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Simplifica estas fracciones:

\[ \frac{20}{50} = \square \]

\[ \frac{12}{16} = \square \]

\[ \frac{14}{21} = \square \]

\[ \frac{42}{27} = \square \]

\[ \frac{16}{18} = \square \]

Amplifica estas fracciones:

\[ \frac{2}{9} = \square \]

\[ \frac{4}{5} = \square \]

\[ \frac{1}{12} = \square \]

\[ \frac{7}{8} = \square \]

\[ \frac{2}{3} = \square \]

Answer :

Sure! Let's go through simplifying and amplifying the fractions step by step.

### Simplifying Fractions

1. Simplify [tex]\(\frac{20}{50}\)[/tex]:
- Find the greatest common divisor (GCD) of 20 and 50. The GCD is 10.
- Divide the numerator and the denominator by the GCD:
[tex]\[
\frac{20 \div 10}{50 \div 10} = \frac{2}{5}
\][/tex]

2. Simplify [tex]\(\frac{12}{16}\)[/tex]:
- Find the GCD of 12 and 16. The GCD is 4.
- Divide the numerator and the denominator by the GCD:
[tex]\[
\frac{12 \div 4}{16 \div 4} = \frac{3}{4}
\][/tex]

3. Simplify [tex]\(\frac{14}{21}\)[/tex]:
- Find the GCD of 14 and 21. The GCD is 7.
- Divide the numerator and the denominator by the GCD:
[tex]\[
\frac{14 \div 7}{21 \div 7} = \frac{2}{3}
\][/tex]

4. Simplify [tex]\(\frac{42}{27}\)[/tex]:
- Find the GCD of 42 and 27. The GCD is 3.
- Divide the numerator and the denominator by the GCD:
[tex]\[
\frac{42 \div 3}{27 \div 3} = \frac{14}{9}
\][/tex]

5. Simplify [tex]\(\frac{16}{18}\)[/tex]:
- Find the GCD of 16 and 18. The GCD is 2.
- Divide the numerator and the denominator by the GCD:
[tex]\[
\frac{16 \div 2}{18 \div 2} = \frac{8}{9}
\][/tex]

### Amplifying Fractions

To amplify fractions, we multiply the numerator and the denominator by the same number. In this case, let's use an amplification factor of 10.

1. Amplify [tex]\(\frac{2}{9}\)[/tex]:
[tex]\[
\frac{2 \times 10}{9 \times 10} = \frac{20}{90}
\][/tex]

2. Amplify [tex]\(\frac{4}{5}\)[/tex]:
[tex]\[
\frac{4 \times 10}{5 \times 10} = \frac{40}{50}
\][/tex]

3. Amplify [tex]\(\frac{1}{12}\)[/tex]:
[tex]\[
\frac{1 \times 10}{12 \times 10} = \frac{10}{120}
\][/tex]

4. Amplify [tex]\(\frac{7}{8}\)[/tex]:
[tex]\[
\frac{7 \times 10}{8 \times 10} = \frac{70}{80}
\][/tex]

5. Amplify [tex]\(\frac{2}{3}\)[/tex]:
[tex]\[
\frac{2 \times 10}{3 \times 10} = \frac{20}{30}
\][/tex]

These calculations simplify and amplify the given fractions as shown above.

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