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Use the model below and partial products to find .1.3 x1.6

The top left hundredths grid is whole, and the grid to the right of it has 30 squares. The grid below the whole grid has 60 squares. The grid to in the bottom right has 18 squares. The whole hundredths grid is labeled 1 on the top side and the left side. The grid with 30 squares is labeled 0.3 on the top side. The grid with 60 squares is labeled 0.6 along the left side.

1 answer

To calculate \(1.3 \times 1.6\) using partial products, we can break the numbers down into their place values:

  • \(1.3 = 1 + 0.3\)
  • \(1.6 = 1 + 0.6\)

Now, we can use the distributive property (also known as the area model or partial products) to calculate the product:

\[ 1.3 \times 1.6 = (1 + 0.3) \times (1 + 0.6) \]

Now let's distribute:

  1. \(1 \times 1 = 1\)
  2. \(1 \times 0.6 = 0.6\)
  3. \(0.3 \times 1 = 0.3\)
  4. \(0.3 \times 0.6 = 0.18\) (Calculating \(0.3 \times 0.6\) requires \((3 \times 6) / 100 = 18 / 100 = 0.18\))

Now, we can add all these results together:

\[ 1 + 0.6 + 0.3 + 0.18 \]

Calculating step-by-step:

  1. \(1 + 0.6 = 1.6\)
  2. \(1.6 + 0.3 = 1.9\)
  3. \(1.9 + 0.18 = 2.08\)

Therefore, the result of \(1.3 \times 1.6\) is:

\[ \boxed{2.08} \]