Andrew wants to rename 2/7 and 3/4 using a common denominator. which of the following shows these fractions renamed correctly.

a 8/28 and 21/28
b 2/28 and 3/28
c 4/28 and 6/28
d 2/7 and 3/7

To rename fractions using a common denominator, you need to find the least common multiple (LCM) of the denominators, which is the smallest number that both denominators can evenly divide into.

The denominators of the fractions 2/7 and 3/4 are 7 and 4. To find the LCM, you can list the multiples of each denominator and find the smallest common multiple.

For the denominator 7, the multiples are: 7, 14, 21, 28, 35, ...

For the denominator 4, the multiples are: 4, 8, 12, 16, 20, 24, 28, 32, ...

The LCM of 7 and 4 is 28 since it is the smallest number that both denominators have in common.

Now, to rename the fractions using the common denominator 28, you need to determine the equivalent fractions by multiplying the numerator and denominator of each fraction by the same number so that the denominator becomes 28.

Let's check the given options:

a) 8/28 and 21/28: When multiplying the numerator and denominator of the first fraction (2/7) by 4 and the second fraction (3/4) by 7 respectively, you get 8/28 and 21/28. These fractions are correctly renamed using the common denominator 28.

b) 2/28 and 3/28: These fractions are not correctly renamed using the common denominator 28 since the numerators are not multiples of the original numerators.

c) 4/28 and 6/28: These fractions are not correctly renamed using the common denominator 28 since the numerators are not equal to the numerators of the original fractions.

d) 2/7 and 3/7: These fractions are not renamed using the common denominator 28 as they retain their original denominators, 7.

Therefore, the correct option is a) 8/28 and 21/28, which correctly shows fractions 2/7 and 3/4 renamed using the common denominator 28.