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Reduce the following fractions to lowest terms:

19. [tex]\(\frac{18}{30}\)[/tex]
A. [tex]\(\frac{9}{15}\)[/tex]
B. [tex]\(\frac{3}{5}\)[/tex]
C. [tex]\(\frac{1}{6}\)[/tex]
D. [tex]\(\frac{1}{30}\)[/tex]

20. [tex]\(\frac{19}{20}\)[/tex]
A. 1
B. [tex]\(\frac{1}{2}\)[/tex]
C. [tex]\(\frac{19}{20}\)[/tex]
D. 21

21. [tex]\(\frac{21}{7}\)[/tex]
A. [tex]\(2 \frac{7}{14}\)[/tex]
B. [tex]\(1 \frac{1}{2}\)[/tex]
C. [tex]\(1 \frac{1}{5}\)[/tex]
D. 3

Sagot :

GinnyAnswer
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
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