Question

Nicole is running for school president. Her best friend designed her campaign poster, which measured 3 feet by 2 feet. Nicole liked the poster so much, she reproduced the artwork on rectangular buttons that measured 2 inches by 1 1/3 inches. What is the scale factor as a fraction (and how would I do this!?)

Answer 1

9/16 is the scale factor.

Explanation:

Every transformation has an original figure and a transformed figure.

In order to find the scale factor fo the transformation, we need to divide the transformed dimensions by the original ones.

So, in this case, the poster originally had 3 feet by 2 feet. Then, the reproduced artwork has 2 inches by 1 1/3 inches. Before we divide, we need to transform feet to inches.

We know that 1 feet equals 12 inches, that means

`3ft (12in)/(1ft) =36in`

`2ft(12in)/(1ft)=24in`

Then, we do the divisions

`(36in)/(2in)=18\\(24in)/(1(1)/(3)in )=(24in)/((4)/(3)in )=(96)/(3)=32`

Therefore, the scale factor is
`(18)/(32)=(9)/(16)`

Answer 2

`(3 (ft))/(2(in)) by (2(ft))/((4)/(3)(in))`

=
`(3 (ft))/(2(in)) by (2(3)(ft))/(4(in))`

=
`(3 (ft))/(2(in)) by (3(ft))/(2(in))`

Scale factor is:
`(3(ft))/(2(in))`