Translucent Lab: Multiplying Fractions with Overlays

In everyday language, the word “of” often means multiply. Half of a quarter pizza, a third of two thirds of a chocolate bar — both are fraction multiplication problems in disguise. Each one starts with a fraction of a whole, then takes only a fraction of that piece.

Draw a square and shade vertical stripes across three of its four columns to show 3⁄4. On the very same square, shade horizontal stripes across two of its three rows to show 2⁄3. Some cells now have both stripe directions — they are shaded twice. That doubly-shaded region is the product, 3⁄4 × 2⁄3.

Splitting the square into columns and rows creates a grid of small equal cells — the total number of cells is columns × rows, which becomes the new denominator. The cells shaded in both directions are the overlap — shaded columns × shaded rows — which becomes the new numerator.