Question

Is there a proportional relationship between the length and width of tvs? Check the table for equivalent ratios to support your answer. Show work.

Length Width
16 9
20 11.25
24 13.50

Answer 1

Divide each length over its corresponding width

16/9 = 1.77777777777778
20/11.25 = 1.77777777777778
24/13.50 = 1.77777777777778
The decimal results are approximate. The 7's should go forever

Since we get the same result each time (1.77777777777778), this means that the lengths and widths are proportional to each other.

Answer 2

Yes, there is a proportional relationship, because the ratio length/width is the same for all cases

Explanation:

If the ratio length/width is the same for all cases, then they are proportional between them.

16/9 ≈ 1.78

20/11.25 ≈ 1.78

24/13.50 ≈ 1.78

Another way is to prove that they are proportional is to multiply and divide 16/9 by a constant, as follows:

16/9 = 16/9 * 1.25/1.25 = (16*1.25) / (9*1.25) = 20/11.25

16/9 = 16/9 * 1.5/1.5 = (16*1.5) / (9*1.5) = 24/13.5