Please help with number 14.

This is because when you can multiply both the numerator and the denominator by the same number, it becomes equivalent as you can simplify it by dividing by two or any number you multiplied the numerator and the denominator with.

Let's take 1/2 as an example...

This means that the rectangle will have two parts (one shaded). If we further divide the rectangles by 2, we get 2 rectangles shaded with 4 rectangles in total. This proves that:

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2