Answer :
Sure, let's work through this step-by-step!
### Simplifying Fractions
1. Simplify [tex]\(\frac{20}{50}\)[/tex]:
- Both 20 and 50 can be divided by 10 (their greatest common divisor).
- [tex]\(\frac{20 \div 10}{50 \div 10} = \frac{2}{5}\)[/tex]
2. Simplify [tex]\(\frac{42}{27}\)[/tex]:
- Both 42 and 27 can be divided by 3 (their greatest common divisor).
- [tex]\(\frac{42 \div 3}{27 \div 3} = \frac{14}{9}\)[/tex]
3. Simplify [tex]\(\frac{14}{21}\)[/tex]:
- Both 14 and 21 can be divided by 7 (their greatest common divisor).
- [tex]\(\frac{14 \div 7}{21 \div 7} = \frac{2}{3}\)[/tex]
4. Simplify [tex]\(\frac{12}{16}\)[/tex]:
- Both 12 and 16 can be divided by 4 (their greatest common divisor).
- [tex]\(\frac{12 \div 4}{16 \div 4} = \frac{3}{4}\)[/tex]
5. Simplify [tex]\(\frac{16}{18}\)[/tex]:
- Both 16 and 18 can be divided by 2 (their greatest common divisor).
- [tex]\(\frac{16 \div 2}{18 \div 2} = \frac{8}{9}\)[/tex]
### Amplifying Fractions
Assuming we are amplifying each fraction by multiplying both the numerator and the denominator by 10:
1. Amplify [tex]\(\frac{2}{9}\)[/tex]:
- Multiply both the numerator and denominator by 10.
- [tex]\(\frac{2 \times 10}{9 \times 10} = \frac{20}{9}\)[/tex]
2. Amplify [tex]\(\frac{4}{5}\)[/tex]:
- Multiply both the numerator and denominator by 10.
- [tex]\(\frac{4 \times 10}{5 \times 10} = \frac{40}{50} = \frac{8}{1}\)[/tex] (simplified)
3. Amplify [tex]\(\frac{1}{12}\)[/tex]:
- Multiply both the numerator and denominator by 10.
- [tex]\(\frac{1 \times 10}{12 \times 10} = \frac{10}{12} = \frac{5}{6}\)[/tex] (simplified)
These are the simplified and amplified fractions. I hope this helps you understand the process!
### Simplifying Fractions
1. Simplify [tex]\(\frac{20}{50}\)[/tex]:
- Both 20 and 50 can be divided by 10 (their greatest common divisor).
- [tex]\(\frac{20 \div 10}{50 \div 10} = \frac{2}{5}\)[/tex]
2. Simplify [tex]\(\frac{42}{27}\)[/tex]:
- Both 42 and 27 can be divided by 3 (their greatest common divisor).
- [tex]\(\frac{42 \div 3}{27 \div 3} = \frac{14}{9}\)[/tex]
3. Simplify [tex]\(\frac{14}{21}\)[/tex]:
- Both 14 and 21 can be divided by 7 (their greatest common divisor).
- [tex]\(\frac{14 \div 7}{21 \div 7} = \frac{2}{3}\)[/tex]
4. Simplify [tex]\(\frac{12}{16}\)[/tex]:
- Both 12 and 16 can be divided by 4 (their greatest common divisor).
- [tex]\(\frac{12 \div 4}{16 \div 4} = \frac{3}{4}\)[/tex]
5. Simplify [tex]\(\frac{16}{18}\)[/tex]:
- Both 16 and 18 can be divided by 2 (their greatest common divisor).
- [tex]\(\frac{16 \div 2}{18 \div 2} = \frac{8}{9}\)[/tex]
### Amplifying Fractions
Assuming we are amplifying each fraction by multiplying both the numerator and the denominator by 10:
1. Amplify [tex]\(\frac{2}{9}\)[/tex]:
- Multiply both the numerator and denominator by 10.
- [tex]\(\frac{2 \times 10}{9 \times 10} = \frac{20}{9}\)[/tex]
2. Amplify [tex]\(\frac{4}{5}\)[/tex]:
- Multiply both the numerator and denominator by 10.
- [tex]\(\frac{4 \times 10}{5 \times 10} = \frac{40}{50} = \frac{8}{1}\)[/tex] (simplified)
3. Amplify [tex]\(\frac{1}{12}\)[/tex]:
- Multiply both the numerator and denominator by 10.
- [tex]\(\frac{1 \times 10}{12 \times 10} = \frac{10}{12} = \frac{5}{6}\)[/tex] (simplified)
These are the simplified and amplified fractions. I hope this helps you understand the process!
