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Answer :
To determine which of these fractions is in its simplest form, we can simplify each one and see if it equals the original fraction:
a. [tex]\(\frac{12}{21}\)[/tex]
- Find the greatest common divisor (GCD) of 12 and 21, which is 3.
- Divide both the numerator and the denominator by 3: [tex]\(\frac{12 \div 3}{21 \div 3} = \frac{4}{7}\)[/tex].
- [tex]\(\frac{12}{21}\)[/tex] simplifies to [tex]\(\frac{4}{7}\)[/tex], so it is not in simplest form.
b. [tex]\(\frac{91}{100}\)[/tex]
- Since 91 and 100 have no common factors other than 1 (GCD of 91 and 100 is 1), it cannot be simplified further.
- [tex]\(\frac{91}{100}\)[/tex] is already in its simplest form.
c. [tex]\(\frac{19}{95}\)[/tex]
- Find the GCD of 19 and 95, which is 19.
- Divide both the numerator and the denominator by 19: [tex]\(\frac{19 \div 19}{95 \div 19} = \frac{1}{5}\)[/tex].
- [tex]\(\frac{19}{95}\)[/tex] simplifies to [tex]\(\frac{1}{5}\)[/tex], so it is not in simplest form.
d. [tex]\(\frac{34}{50}\)[/tex]
- Find the GCD of 34 and 50, which is 2.
- Divide both the numerator and the denominator by 2: [tex]\(\frac{34 \div 2}{50 \div 2} = \frac{17}{25}\)[/tex].
- [tex]\(\frac{34}{50}\)[/tex] simplifies to [tex]\(\frac{17}{25}\)[/tex], so it is not in simplest form.
The fraction [tex]\(\frac{91}{100}\)[/tex] is already in its simplest form since it cannot be simplified any further.
a. [tex]\(\frac{12}{21}\)[/tex]
- Find the greatest common divisor (GCD) of 12 and 21, which is 3.
- Divide both the numerator and the denominator by 3: [tex]\(\frac{12 \div 3}{21 \div 3} = \frac{4}{7}\)[/tex].
- [tex]\(\frac{12}{21}\)[/tex] simplifies to [tex]\(\frac{4}{7}\)[/tex], so it is not in simplest form.
b. [tex]\(\frac{91}{100}\)[/tex]
- Since 91 and 100 have no common factors other than 1 (GCD of 91 and 100 is 1), it cannot be simplified further.
- [tex]\(\frac{91}{100}\)[/tex] is already in its simplest form.
c. [tex]\(\frac{19}{95}\)[/tex]
- Find the GCD of 19 and 95, which is 19.
- Divide both the numerator and the denominator by 19: [tex]\(\frac{19 \div 19}{95 \div 19} = \frac{1}{5}\)[/tex].
- [tex]\(\frac{19}{95}\)[/tex] simplifies to [tex]\(\frac{1}{5}\)[/tex], so it is not in simplest form.
d. [tex]\(\frac{34}{50}\)[/tex]
- Find the GCD of 34 and 50, which is 2.
- Divide both the numerator and the denominator by 2: [tex]\(\frac{34 \div 2}{50 \div 2} = \frac{17}{25}\)[/tex].
- [tex]\(\frac{34}{50}\)[/tex] simplifies to [tex]\(\frac{17}{25}\)[/tex], so it is not in simplest form.
The fraction [tex]\(\frac{91}{100}\)[/tex] is already in its simplest form since it cannot be simplified any further.
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