First of all, you can clearly see that the whole rectangle is divided into quarters. Look at rectangle 1. It is half of the first quarter, and ½ of ¼ is ⅛ (you multiply ½ by 2 to get half of ¼ ). Rectangle 1 is ⅛ .
Here's another example. Let's look at triangle 4. It is in the third quarter of the whole rectangle. And looking at that quarter, it is divided into two parts again, and each part equal ⅛ (¼ multiplied by 2 gives us ⅛ ).Now, to find what fractional part triangle 4 is, we imagine that there’s a vertical line running down the middle of the ⅛ section triangle 4 is in. Now you see 4 identical triangles. The green triangle 4 consists of 2 of the triangles, but there is still two triangles left. Which means, that triangle 4 is half of the ⅛ section. Half of ⅛ is 1/16 (double ⅛ and you get half the original amount). Triangle 4 is 1/16.
The third quarter that triangle 4 is in are made up of triangles. We know that half of the the third quarter is made out of 4 triangles, so the other half must be the same. Altogether, the third quarter is made from 8 triangles. Triangle 4 is made from 2. Divide triangle 4 by 2, and you get the fractional part of 1 triangle, 1/32. Triangle 8 is 1/32.
Triangle 7 kind of resembles triangle 4. We can imagine it as 3 triangles, right? One triangle is 1/32, three of that equals triangle 7. Triangle
7 is 3/32.
Rectangle 5 is equivalent to rectangle 1. Why? Because we know now that rectangle one is clearly half of the first quarter, correct? And looking at rectangle 5, it is also half of the last quarter, only presented in a different shape. Rectangle 1 is also â…› .
Rectangles 6, 9 and 10 are all in a cube that is equivalent to rectangles 5 and 1. Rectangle 6 is half of rectangle 5, half of â…› equals 1/16. 9 is half of rectangle 6, making it 1/32. Rectangle 10 is half of rectangle 9, so it is 1/64.