To simplify each fraction, we will reduce it by dividing both the numerator and the denominator by their greatest common divisor (GCD). Let's simplify each fraction step by step.
1. Fraction: [tex]\(\frac{24}{36}\)[/tex]
- The GCD of 24 and 36 is 12.
- Dividing both the numerator and the denominator by 12, we get:
[tex]\[
\frac{24 \div 12}{36 \div 12} = \frac{2}{3}
\][/tex]
- Simplest form: [tex]\(\frac{2}{3}\)[/tex]
2. Fraction: [tex]\(\frac{34}{85}\)[/tex]
- The GCD of 34 and 85 is 17.
- Dividing both the numerator and the denominator by 17, we get:
[tex]\[
\frac{34 \div 17}{85 \div 17} = \frac{2}{5}
\][/tex]
- Simplest form: [tex]\(\frac{2}{5}\)[/tex]
3. Fraction: [tex]\(\frac{36}{12}\)[/tex]
- The GCD of 36 and 12 is 12.
- Dividing both the numerator and the denominator by 12, we get:
[tex]\[
\frac{36 \div 12}{12 \div 12} = \frac{3}{1}
\][/tex]
- Simplest form: [tex]\(\frac{3}{1}\)[/tex]
4. Fraction: [tex]\(\frac{27}{45}\)[/tex]
- The GCD of 27 and 45 is 9.
- Dividing both the numerator and the denominator by 9, we get:
[tex]\[
\frac{27 \div 9}{45 \div 9} = \frac{3}{5}
\][/tex]
- Simplest form: [tex]\(\frac{3}{5}\)[/tex]
5. Fraction: [tex]\(\frac{11}{18}\)[/tex]
- The GCD of 11 and 18 is 1 (since they are relatively prime).
- Therefore, [tex]\(\frac{11}{18}\)[/tex] is already in its simplest form.
- Simplest form: [tex]\(\frac{11}{18}\)[/tex]
6. Fraction: [tex]\(\frac{5}{65}\)[/tex]
- The GCD of 5 and 65 is 5.
- Dividing both the numerator and the denominator by 5, we get:
[tex]\[
\frac{5 \div 5}{65 \div 5} = \frac{1}{13}
\][/tex]
- Simplest form: [tex]\(\frac{1}{13}\)[/tex]
7. Fraction: [tex]\(\frac{19}{1}\)[/tex]
- The GCD of 19 and 1 is 1.
- Therefore, [tex]\(\frac{19}{1}\)[/tex] is already in its simplest form.
- Simplest form: [tex]\(\frac{19}{1}\)[/tex]
8. Fraction: [tex]\(\frac{16}{44}\)[/tex]
- The GCD of 16 and 44 is 4.
- Dividing both the numerator and the denominator by 4, we get:
[tex]\[
\frac{16 \div 4}{44 \div 4} = \frac{4}{11}
\][/tex]
- Simplest form: [tex]\(\frac{4}{11}\)[/tex]
9. Fraction: [tex]\(\frac{64}{88}\)[/tex]
- The GCD of 64 and 88 is 8.
- Dividing both the numerator and the denominator by 8, we get:
[tex]\[
\frac{64 \div 8}{88 \div 8} = \frac{8}{11}
\][/tex]
- Simplest form: [tex]\(\frac{8}{11}\)[/tex]
In summary, the simplified forms of the fractions are:
1. [tex]\(\frac{24}{36} = \frac{2}{3}\)[/tex]
2. [tex]\(\frac{34}{85} = \frac{2}{5}\)[/tex]
3. [tex]\(\frac{36}{12} = \frac{3}{1}\)[/tex]
4. [tex]\(\frac{27}{45} = \frac{3}{5}\)[/tex]
5. [tex]\(\frac{11}{18} = \frac{11}{18}\)[/tex]
6. [tex]\(\frac{5}{65} = \frac{1}{13}\)[/tex]
7. [tex]\(\frac{19}{1} = \frac{19}{1}\)[/tex]
8. [tex]\(\frac{16}{44} = \frac{4}{11}\)[/tex]
9. [tex]\(\frac{64}{88} = \frac{8}{11}\)[/tex]
