Question
Which of the following fraction pairs is equivalent?
A) 8/18 and 8/20
B) 2/8 and 7/28
C) 16/20 and 9/12
D) 6/21 and 14/35
A) 8/18 and 8/20
B) 2/8 and 7/28
C) 16/20 and 9/12
D) 6/21 and 14/35
Answers
GPT 3.5
To determine which fraction pairs are equivalent, we can simplify each of the fractions.
A) 8/18 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2. This gives us 4/9. 8/20 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is also 2. This gives us 4/10. Since 4/9 and 4/10 are not equal, this pair is not equivalent.
B) 2/8 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2. This gives us 1/4. 7/28 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 7. This gives us 1/4. Since 1/4 and 1/4 are equal, this pair is equivalent.
C) 16/20 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4. This gives us 4/5. 9/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3. This gives us 3/4. Since 4/5 and 3/4 are not equal, this pair is not equivalent.
D) 6/21 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3. This gives us 2/7. 14/35 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 7. This gives us 2/5. Since 2/7 and 2/5 are not equal, this pair is not equivalent.
Therefore, the only pair of equivalent fractions is B) 2/8 and 7/28. Answer: \boxed{\text{B)}}.
A) 8/18 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2. This gives us 4/9. 8/20 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is also 2. This gives us 4/10. Since 4/9 and 4/10 are not equal, this pair is not equivalent.
B) 2/8 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2. This gives us 1/4. 7/28 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 7. This gives us 1/4. Since 1/4 and 1/4 are equal, this pair is equivalent.
C) 16/20 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4. This gives us 4/5. 9/12 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3. This gives us 3/4. Since 4/5 and 3/4 are not equal, this pair is not equivalent.
D) 6/21 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3. This gives us 2/7. 14/35 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 7. This gives us 2/5. Since 2/7 and 2/5 are not equal, this pair is not equivalent.
Therefore, the only pair of equivalent fractions is B) 2/8 and 7/28. Answer: \boxed{\text{B)}}.