Two classmates are preparing research papers and are organizing their information on index cards.

keiko is using 3 in. x 5 in. cards.

william is using 4 in. x 6 in. cards.

a. set up a proportion to determine if the students are using index cards that are similar. are they similar?

b. a third student, joel, is writing his information on paper that measures 12 in. x 8 in.

is this similar to either keiko's or william's cards? show your setup and work to support your answer.

So proprtion
A.
keiko=3:5
will=4:6
make as fractions
3/5 and 4/6
simplify
3/5=3/5
4/6=2/3
3/5 not equal to 2/3, so NOT similar

B. Joel=12:8 conver to fractions
12/8=6/4=3/2
this is similar to 2/3 since the cards can be flipped to be similar
Joel's card is similar to will's card

Options:

(A)x = StartFraction 6 over 4 EndFraction

(B)x = Negative StartFraction 6 over 4 EndFraction

(C)x minus one-fourth = negative StartFraction 5 over 4 EndFraction

(D)x = negative three-halves

(E)x = negative three-fourths

(B)x = Negative StartFraction 6 over 4 EndFraction

(D)x = negative three-halves

Step-by-step explanation:

We want to determine which fraction is equivalent to

This value of x is the result in Option B.

Reducing to its lowest form:

which is Option D.

Therefore, the correct options are: B and D