# Scaling the 16:9 ratio to A3, A4, and A5 and my sketch pad!

#### Thomas Casson

##### New member
Hello there!

This may not be the most common question posed and im sure it will be easy for most of you! But I need to draw images on a pad of paper to a ratio met by most screens - 16:9

I have a pad of 30.5 x 22.5 cm / 12 x 9 inches.

I was never good at maths only art drama and music! So was hoping to ask you clever clogs this and get an answer.

If someone can figure this out for me and tell me how many cms/inches height and width within in my pad that would be wonderful. The A3, A4, and A5 in the title is just for a bonus for me if possible also. I've tried to work it out as you can see in my picture but i don't trust myself.

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#### Otis

##### Senior Member
Hello. The dogs are all napping, so I'll help. If we choose one dimension of your pad, we can find the other dimension by writing and solving a proportion.

$$\displaystyle \frac{16}{9} = \frac{30.5}{?}$$

This proportion is read out loud as, "16 compares to 9 in the same way that 30.5 compares to ?"

Arithmetic lesson of the day: When you know three of the numbers in a proportion, you can calculate the missing number by (1) multiplying on the diagonal and (2) dividing by the number not used.

9 × 30.5 = 274.5

274.5 ÷ 16 = 17.2 (rounded)

In other words, 30.5 by 17.2 is proportional to 16 by 9.

If we choose the other dimension, then we get:

$$\displaystyle \frac{16}{9} = \frac{22.5}{?}$$

9 × 22.5 = 202.5

202.5 ÷ 16 = 12.7 (rounded)

So, 22.5 by 12.7 is proportional to 16 by 9.

Finally, if you wanted 22.5 to be the shorter side, then you would discover that the long side of your pad is not long enough:

$$\displaystyle \frac{16}{9} = \frac{?}{22.5}$$

16 × 22.5 = 360

360 ÷ 9 = 40

So, 40 by 22.5 is proportional to 16 by 9.

Questions about any of this? If not, then you can work things out for paper sizes A3, A4 and A5. Cheers!

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#### Thomas Casson

##### New member
Hello!!

are the results in inches or cms? Or would it matter?

Im afraid i woiuldnt be able to work it out still.. but thank you so so much for this.

#### Otis

##### Senior Member
… are the results in inches or cms? Or would it matter? …
Hello again. Yes, it matters. The units are the same as what you start with. In post #2, each of my worked examples started with a measurement that you had provided in centimeters, so the results are in centimeters. (Note: The 16 by 9 ratio has no units.)

Below are two more examples, using your rectangle that measures 12 inches by 9 inches.

If you would like a new rectangle (proportional to 16 by 9) that measures 12 inches on its longest sides:

$$\displaystyle \displaystyle \frac{16}{9} = \frac{12}{?}$$

9 × 12 = 108

108 ÷ 16 = 6.75

A 12-inch by 6.75-inch rectangle is proportional to 16 by 9.

If you would like a new rectangle (proportional to 16 by 9) that measures 9 inches on its longest sides:

$$\displaystyle \displaystyle \frac{16}{9} = \frac{9}{?}$$

9 × 9 = 81

81 ÷ 16 = 5.1 (rounded)

A 9-inch by 5.1-inch rectangle is closely proportional to 16 by 9.

… i woiuldnt be able to work it out still …
Can you explain where you get stuck, when you try? We can go over that part again. Cheers