Answer :
Of course! Let's go through the simplification and amplification of the fractions step by step.
### Simplifying Fractions
1. Simplify [tex]\(\frac{20}{50}\)[/tex]:
- Find the greatest common divisor (GCD) of 20 and 50, which is 10.
- Divide both the numerator and denominator by 10: [tex]\(\frac{20}{50} = \frac{20 \div 10}{50 \div 10} = \frac{2}{5}\)[/tex].
- So, [tex]\(\frac{20}{50} = 0.4\)[/tex].
2. Simplify [tex]\(\frac{42}{27}\)[/tex]:
- The GCD of 42 and 27 is 3.
- Divide both the numerator and denominator by 3: [tex]\(\frac{42}{27} = \frac{42 \div 3}{27 \div 3} = \frac{14}{9}\)[/tex].
- So, [tex]\(\frac{42}{27} \approx 1.56\)[/tex].
3. Simplify [tex]\(\frac{14}{21}\)[/tex]:
- The GCD of 14 and 21 is 7.
- Divide by 7: [tex]\(\frac{14}{21} = \frac{14 \div 7}{21 \div 7} = \frac{2}{3}\)[/tex].
- So, [tex]\(\frac{14}{21} \approx 0.67\)[/tex].
4. Simplify [tex]\(\frac{12}{16}\)[/tex]:
- The GCD of 12 and 16 is 4.
- Divide by 4: [tex]\(\frac{12}{16} = \frac{12 \div 4}{16 \div 4} = \frac{3}{4}\)[/tex].
- So, [tex]\(\frac{12}{16} = 0.75\)[/tex].
5. Simplify [tex]\(\frac{16}{18}\)[/tex]:
- The GCD of 16 and 18 is 2.
- Divide by 2: [tex]\(\frac{16}{18} = \frac{16 \div 2}{18 \div 2} = \frac{8}{9}\)[/tex].
- So, [tex]\(\frac{16}{18} \approx 0.89\)[/tex].
### Amplifying Fractions
To amplify, we'll multiply both the numerator and the denominator of each fraction by a common factor, which we assume is 2 in this case.
1. Amplify [tex]\(\frac{2}{9}\)[/tex]:
- Multiply both the numerator and the denominator by 2: [tex]\(\frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18}\)[/tex].
- So, [tex]\(\frac{2}{9} \approx 0.44\)[/tex].
2. Amplify [tex]\(\frac{4}{5}\)[/tex]:
- Multiply by 2: [tex]\(\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}\)[/tex].
- So, [tex]\(\frac{4}{5} = 1.6\)[/tex].
3. Amplify [tex]\(\frac{1}{12}\)[/tex]:
- Multiply by 2: [tex]\(\frac{1}{12} = \frac{1 \times 2}{12 \times 2} = \frac{2}{24}\)[/tex].
- So, [tex]\(\frac{1}{12} \approx 0.17\)[/tex].
4. Amplify [tex]\(\frac{7}{8}\)[/tex]:
- Multiply by 2: [tex]\(\frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16}\)[/tex].
- So, [tex]\(\frac{7}{8} = 1.75\)[/tex].
5. Amplify [tex]\(\frac{2}{3}\)[/tex]:
- Multiply by 2: [tex]\(\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}\)[/tex].
- So, [tex]\(\frac{2}{3} \approx 1.33\)[/tex].
These are the simplified and amplified results of the fractions. If you have further questions or need more explanations, feel free to ask!
### Simplifying Fractions
1. Simplify [tex]\(\frac{20}{50}\)[/tex]:
- Find the greatest common divisor (GCD) of 20 and 50, which is 10.
- Divide both the numerator and denominator by 10: [tex]\(\frac{20}{50} = \frac{20 \div 10}{50 \div 10} = \frac{2}{5}\)[/tex].
- So, [tex]\(\frac{20}{50} = 0.4\)[/tex].
2. Simplify [tex]\(\frac{42}{27}\)[/tex]:
- The GCD of 42 and 27 is 3.
- Divide both the numerator and denominator by 3: [tex]\(\frac{42}{27} = \frac{42 \div 3}{27 \div 3} = \frac{14}{9}\)[/tex].
- So, [tex]\(\frac{42}{27} \approx 1.56\)[/tex].
3. Simplify [tex]\(\frac{14}{21}\)[/tex]:
- The GCD of 14 and 21 is 7.
- Divide by 7: [tex]\(\frac{14}{21} = \frac{14 \div 7}{21 \div 7} = \frac{2}{3}\)[/tex].
- So, [tex]\(\frac{14}{21} \approx 0.67\)[/tex].
4. Simplify [tex]\(\frac{12}{16}\)[/tex]:
- The GCD of 12 and 16 is 4.
- Divide by 4: [tex]\(\frac{12}{16} = \frac{12 \div 4}{16 \div 4} = \frac{3}{4}\)[/tex].
- So, [tex]\(\frac{12}{16} = 0.75\)[/tex].
5. Simplify [tex]\(\frac{16}{18}\)[/tex]:
- The GCD of 16 and 18 is 2.
- Divide by 2: [tex]\(\frac{16}{18} = \frac{16 \div 2}{18 \div 2} = \frac{8}{9}\)[/tex].
- So, [tex]\(\frac{16}{18} \approx 0.89\)[/tex].
### Amplifying Fractions
To amplify, we'll multiply both the numerator and the denominator of each fraction by a common factor, which we assume is 2 in this case.
1. Amplify [tex]\(\frac{2}{9}\)[/tex]:
- Multiply both the numerator and the denominator by 2: [tex]\(\frac{2}{9} = \frac{2 \times 2}{9 \times 2} = \frac{4}{18}\)[/tex].
- So, [tex]\(\frac{2}{9} \approx 0.44\)[/tex].
2. Amplify [tex]\(\frac{4}{5}\)[/tex]:
- Multiply by 2: [tex]\(\frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10}\)[/tex].
- So, [tex]\(\frac{4}{5} = 1.6\)[/tex].
3. Amplify [tex]\(\frac{1}{12}\)[/tex]:
- Multiply by 2: [tex]\(\frac{1}{12} = \frac{1 \times 2}{12 \times 2} = \frac{2}{24}\)[/tex].
- So, [tex]\(\frac{1}{12} \approx 0.17\)[/tex].
4. Amplify [tex]\(\frac{7}{8}\)[/tex]:
- Multiply by 2: [tex]\(\frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16}\)[/tex].
- So, [tex]\(\frac{7}{8} = 1.75\)[/tex].
5. Amplify [tex]\(\frac{2}{3}\)[/tex]:
- Multiply by 2: [tex]\(\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}\)[/tex].
- So, [tex]\(\frac{2}{3} \approx 1.33\)[/tex].
These are the simplified and amplified results of the fractions. If you have further questions or need more explanations, feel free to ask!
