Sure! Let's go through each fraction and simplify them step-by-step.
a) [tex]\(\frac{4}{8}\)[/tex]
- Find the greatest common divisor (GCD) of 4 and 8, which is 4.
- Divide both the numerator and the denominator by the GCD: [tex]\(\frac{4 \div 4}{8 \div 4} = \frac{1}{2}\)[/tex].
Simplified result: [tex]\(\frac{1}{2}\)[/tex]
b) [tex]\(\frac{21}{35}\)[/tex]
- Find the greatest common divisor (GCD) of 21 and 35, which is 7.
- Divide both the numerator and the denominator by the GCD: [tex]\(\frac{21 \div 7}{35 \div 7} = \frac{3}{5}\)[/tex].
Simplified result: [tex]\(\frac{3}{5}\)[/tex]
c) [tex]\(\frac{3}{15}\)[/tex]
- Find the greatest common divisor (GCD) of 3 and 15, which is 3.
- Divide both the numerator and the denominator by the GCD: [tex]\(\frac{3 \div 3}{15 \div 3} = \frac{1}{5}\)[/tex].
Simplified result: [tex]\(\frac{1}{5}\)[/tex]
d) [tex]\(\frac{8}{12}\)[/tex]
- Find the greatest common divisor (GCD) of 8 and 12, which is 4.
- Divide both the numerator and the denominator by the GCD: [tex]\(\frac{8 \div 4}{12 \div 4} = \frac{2}{3}\)[/tex].
Simplified result: [tex]\(\frac{2}{3}\)[/tex]
l) [tex]\(\frac{3}{8}\)[/tex]
- The GCD of 3 and 8 is 1 (since 3 and 8 are co-primes).
- The fraction is already in its simplest form.
Simplified result: [tex]\(\frac{3}{8}\)[/tex]
f) [tex]\(\frac{14}{18}\)[/tex]
- Find the greatest common divisor (GCD) of 14 and 18, which is 2.
- Divide both the numerator and the denominator by the GCD: [tex]\(\frac{14 \div 2}{18 \div 2} = \frac{7}{9}\)[/tex].
Simplified result: [tex]\(\frac{7}{9}\)[/tex]
g) [tex]\(\frac{\text{e}}{9}\)[/tex]
- Since "e" is a variable and not a number, it remains as is. The fraction cannot be simplified further.
Simplified result: [tex]\(\frac{\text{e}}{9}\)[/tex]
h) [tex]\(\frac{54}{90}\)[/tex]
- Find the greatest common divisor (GCD) of 54 and 90, which is 18.
- Divide both the numerator and the denominator by the GCD: [tex]\(\frac{54 \div 18}{90 \div 18} = \frac{3}{5}\)[/tex].
Simplified result: [tex]\(\frac{3}{5}\)[/tex]
Therefore, the simplified fractions for the given problems are:
a) [tex]\(\frac{1}{2}\)[/tex]
b) [tex]\(\frac{3}{5}\)[/tex]
c) [tex]\(\frac{1}{5}\)[/tex]
d) [tex]\(\frac{2}{3}\)[/tex]
l) [tex]\(\frac{3}{8}\)[/tex]
f) [tex]\(\frac{7}{9}\)[/tex]
g) [tex]\(\frac{\text{e}}{9}\)[/tex]
h) [tex]\(\frac{3}{5}\)[/tex]
