Grade 3 Geometry: Fractions of Shapes

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   Is this square split into parts with equal areas?

   1. Parts with equal areas each cover the same amount of the whole shape.
   2. Compare the parts. Parts can have different shapes and still have equal areas.
   3. The answer is yes: every part covers the same amount of the shape.

   Answer: yes

2. Example 2

   A square is partitioned into equal parts. Each part is 1/3 of the square and has an area of 3 square units. What is the area of the whole square, in square units?

   1. 1/3 means the whole is cut into that many equal parts.
   2. Every part has the same area, so multiply the area of one part by the number of parts.
   3. 3 × 3 = 9, so the whole is 9 square units.

   Answer: 9 square units

3. Example 3

   A rectangle is cut into equal parts. Each part is 1/6 of the rectangle. If 5 parts are shaded, how many parts are NOT shaded?

   1. 1/6 means the whole is cut into that many equal parts.
   2. Take the shaded parts away from all the parts.
   3. 6 − 5 = 1, so 1 part is not shaded.

   Answer: 1