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Sagot :
Let's reduce each of the fractions to their lowest terms one by one and match them with the given options.
### Problem 19: Reduce [tex]\( \frac{18}{30} \)[/tex]
1. Find the greatest common divisor (GCD) of 18 and 30.
- The GCD of 18 and 30 is 6.
2. Divide both the numerator and the denominator by their GCD.
- Numerator: [tex]\( 18 \div 6 = 3 \)[/tex]
- Denominator: [tex]\( 30 \div 6 = 5 \)[/tex]
3. The fraction in the lowest terms is:
- [tex]\( \frac{3}{5} \)[/tex]
Matching with the given options:
- A) [tex]\( \frac{9}{15} \)[/tex]
- B) [tex]\( \frac{3}{5} \)[/tex] ← [Correct answer]
- C) [tex]\( \frac{1}{6} \)[/tex]
- D) [tex]\( \frac{1}{30} \)[/tex]
So, the answer is B) [tex]\( \frac{3}{5} \)[/tex].
### Problem 20: Reduce [tex]\( \frac{19}{20} \)[/tex]
1. Find the greatest common divisor (GCD) of 19 and 20.
- Since 19 is a prime number and doesn't have common factors with 20 other than 1, their GCD is 1.
2. Divide both the numerator and the denominator by their GCD.
- Numerator: [tex]\( 19 \div 1 = 19 \)[/tex]
- Denominator: [tex]\( 20 \div 1 = 20 \)[/tex]
3. The fraction in the lowest terms is:
- [tex]\( \frac{19}{20} \)[/tex]
Matching with the given options:
- A) 1
- B) [tex]\( \frac{1}{2} \)[/tex]
- C) [tex]\( \frac{19}{20} \)[/tex] ← [Correct answer]
- D) 21
So, the answer is C) [tex]\( \frac{19}{20} \)[/tex].
### Problem 21: Reduce [tex]\( \frac{21}{7} \)[/tex]
1. Find the greatest common divisor (GCD) of 21 and 7.
- The GCD of 21 and 7 is 7.
2. Divide both the numerator and the denominator by their GCD.
- Numerator: [tex]\( 21 \div 7 = 3 \)[/tex]
- Denominator: [tex]\( 7 \div 7 = 1 \)[/tex]
3. The fraction in the lowest terms is:
- [tex]\( \frac{3}{1} \)[/tex] (which simplifies to just 3)
Matching with the given options:
- A) [tex]\( 2 \frac{7}{14} \)[/tex]
- B) [tex]\( 1 \frac{1}{2} \)[/tex]
- C) [tex]\( 1 \frac{1}{5} \)[/tex]
- D) 3 ← [Correct answer]
So, the answer is D) 3.
In summary:
- Question 19) Answer is B) [tex]\( \frac{3}{5} \)[/tex]
- Question 20) Answer is C) [tex]\( \frac{19}{20} \)[/tex]
- Question 21) Answer is D) 3
### Problem 19: Reduce [tex]\( \frac{18}{30} \)[/tex]
1. Find the greatest common divisor (GCD) of 18 and 30.
- The GCD of 18 and 30 is 6.
2. Divide both the numerator and the denominator by their GCD.
- Numerator: [tex]\( 18 \div 6 = 3 \)[/tex]
- Denominator: [tex]\( 30 \div 6 = 5 \)[/tex]
3. The fraction in the lowest terms is:
- [tex]\( \frac{3}{5} \)[/tex]
Matching with the given options:
- A) [tex]\( \frac{9}{15} \)[/tex]
- B) [tex]\( \frac{3}{5} \)[/tex] ← [Correct answer]
- C) [tex]\( \frac{1}{6} \)[/tex]
- D) [tex]\( \frac{1}{30} \)[/tex]
So, the answer is B) [tex]\( \frac{3}{5} \)[/tex].
### Problem 20: Reduce [tex]\( \frac{19}{20} \)[/tex]
1. Find the greatest common divisor (GCD) of 19 and 20.
- Since 19 is a prime number and doesn't have common factors with 20 other than 1, their GCD is 1.
2. Divide both the numerator and the denominator by their GCD.
- Numerator: [tex]\( 19 \div 1 = 19 \)[/tex]
- Denominator: [tex]\( 20 \div 1 = 20 \)[/tex]
3. The fraction in the lowest terms is:
- [tex]\( \frac{19}{20} \)[/tex]
Matching with the given options:
- A) 1
- B) [tex]\( \frac{1}{2} \)[/tex]
- C) [tex]\( \frac{19}{20} \)[/tex] ← [Correct answer]
- D) 21
So, the answer is C) [tex]\( \frac{19}{20} \)[/tex].
### Problem 21: Reduce [tex]\( \frac{21}{7} \)[/tex]
1. Find the greatest common divisor (GCD) of 21 and 7.
- The GCD of 21 and 7 is 7.
2. Divide both the numerator and the denominator by their GCD.
- Numerator: [tex]\( 21 \div 7 = 3 \)[/tex]
- Denominator: [tex]\( 7 \div 7 = 1 \)[/tex]
3. The fraction in the lowest terms is:
- [tex]\( \frac{3}{1} \)[/tex] (which simplifies to just 3)
Matching with the given options:
- A) [tex]\( 2 \frac{7}{14} \)[/tex]
- B) [tex]\( 1 \frac{1}{2} \)[/tex]
- C) [tex]\( 1 \frac{1}{5} \)[/tex]
- D) 3 ← [Correct answer]
So, the answer is D) 3.
In summary:
- Question 19) Answer is B) [tex]\( \frac{3}{5} \)[/tex]
- Question 20) Answer is C) [tex]\( \frac{19}{20} \)[/tex]
- Question 21) Answer is D) 3
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