2}{7} \)
Answer: \( \frac{2}{7} \)
---
- Ratio: \( \frac{22}{24} \)
- GCD of 22 and 24 is 2.
- Simplify: \( \frac{22 \div 2}{24 \div 2} = \frac{11}{12} \)
Answer: \( \frac{11}{12} \)
---
- Ratio: \( \frac{10}{18} \)
- GCD of 10 and 18 is 2.
- Simplify: \( \frac{10 \div 2}{18 \div 2} = \frac{5}{9} \)
Answer: \( \frac{5}{9} \)
---
- Ratio: \( \frac{21}{25} \)
- GCD of 21 and 25 is 1 (they are relatively prime).
- Simplify: \( \frac{21}{25} \) (already in simplest form).
Answer: \( \frac{21}{25} \)
---
- Ratio: \( \frac{20}{45} \)
- GCD of 20 and 45 is 5.
- Simplify: \( \frac{20 \div 5}{45 \div 5} = \frac{4}{9} \)
Answer: \( \frac{4}{9} \)
---
- Ratio: \( \frac{7}{56} \)
- GCD of 7 and 56 is 7.
- Simplify: \( \frac{7 \div 7}{56 \div 7} = \frac{1}{8} \)
Answer: \( \frac{1}{8} \)
---
- Ratio: \( \frac{18}{24} \)
- GCD of 18 and 24 is 6.
- Simplify: \( \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \)
Answer: \( \frac{3}{4} \)
---
- Ratio: \( \frac{60}{72} \)
- GCD of 60 and 72 is 12.
- Simplify: \( \frac{60 \div 12}{72 \div 12} = \frac{5}{6} \)
Answer: \( \frac{5}{6} \)
---
1. \( \frac{9}{11} \)
2. \( \frac{1}{3} \)
3. \( \frac{8}{9} \)
4. \( \frac{5}{12} \)
5. \( \frac{1}{2} \)
6. \( \frac{3}{10} \)
7. \( \frac{1}{4} \)
8. \( \frac{2}{3} \)
9. \( \frac{1}{7} \)
10. \( \frac{6}{7} \)
11. \( \frac{4}{7} \)
12. \( \frac{7}{8} \)
13. \( \frac{2}{7} \)
14. \( \frac{11}{12} \)
15. \( \frac{5}{9} \)
16. \( \frac{21}{25} \)
17. \( \frac{4}{9} \)
18. \( \frac{1}{8} \)
19. \( \frac{3}{4} \)
20. \( \frac{5}{6} \)
\boxed{\text{See above for detailed solutions and final answers.}}
Let's go through each problem step by step:
---
1) 18 pounds to 22 pounds
- Ratio: \( \frac{18}{22} \)
- GCD of 18 and 22 is 2.
- Simplify: \( \frac{18 \div 2}{22 \div 2} = \frac{9}{11} \)
Answer: \( \frac{9}{11} \)
---
2) 12 pints to 36 pints
- Ratio: \( \frac{12}{36} \)
- GCD of 12 and 36 is 12.
- Simplify: \( \frac{12 \div 12}{36 \div 12} = \frac{1}{3} \)
Answer: \( \frac{1}{3} \)
---
3) 16 feet out of 18 feet
- Ratio: \( \frac{16}{18} \)
- GCD of 16 and 18 is 2.
- Simplify: \( \frac{16 \div 2}{18 \div 2} = \frac{8}{9} \)
Answer: \( \frac{8}{9} \)
---
4) 25 red bikes out of 60 bikes
- Ratio: \( \frac{25}{60} \)
- GCD of 25 and 60 is 5.
- Simplify: \( \frac{25 \div 5}{60 \div 5} = \frac{5}{12} \)
Answer: \( \frac{5}{12} \)
---
5) 12 pennies to 24 pennies
- Ratio: \( \frac{12}{24} \)
- GCD of 12 and 24 is 12.
- Simplify: \( \frac{12 \div 12}{24 \div 12} = \frac{1}{2} \)
Answer: \( \frac{1}{2} \)
---
6) 9 snow days out of 30 days
- Ratio: \( \frac{9}{30} \)
- GCD of 9 and 30 is 3.
- Simplify: \( \frac{9 \div 3}{30 \div 3} = \frac{3}{10} \)
Answer: \( \frac{3}{10} \)
---
7) 12 blue cars out of 48 cars
- Ratio: \( \frac{12}{48} \)
- GCD of 12 and 48 is 12.
