Let’s solve these problems step-by-step by writing each ratio as a fraction in its simplest form.

Exercise A:

1. 12 to 20
   Fraction: $\frac{12}{20}$
   Simplify: $\frac{12 \div 4}{20 \div 4} = \frac{3}{5}$

2. 18 to 21
   Fraction: $\frac{18}{21}$
   Simplify: $\frac{18 \div 3}{21 \div 3} = \frac{6}{7}$

3. 12 to 8
   Fraction: $\frac{12}{8}$
   Simplify: $\frac{12 \div 4}{8 \div 4} = \frac{3}{2}$

4. 4 to 6
   Fraction: $\frac{4}{6}$
   Simplify: $\frac{4 \div 2}{6 \div 2} = \frac{2}{3}$

5. 12 to 15
   Fraction: $\frac{12}{15}$
   Simplify: $\frac{12 \div 3}{15 \div 3} = \frac{4}{5}$

6. 14 to 21
   Fraction: $\frac{14}{21}$
   Simplify: $\frac{14 \div 7}{21 \div 7} = \frac{2}{3}$

7. 21 to 14
   Fraction: $\frac{21}{14}$
   Simplify: $\frac{21 \div 7}{14 \div 7} = \frac{3}{2}$

8. 8 to 36
   Fraction: $\frac{8}{36}$
   Simplify: $\frac{8 \div 4}{36 \div 4} = \frac{2}{9}$

9. 15 to 19
   Fraction: $\frac{15}{19}$
   Already simplified (no common factor).

10. 6 to 15
    Fraction: $\frac{6}{15}$
    Simplify: $\frac{6 \div 3}{15 \div 3} = \frac{2}{5}$

11. 8 to 2
    Fraction: $\frac{8}{2}$
    Simplify: $\frac{8 \div 2}{2 \div 2} = \frac{4}{1}$ (or just 4)

12. 9 to 12
    Fraction: $\frac{9}{12}$
    Simplify: $\frac{9 \div 3}{12 \div 3} = \frac{3}{4}$

13. 20 to 24
    Fraction: $\frac{20}{24}$
    Simplify: $\frac{20 \div 4}{24 \div 4} = \frac{5}{6}$

14. 16 to 12
    Fraction: $\frac{16}{12}$
    Simplify: $\frac{16 \div 4}{12 \div 4} = \frac{4}{3}$

15. 8 to 19
    Fraction: $\frac{8}{19}$
    Already simplified (no common factor).

Would you like further explanations on any of these?

Related Questions:

1. What is the process for identifying the greatest common divisor (GCD) when simplifying fractions?
2. Can all ratios be simplified? If not, why?
3. How do you convert a ratio to a percentage?
4. What are some real-world examples of using ratios?
5. How do you write a ratio in decimal form?

Tip:

Always check for the greatest common divisor (GCD) when simplifying fractions to ensure your result is in its simplest form.