Question

Jen wrote cross-multiplication property for her proportion:

x∙ t=u ∙y
Which of the following could her proportion? Choose all that apply.
(A) x:u=y:t
(B) x:y=u:t
(C) x:t=y:u
(D) t:y=u:x
(E) u:x=t:y
(F) x:u=y:t
(G) x:y=t:u
(H) y:x=t:u
hahah i know it's a lot!

Answer 1

The correct answers are A, B, D, E, F, and H.

Please see the attached work for the cross multiplication work for each!

Answer 2

The correct options are:

(A) x:u=y:t

(B) x:y=u:t

(D) t:y=u:x

(E) u:x=t:y

(F) x:u=y:t

(H) y:x=t:u

Explanation:

The cross multiplication expression is given by:

`x\cdot t=u\cdot y`

• Now, as a proportion it could also be represented by:

`(x)/(u)=(y)/(t)`

i.e.

`x:u=y:t`

Hence, option: A is correct.

• Also,

`(x)/(y)=(u)/(t)`

i.e.
`x:y=u:t`

Option: B is correct.

• Option: C is incorrect.

Since, they are in multiplication and not in proportion.

• Also, we may represent it by:

`(t)/(y)=(u)/(x)`

Hence, option: D is correct.

• 
  `Also,\\\\(u)/(x)=(t)/(y)`

i.e.
`u:x=t:y`

Hence, option: E is correct.

Option: A and option: F is correct.

• 
  `(x)/(u)=(u)/(t)`

Hence, option: G is incorrect.

• Also,

`(y)/(x)=(t)/(u)`

i.e.
`y:x=t:u`

Hence, option: H is correct.