Answer :
To determine which of the fractions is in its simplest form, we need to check if the greatest common divisor (GCD) of the numerator and the denominator of each fraction is 1.
Let's evaluate each fraction:
a. [tex]\(\frac{12}{21}\)[/tex]:
- Find the GCD of 12 and 21. The GCD is 3 (both are divisible by 3).
- Since the GCD is not 1, this fraction is not in its simplest form.
b. [tex]\(\frac{91}{100}\)[/tex]:
- Find the GCD of 91 and 100. The GCD is 1 (no common divisors except 1).
- Since the GCD is 1, this fraction is in its simplest form.
c. [tex]\(\frac{19}{95}\)[/tex]:
- Find the GCD of 19 and 95. The GCD is 19 (both are divisible by 19).
- Since the GCD is not 1, this fraction is not in its simplest form.
d. [tex]\(\frac{34}{50}\)[/tex]:
- Find the GCD of 34 and 50. The GCD is 2 (both are divisible by 2).
- Since the GCD is not 1, this fraction is not in its simplest form.
Among the options given, [tex]\(\frac{91}{100}\)[/tex] is the only fraction in its simplest form.
Let's evaluate each fraction:
a. [tex]\(\frac{12}{21}\)[/tex]:
- Find the GCD of 12 and 21. The GCD is 3 (both are divisible by 3).
- Since the GCD is not 1, this fraction is not in its simplest form.
b. [tex]\(\frac{91}{100}\)[/tex]:
- Find the GCD of 91 and 100. The GCD is 1 (no common divisors except 1).
- Since the GCD is 1, this fraction is in its simplest form.
c. [tex]\(\frac{19}{95}\)[/tex]:
- Find the GCD of 19 and 95. The GCD is 19 (both are divisible by 19).
- Since the GCD is not 1, this fraction is not in its simplest form.
d. [tex]\(\frac{34}{50}\)[/tex]:
- Find the GCD of 34 and 50. The GCD is 2 (both are divisible by 2).
- Since the GCD is not 1, this fraction is not in its simplest form.
Among the options given, [tex]\(\frac{91}{100}\)[/tex] is the only fraction in its simplest form.
