A free visual tool for modeling decimal multiplication: shade two decimals on a 10x10 hundredths grid, watch the overlap reveal the product, and follow the place-value shift step by step.
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The Decimal Multiplication Area/Grid Model turns any multiplication of two decimals between 0.01 and 1 into a picture. The first factor is shaded down the rows of a 10x10 hundredths grid and the second factor across the columns, so the overlapping region is the product.
Every result comes with a five-step worked solution covering the place-value shift rule — multiply as whole numbers, then divide by the matching power of ten — plus an exact area reconciliation between the shaded cells and the product.
Use a 10x10 grid where the whole square is 1 and each small cell is 0.01. Shade the first factor down the rows and the second factor across the columns. The overlap of the two shaded bands is the product, because its area in hundredths equals the two factors multiplied together.
Each row of the grid is worth 0.1 and each column is worth 0.1, so a cell in the overlap is worth 0.1 × 0.1 = 0.01 of the whole. Counting the overlap area is the area model of multiplication: factor × factor = product.
Multiply the factors as if they were whole numbers, then count the total number of decimal places in both factors and move the decimal point that many places left. For 0.3 × 0.6 that is 3 × 6 = 18 with 1 + 1 = 2 decimal places, so the product is 0.18.
Each factor keeps only a fraction of the other. On the grid the product is the overlap of the two shaded bands, which is visibly smaller than either band — multiplying by a number less than 1 always shrinks the other factor.
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