Question

18 × 26 (multiplication algorithm with empty boxes: first partial product row, second partial product row with a 0, total product row) and an area model with top segments 10, 8 and left segments 20, 6, dividing the rectangle into four parts.

Explanation:

Left: Multiplication Calculation (18 × 26)

Step1: Multiply 18 by 6

To calculate the first partial product, we multiply the top number (18) by the ones digit of the bottom number (6).
$18 \times 6 = 108$
So the first row of boxes (partial product) is 1, 0, 8.

Step2: Multiply 18 by 20

Next, we multiply the top number (18) by the tens digit of the bottom number (2, which represents 20).
$18 \times 20 = 360$
So the second row of boxes (partial product) is 3, 6, 0 (note the trailing 0 from the tens place multiplication).

Step3: Add the partial products

Now we add the two partial products: $108 + 360$.
$108 + 360 = 468$
So the final row of boxes (sum) is 4, 6, 8.

Right: Area Calculation (Using Rectangle Division)

The large rectangle is divided into four smaller rectangles. To find the total area, we calculate the area of each small rectangle and sum them:

1. Top - left: $20 \times 10 = 200$
2. Top - right: $20 \times 8 = 160$
3. Bottom - left: $6 \times 10 = 60$
4. Bottom - right: $6 \times 8 = 48$

Total area: $200 + 160 + 60 + 48 = 468$ (matches the multiplication result, showing the area model for $18 \times 26$ since $18 = 10 + 8$ and $26 = 20 + 6$).

Answer:

(Left Multiplication Boxes):
First partial product (×6): $\boldsymbol{1, 0, 8}$
Second partial product (×20): $\boldsymbol{3, 6, 0}$
Final sum: $\boldsymbol{4, 6, 8}$

(For the area model, total area is $\boldsymbol{468}$.)