Answer :
Sure! Let's simplify each fraction until they become irreducible step by step:
a) Fraction: [tex]\(\frac{30}{12}\)[/tex]
- Find the greatest common divisor (GCD) of 30 and 12, which is 6.
- Divide both the numerator and the denominator by 6:
[tex]\(\frac{30 \div 6}{12 \div 6} = \frac{5}{2}\)[/tex].
b) Fraction: [tex]\(\frac{28}{42}\)[/tex]
- The GCD of 28 and 42 is 14.
- Divide both parts of the fraction by 14:
[tex]\(\frac{28 \div 14}{42 \div 14} = \frac{2}{3}\)[/tex].
c) Fraction: [tex]\(\frac{32}{40}\)[/tex]
- The GCD of 32 and 40 is 8.
- Simplify by dividing by 8:
[tex]\(\frac{32 \div 8}{40 \div 8} = \frac{4}{5}\)[/tex].
d) Fraction: [tex]\(\frac{45}{27}\)[/tex]
- The GCD for 45 and 27 is 9.
- Simplify by dividing both terms by 9:
[tex]\(\frac{45 \div 9}{27 \div 9} = \frac{5}{3}\)[/tex].
e) Fraction: [tex]\(\frac{36}{48}\)[/tex]
- The GCD of 36 and 48 is 12.
- Simplify by dividing by 12:
[tex]\(\frac{36 \div 12}{48 \div 12} = \frac{3}{4}\)[/tex].
f) Fraction: [tex]\(\frac{48}{54}\)[/tex]
- The GCD is 6.
- Divide both by 6:
[tex]\(\frac{48 \div 6}{54 \div 6} = \frac{8}{9}\)[/tex].
g) Fraction: [tex]\(\frac{75}{50}\)[/tex]
- The GCD is 25.
- Divide to simplify:
[tex]\(\frac{75 \div 25}{50 \div 25} = \frac{3}{2}\)[/tex].
h) Fraction: [tex]\(\frac{80}{64}\)[/tex]
- Their GCD is 16.
- Simplify by dividing:
[tex]\(\frac{80 \div 16}{64 \div 16} = \frac{5}{4}\)[/tex].
i) Fraction: [tex]\(\frac{81}{54}\)[/tex]
- The GCD is 27.
- Divide by 27:
[tex]\(\frac{81 \div 27}{54 \div 27} = \frac{3}{2}\)[/tex].
j) Fraction: [tex]\(\frac{72}{90}\)[/tex]
- The GCD is 18.
- Divide the terms by 18:
[tex]\(\frac{72 \div 18}{90 \div 18} = \frac{4}{5}\)[/tex].
k) Fraction: [tex]\(\frac{60}{84}\)[/tex]
- Their GCD is 12.
- Divide both terms by 12:
[tex]\(\frac{60 \div 12}{84 \div 12} = \frac{5}{7}\)[/tex].
l) Fraction: [tex]\(\frac{84}{96}\)[/tex]
- The GCD is 12.
- Simplify by division:
[tex]\(\frac{84 \div 12}{96 \div 12} = \frac{7}{8}\)[/tex].
These simplified fractions are now irreducible, meaning they cannot be simplified any further.
a) Fraction: [tex]\(\frac{30}{12}\)[/tex]
- Find the greatest common divisor (GCD) of 30 and 12, which is 6.
- Divide both the numerator and the denominator by 6:
[tex]\(\frac{30 \div 6}{12 \div 6} = \frac{5}{2}\)[/tex].
b) Fraction: [tex]\(\frac{28}{42}\)[/tex]
- The GCD of 28 and 42 is 14.
- Divide both parts of the fraction by 14:
[tex]\(\frac{28 \div 14}{42 \div 14} = \frac{2}{3}\)[/tex].
c) Fraction: [tex]\(\frac{32}{40}\)[/tex]
- The GCD of 32 and 40 is 8.
- Simplify by dividing by 8:
[tex]\(\frac{32 \div 8}{40 \div 8} = \frac{4}{5}\)[/tex].
d) Fraction: [tex]\(\frac{45}{27}\)[/tex]
- The GCD for 45 and 27 is 9.
- Simplify by dividing both terms by 9:
[tex]\(\frac{45 \div 9}{27 \div 9} = \frac{5}{3}\)[/tex].
e) Fraction: [tex]\(\frac{36}{48}\)[/tex]
- The GCD of 36 and 48 is 12.
- Simplify by dividing by 12:
[tex]\(\frac{36 \div 12}{48 \div 12} = \frac{3}{4}\)[/tex].
f) Fraction: [tex]\(\frac{48}{54}\)[/tex]
- The GCD is 6.
- Divide both by 6:
[tex]\(\frac{48 \div 6}{54 \div 6} = \frac{8}{9}\)[/tex].
g) Fraction: [tex]\(\frac{75}{50}\)[/tex]
- The GCD is 25.
- Divide to simplify:
[tex]\(\frac{75 \div 25}{50 \div 25} = \frac{3}{2}\)[/tex].
h) Fraction: [tex]\(\frac{80}{64}\)[/tex]
- Their GCD is 16.
- Simplify by dividing:
[tex]\(\frac{80 \div 16}{64 \div 16} = \frac{5}{4}\)[/tex].
i) Fraction: [tex]\(\frac{81}{54}\)[/tex]
- The GCD is 27.
- Divide by 27:
[tex]\(\frac{81 \div 27}{54 \div 27} = \frac{3}{2}\)[/tex].
j) Fraction: [tex]\(\frac{72}{90}\)[/tex]
- The GCD is 18.
- Divide the terms by 18:
[tex]\(\frac{72 \div 18}{90 \div 18} = \frac{4}{5}\)[/tex].
k) Fraction: [tex]\(\frac{60}{84}\)[/tex]
- Their GCD is 12.
- Divide both terms by 12:
[tex]\(\frac{60 \div 12}{84 \div 12} = \frac{5}{7}\)[/tex].
l) Fraction: [tex]\(\frac{84}{96}\)[/tex]
- The GCD is 12.
- Simplify by division:
[tex]\(\frac{84 \div 12}{96 \div 12} = \frac{7}{8}\)[/tex].
These simplified fractions are now irreducible, meaning they cannot be simplified any further.
