Exam 14: Developing Aspects of Proportional Reasoning: Ratio, Proportion, and Percent

Correct Answer:

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To answer this question, we need to understand the composition of a tangram set. A tangram is a Chinese geometric puzzle consisting of seven pieces, called tans, which are used to create various shapes, including a square. The seven pieces are:

1. Two large right triangles
2. One medium right triangle
3. Two small right triangles
4. One square
5. One parallelogram

If the entire square made with all seven tangram pieces is considered to be 1/2 (or 50%), we can determine the size of each piece relative to the whole. The traditional tangram set has the following size relationships:

- The two large right triangles together are half the area of the square.
- The medium right triangle is half the area of one large right triangle.
- The two small right triangles together are half the area of the medium right triangle.
- The square is the same area as one of the small right triangles.
- The parallelogram is the same area as one of the small right triangles.

Given these relationships, we can calculate the size of each piece as a fraction of the whole square:

1. Each large right triangle is 1/4 of the whole square (since both together are 1/2).
2. The medium right triangle is 1/8 of the whole square (since it is half the area of one large right triangle).
3. Each small right triangle is 1/16 of the whole square (since both together are 1/8, which is half the area of the medium right triangle).
4. The square is 1/16 of the whole square (since it is the same area as one small right triangle).
5. The parallelogram is 1/16 of the whole square (since it is the same area as one small right triangle).

Now, let's convert these fractions to decimal fractions and percentages:

1. Large right triangle: 1/4 = 0.25 (or 25% of the whole square)
2. Medium right triangle: 1/8 = 0.125 (or 12.5% of the whole square)
3. Small right triangle: 1/16 = 0.0625 (or 6.25% of the whole square)
4. Square: 1/16 = 0.0625 (or 6.25% of the whole square)
5. Parallelogram: 1/16 = 0.0625 (or 6.25% of the whole square)

Remember, these percentages are relative to the whole tangram square being considered as 1/2 (or 50%). If the whole tangram square were considered as a full unit (100%), the percentages would be doubled.