Question

do you notice a pattern?
what is the pattern?
type here
(image shows two rows of shapes with multiplication-like symbols. first row: orange circle × (light blue pentagon over orange circle) × (red star over light blue pentagon) = red star. second row: beige octagon × (light pink triangle over beige octagon) × (blue star over light pink triangle) = blue star.)

Explanation:

Step1: Analyze first row

First row: Circle (orange) × (Pentagon (cyan) over Circle (orange)) × (Star (red) over Pentagon (cyan)) = Star (red). Simplify: The orange circles cancel, cyan pentagons cancel, leaving red star.

Step2: Analyze second row

Second row: Octagon (beige) × (Triangle (pink) over Octagon (beige)) × (Sun (blue) over Triangle (pink)) = Sun (blue). Simplify: Beige octagons cancel, pink triangles cancel, leaving blue sun.

Step3: Identify pattern

In both rows, when multiplying three terms (a × (b/a) × (c/b)), the intermediate terms (a, b) cancel, leaving the last term (c). So the pattern is: When multiplying a shape, a fraction with the next shape over the first, and a fraction with the third shape over the second, the result is the third shape (canceling the first two shapes).

Answer:

When multiplying a shape, a fraction with a second shape over the first, and a fraction with a third shape over the second, the first two shapes cancel, leaving the third shape (e.g., \( \text{Shape}_1 \times \frac{\text{Shape}_2}{\text{Shape}_1} \times \frac{\text{Shape}_3}{\text{Shape}_2} = \text{Shape}_3 \)).