- Simplify: \( \frac{12 \div 12}{48 \div 12} = \frac{1}{4} \)
Answer: \( \frac{1}{4} \)
---
8) 32 quarts to 48 quarts
- Ratio: \( \frac{32}{48} \)
- GCD of 32 and 48 is 16.
- Simplify: \( \frac{32 \div 16}{48 \div 16} = \frac{2}{3} \)
Answer: \( \frac{2}{3} \)
---
9) 6 gallons to 42 gallons
- Ratio: \( \frac{6}{42} \)
- GCD of 6 and 42 is 6.
- Simplify: \( \frac{6 \div 6}{42 \div 6} = \frac{1}{7} \)
Answer: \( \frac{1}{7} \)
---
10) 30 beetles out of 35 insects
- Ratio: \( \frac{30}{35} \)
- GCD of 30 and 35 is 5.
- Simplify: \( \frac{30 \div 5}{35 \div 5} = \frac{6}{7} \)
Answer: \( \frac{6}{7} \)
---
11) 12 cups to 21 cups
- Ratio: \( \frac{12}{21} \)
- GCD of 12 and 21 is 3.
- Simplify: \( \frac{12 \div 3}{21 \div 3} = \frac{4}{7} \)
Answer: \( \frac{4}{7} \)
---
12) 21 dimes to 24 dimes
- Ratio: \( \frac{21}{24} \)
- GCD of 21 and 24 is 3.
- Simplify: \( \frac{21 \div 3}{24 \div 3} = \frac{7}{8} \)
Answer: \( \frac{7}{8} \)
---
13) 10 dimes out of 35 coins
- Ratio: \( \frac{10}{35} \)
- GCD of 10 and 35 is 5.
- Simplify: \( \frac{10 \div 5}{35 \div 5} = \frac{2}{7} \)
Answer: \( \frac{2}{7} \)
---
14) 22 cakes out of 24 cakes
- Ratio: \( \frac{22}{24} \)
- GCD of 22 and 24 is 2.
- Simplify: \( \frac{22 \div 2}{24 \div 2} = \frac{11}{12} \)
Answer: \( \frac{11}{12} \)
---
15) 10 nickels to 18 nickels
- Ratio: \( \frac{10}{18} \)
- GCD of 10 and 18 is 2.
- Simplify: \( \frac{10 \div 2}{18 \div 2} = \frac{5}{9} \)
Answer: \( \frac{5}{9} \)
---
16) 21 inches to 25 inches
- Ratio: \( \frac{21}{25} \)
- GCD of 21 and 25 is 1 (they are relatively prime).
- Simplify: \( \frac{21}{25} \) (already in simplest form).
Answer: \( \frac{21}{25} \)
---
17) 20 points out of 45 points
- Ratio: \( \frac{20}{45} \)
- GCD of 20 and 45 is 5.
- Simplify: \( \frac{20 \div 5}{45 \div 5} = \frac{4}{9} \)
Answer: \( \frac{4}{9} \)
---
18) 7 footballs to 56 fooballs
- Ratio: \( \frac{7}{56} \)
- GCD of 7 and 56 is 7.
- Simplify: \( \frac{7 \div 7}{56 \div 7} = \frac{1}{8} \)
Answer: \( \frac{1}{8} \)
---
19) 18 rainy days out of 24 days
- Ratio: \( \frac{18}{24} \)
- GCD of 18 and 24 is 6.
- Simplify: \( \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \)
Answer: \( \frac{3}{4} \)
---
20) 60 miles out of 72 miles
- Ratio: \( \frac{60}{72} \)
- GCD of 60 and 72 is 12.
- Simplify: \( \frac{60 \div 12}{72 \div 12} = \frac{5}{6} \)
Answer: \( \frac{5}{6} \)
---
Final Answers:
1. \( \frac{9}{11} \)
2. \( \frac{1}{3} \)
3. \( \frac{8}{9} \)
4. \( \frac{5}{12} \)
5. \( \frac{1}{2} \)
6. \( \frac{3}{10} \)
7. \( \frac{1}{4} \)
8. \( \frac{2}{3} \)
9. \( \frac{1}{7} \)
10. \( \frac{6}{7} \)
11. \( \frac{4}{7} \)
12. \( \frac{7}{8} \)
13. \( \frac{2}{7} \)
14. \( \frac{11}{12} \)
15. \( \frac{5}{9} \)
16. \( \frac{21}{25} \)
17. \( \frac{4}{9} \)
18. \( \frac{1}{8} \)
19. \( \frac{3}{4} \)
20. \( \frac{5}{6} \)
\boxed{\text{See above for detailed solutions and final answers.}}
Parent Tip: Review the logic above to help your child master the concept of ratios and percents worksheet.
