How to add percentage value by multiplication?

Question

I'm studying the APL language and doing the exercises here: One of the questions is:

b) Add 15% to each number in the list 14 5 78 145.

I tried this:

14 5 78 145 + (14 × 15 ÷ 100) (5 × 15 ÷ 100) (78 × 15 ÷ 100) (145 × 15 ÷ 100)

I get the correct results but this is ugly since I had to write each number. The better answer is given as:

14 5 78 145 × 1.15

I could not figure out how they got 1.15? How can 1.15 work for each different number? Can you help?

Answer 1

Given a number N the $15\%$ of that number is given by

$$\frac{15}{100}\times N=0.15\times N$$

then

$$N+0.15\times N=1.15 \times N$$