Question

16×48 = ___
\frac{10}{\quad}\quad\frac{6}{\quad}
\frac{40}{\quad}\quad\frac{8}{\quad}
\

$$\begin{array}{|c|c|} \\hline ___ & ___ \\\\ \\hline ___ & ___ \\\\ \\hline \\end{array}$$

= ___
= ___

Explanation:

Step1: Decompose 48 into 40 + 8 and 16 remains, then use area model (distributive property)

First, calculate \(16\times40\) and \(16\times8\), also decompose 16? Wait, no, looking at the table, maybe decompose 48 into 40 + 8 and 16 into 10 + 6? Wait, the table has rows 10 and 6, columns 40 and 8. So it's using the distributive property: \((10 + 6)\times(40 + 8)\). Let's compute each cell:

Step2: Calculate each cell of the area model

• Top - left cell: \(10\times40 = 400\)
• Top - right cell: \(10\times8 = 80\)
• Bottom - left cell: \(6\times40 = 240\)
• Bottom - right cell: \(6\times8 = 48\)

Step3: Sum the four products

Now sum these four results: \(400+80 + 240+48\). First, \(400 + 80=480\), \(240 + 48 = 288\), then \(480+288 = 768\). Also, directly \(16\times48\): \(16\times48=16\times(40 + 8)=16\times40+16\times8 = 640+128 = 768\)

Answer:

First, fill the table cells:

• Top - left: \(10\times40 = 400\)
• Top - right: \(10\times8 = 80\)
• Bottom - left: \(6\times40 = 240\)
• Bottom - right: \(6\times8 = 48\)

Then sum: \(400 + 80+240 + 48=768\), so \(16\times48=\boxed{768}\) (the table cells are 400, 80, 240, 48 in order, and the final answer is 768)