First identify existing fractions in the diagram,
- Yellow shaded triangle is half of the larger rectangle (made up of 5 smaller rectangles)
- blue shaded triangle is half of the smaller blue rectangle (made up of 2 smaller rectangles)

You can then derive the black shaded area as it is the remaining portion after subtracting the yellow and blue shaded triangle from the larger rectangle.

Let the area of 1 smaller rectangle be 2 unit.
Area of larger rectangle = 2 x 5 = 10
Area of yellow triangle = 10 / 2 = 5

Area of blue rectangle = 2 x 2 = 4
Area of blue triangle = 4 / 2 = 2

Area of black shaded area = 10 - 5 - 2 = 3
Fraction of black shaded area = 3 / 10