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To find out what fraction of the total playground the play structure covers, we need to find the fraction of the playground that the children's space covers, and then multiply that by the fraction of the children's space that the play structure covers.
The fraction of the playground that the children's space covers is 1/3.
The fraction of the children's space that the play structure covers is 2/5.
To find the fraction of the total playground that the play structure covers, we multiply these two fractions:
1/3 * 2/5 = 2/15.
Therefore, the fraction of the total playground that the play structure covers is 2/15.