You know equal parts and unit fractions, and you can measure area. Put them together: when a shape is split into parts with equal area, each part is a unit fraction of the whole area.
Por qué funciona
What matters for a fraction of a shape is how much space each part covers, not what the part looks like. The left half of the square is cut into 2 equal rectangles, so each is half of a half: $\frac{1}{4}$. The right half is cut corner to corner into 2 equal triangles, so each is also half of a half: $\frac{1}{4}$. Different shapes, same area.
Idea clave
If a shape is split into $b$ parts with equal area, each part is $\frac{1}{b}$ of the area of the shape. The parts do not need to have the same shape.
Ejemplo resuelto: Six parts
A rectangle is split into 6 parts with equal area. What fraction of the area is one part?
- 6 equal-area parts.
- Each part is $\frac{1}{6}$ of the area.
Respuesta: $\frac{1}{6}$
Ejemplo resuelto: Triangles
A square is cut along both diagonals into 4 triangles. What fraction of the area is each triangle?
- The 4 triangles are the same size.
- So each is $\frac{1}{4}$ of the square.
Respuesta: $\frac{1}{4}$
Error común
Thinking equal parts must look the same. A rectangle piece and a triangle piece can have the same area. Check by comparing each part with a half of the shape, or by counting unit squares, instead of by looking at the shapes.