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Answer :
Sure! Let's go through each fraction step by step and simplify them.
### Example i: Simplify [tex]\(\frac{45}{60}\)[/tex]
1. Find the Greatest Common Divisor (GCD):
- The factors of 45 are 1, 3, 5, 9, 15, and 45.
- The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
- The common factors of 45 and 60 are 1, 3, 5, and 15. The greatest common divisor is 15.
2. Divide the numerator and the denominator by their GCD:
- Divide 45 by 15 to get 3.
- Divide 60 by 15 to get 4.
3. Simplified Fraction:
- The simplified form of [tex]\(\frac{45}{60}\)[/tex] is [tex]\(\frac{3}{4}\)[/tex].
### Example ii: Simplify [tex]\(\frac{14}{42}\)[/tex]
1. Find the Greatest Common Divisor (GCD):
- The factors of 14 are 1, 2, 7, and 14.
- The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
- The common factors of 14 and 42 are 1, 2, 7, and 14. The greatest common divisor is 14.
2. Divide the numerator and the denominator by their GCD:
- Divide 14 by 14 to get 1.
- Divide 42 by 14 to get 3.
3. Simplified Fraction:
- The simplified form of [tex]\(\frac{14}{42}\)[/tex] is [tex]\(\frac{1}{3}\)[/tex].
### Example iii: Simplify [tex]\(\frac{11}{24}\)[/tex]
1. Check for Common Factors:
- The factors of 11 are 1 and 11 (it's a prime number).
- The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
2. Identify Common Factors:
- Since 11 is prime, the only common factor between 11 and 24 is 1.
3. Fraction in Simplest Form:
- Since there are no other common factors, [tex]\(\frac{11}{24}\)[/tex] is already in its simplest form.
In summary, the simplified fractions are:
- [tex]\(\frac{45}{60}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex].
- [tex]\(\frac{14}{42}\)[/tex] simplifies to [tex]\(\frac{1}{3}\)[/tex].
- [tex]\(\frac{11}{24}\)[/tex] is already in its simplest form.
### Example i: Simplify [tex]\(\frac{45}{60}\)[/tex]
1. Find the Greatest Common Divisor (GCD):
- The factors of 45 are 1, 3, 5, 9, 15, and 45.
- The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
- The common factors of 45 and 60 are 1, 3, 5, and 15. The greatest common divisor is 15.
2. Divide the numerator and the denominator by their GCD:
- Divide 45 by 15 to get 3.
- Divide 60 by 15 to get 4.
3. Simplified Fraction:
- The simplified form of [tex]\(\frac{45}{60}\)[/tex] is [tex]\(\frac{3}{4}\)[/tex].
### Example ii: Simplify [tex]\(\frac{14}{42}\)[/tex]
1. Find the Greatest Common Divisor (GCD):
- The factors of 14 are 1, 2, 7, and 14.
- The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
- The common factors of 14 and 42 are 1, 2, 7, and 14. The greatest common divisor is 14.
2. Divide the numerator and the denominator by their GCD:
- Divide 14 by 14 to get 1.
- Divide 42 by 14 to get 3.
3. Simplified Fraction:
- The simplified form of [tex]\(\frac{14}{42}\)[/tex] is [tex]\(\frac{1}{3}\)[/tex].
### Example iii: Simplify [tex]\(\frac{11}{24}\)[/tex]
1. Check for Common Factors:
- The factors of 11 are 1 and 11 (it's a prime number).
- The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
2. Identify Common Factors:
- Since 11 is prime, the only common factor between 11 and 24 is 1.
3. Fraction in Simplest Form:
- Since there are no other common factors, [tex]\(\frac{11}{24}\)[/tex] is already in its simplest form.
In summary, the simplified fractions are:
- [tex]\(\frac{45}{60}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex].
- [tex]\(\frac{14}{42}\)[/tex] simplifies to [tex]\(\frac{1}{3}\)[/tex].
- [tex]\(\frac{11}{24}\)[/tex] is already in its simplest form.
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