What's the percent of mango trees?

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I know this is simple stuff compare to the questions I've seen on this site but please be nice. :) Would be great if anyone could show me how to solve the problem below.

Question:

On a piece of land, 3/8 of the trees are lemon trees. Of the other trees are 8/15 orange trees and 2/5 palm trees. The rest of the trees are mango trees. What's the percent of mango trees? (Answer: 4.2%).

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Lemon trees: $\dfrac{3}{8}$

Other trees: $1-\dfrac{3}{8}=\dfrac{5}{8}$

Orange trees: $\dfrac{5}{8}\cdot\dfrac{8}{15}=\dfrac{1}{3}$

Palm trees: $\dfrac{5}{8}\cdot\dfrac{2}{5}=\dfrac{1}{4}$

Mango trees: $1-\left(\dfrac{3}{8}+\dfrac{1}{3}+\dfrac{1}{4}\right)=\dfrac{1}{24}$