1/7 of the shop's T-shirts are blue, on sale, and size medium.
Two-thirds of the T-shirts in a T-shirt shop are blue. Three-sevenths of those T-shirts are on sale.
One-half of the blue T-shirts that are on sale are size medium.
We can calculate the fraction of the shop's T-shirts that are blue T-shirts that are on sale and are size medium as follows:
Fraction of blue T-shirts: 2/3
Fraction of blue T-shirts on sale: 3/7 * 2/3 = 2/7
Fraction of blue T-shirts on sale that are size medium: 1/2 * 2/7 = 1/7
Total fraction: 2/3 * 3/7 * 1/2 = 1/7
Therefore, 1/7 of the shop's T-shirts are blue, on sale, and size medium.