Answer :
Let's simplify and amplify the given fractions step-by-step.
### Simplification of Fractions
1. Simplifying [tex]\(\frac{20}{50}\)[/tex]:
- Find the greatest common divisor (GCD) of 20 and 50, which is 10.
- Divide both the numerator and the denominator by their GCD: [tex]\(\frac{20 \div 10}{50 \div 10} = \frac{2}{5}\)[/tex].
2. Simplifying [tex]\(\frac{42}{27}\)[/tex]:
- Find the GCD of 42 and 27, which is 3.
- Divide both by their GCD: [tex]\(\frac{42 \div 3}{27 \div 3} = \frac{14}{9}\)[/tex].
3. Simplifying [tex]\(\frac{14}{21}\)[/tex]:
- The GCD of 14 and 21 is 7.
- Simplify: [tex]\(\frac{14 \div 7}{21 \div 7} = \frac{2}{3}\)[/tex].
4. Simplifying [tex]\(\frac{12}{16}\)[/tex]:
- The GCD is 4.
- Simplify: [tex]\(\frac{12 \div 4}{16 \div 4} = \frac{3}{4}\)[/tex].
5. Simplifying [tex]\(\frac{16}{18}\)[/tex]:
- The GCD is 2.
- Simplify: [tex]\(\frac{16 \div 2}{18 \div 2} = \frac{8}{9}\)[/tex].
### Amplification of Fractions
When amplifying fractions, it's common to multiply both the numerator and the denominator by the same number to create an equivalent fraction.
1. Amplifying [tex]\(\frac{2}{9}\)[/tex]:
- The amplified fraction need not change, as specific instructions or a multiplying factor have not been given.
2. Amplifying [tex]\(\frac{4}{5}\)[/tex]:
- The amplified fraction need not change, as specific instructions or a multiplying factor have not been given.
3. Amplifying [tex]\(\frac{1}{12}\)[/tex]:
- The amplified fraction need not change, as specific instructions or a multiplying factor have not been given.
4. Amplifying [tex]\(\frac{7}{8}\)[/tex]:
- The amplified fraction need not change, as specific instructions or a multiplying factor have not been given.
5. Amplifying [tex]\(\frac{2}{3}\)[/tex]:
- The amplified fraction need not change, as specific instructions or a multiplying factor have not been given.
Therefore, the fractions remain as [tex]\(\frac{2}{9}\)[/tex], [tex]\(\frac{4}{5}\)[/tex], [tex]\(\frac{1}{12}\)[/tex], [tex]\(\frac{7}{8}\)[/tex], and [tex]\(\frac{2}{3}\)[/tex].
In conclusion:
- Simplified fractions are [tex]\(\frac{2}{5}\)[/tex], [tex]\(\frac{14}{9}\)[/tex], [tex]\(\frac{2}{3}\)[/tex], [tex]\(\frac{3}{4}\)[/tex], and [tex]\(\frac{8}{9}\)[/tex].
- Amplified fractions are [tex]\(\frac{2}{9}\)[/tex], [tex]\(\frac{4}{5}\)[/tex], [tex]\(\frac{1}{12}\)[/tex], [tex]\(\frac{7}{8}\)[/tex], and [tex]\(\frac{2}{3}\)[/tex]. The amplification step doesn't change them as it relies on a multiplying factor that was not specified.
### Simplification of Fractions
1. Simplifying [tex]\(\frac{20}{50}\)[/tex]:
- Find the greatest common divisor (GCD) of 20 and 50, which is 10.
- Divide both the numerator and the denominator by their GCD: [tex]\(\frac{20 \div 10}{50 \div 10} = \frac{2}{5}\)[/tex].
2. Simplifying [tex]\(\frac{42}{27}\)[/tex]:
- Find the GCD of 42 and 27, which is 3.
- Divide both by their GCD: [tex]\(\frac{42 \div 3}{27 \div 3} = \frac{14}{9}\)[/tex].
3. Simplifying [tex]\(\frac{14}{21}\)[/tex]:
- The GCD of 14 and 21 is 7.
- Simplify: [tex]\(\frac{14 \div 7}{21 \div 7} = \frac{2}{3}\)[/tex].
4. Simplifying [tex]\(\frac{12}{16}\)[/tex]:
- The GCD is 4.
- Simplify: [tex]\(\frac{12 \div 4}{16 \div 4} = \frac{3}{4}\)[/tex].
5. Simplifying [tex]\(\frac{16}{18}\)[/tex]:
- The GCD is 2.
- Simplify: [tex]\(\frac{16 \div 2}{18 \div 2} = \frac{8}{9}\)[/tex].
### Amplification of Fractions
When amplifying fractions, it's common to multiply both the numerator and the denominator by the same number to create an equivalent fraction.
1. Amplifying [tex]\(\frac{2}{9}\)[/tex]:
- The amplified fraction need not change, as specific instructions or a multiplying factor have not been given.
2. Amplifying [tex]\(\frac{4}{5}\)[/tex]:
- The amplified fraction need not change, as specific instructions or a multiplying factor have not been given.
3. Amplifying [tex]\(\frac{1}{12}\)[/tex]:
- The amplified fraction need not change, as specific instructions or a multiplying factor have not been given.
4. Amplifying [tex]\(\frac{7}{8}\)[/tex]:
- The amplified fraction need not change, as specific instructions or a multiplying factor have not been given.
5. Amplifying [tex]\(\frac{2}{3}\)[/tex]:
- The amplified fraction need not change, as specific instructions or a multiplying factor have not been given.
Therefore, the fractions remain as [tex]\(\frac{2}{9}\)[/tex], [tex]\(\frac{4}{5}\)[/tex], [tex]\(\frac{1}{12}\)[/tex], [tex]\(\frac{7}{8}\)[/tex], and [tex]\(\frac{2}{3}\)[/tex].
In conclusion:
- Simplified fractions are [tex]\(\frac{2}{5}\)[/tex], [tex]\(\frac{14}{9}\)[/tex], [tex]\(\frac{2}{3}\)[/tex], [tex]\(\frac{3}{4}\)[/tex], and [tex]\(\frac{8}{9}\)[/tex].
- Amplified fractions are [tex]\(\frac{2}{9}\)[/tex], [tex]\(\frac{4}{5}\)[/tex], [tex]\(\frac{1}{12}\)[/tex], [tex]\(\frac{7}{8}\)[/tex], and [tex]\(\frac{2}{3}\)[/tex]. The amplification step doesn't change them as it relies on a multiplying factor that was not specified.
