To find the product of 48 and 7,326 using a place-value chart, we will break down the numbers into their place values and multiply them accordingly. Here’s how you can fill out the chart:
Place-Value Breakdown
7,326
- Thousands: 7,000
- Hundreds: 300
- Tens: 20
- Ones: 6
48
- 40 (in the tens place)
- 8 (in the ones place)
Place-Value Chart
| Place Value | 7,000 | 300 | 20 | 6 | |-------------|-------|------|------|------| | 40 | 280,000 | 12,000 | 800 | 240 | | 8 | 56,000 | 2,400 | 160 | 48 | | SUM | 336,000 | 14,400 | 960 | 288 |
Calculating the Products
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Multiply each place value of 7,326 by 40:
- \( 7,000 \times 40 = 280,000 \)
- \( 300 \times 40 = 12,000 \)
- \( 20 \times 40 = 800 \)
- \( 6 \times 40 = 240 \)
-
Multiply each place value of 7,326 by 8:
- \( 7,000 \times 8 = 56,000 \)
- \( 300 \times 8 = 2,400 \)
- \( 20 \times 8 = 160 \)
- \( 6 \times 8 = 48 \)
Sum of the Products
Finally, add all the products together:
- \( 280,000 + 12,000 + 800 + 240 = 292,040 \) (from multiplying by 40)
- \( 56,000 + 2,400 + 160 + 48 = 58,608 \) (from multiplying by 8)
Total Product
Now add these sums together:
- \( 292,040 + 58,608 = 350,648 \)
Conclusion
The final product of \( 48 \times 7,326 = 350,648 \).
Relation to Standard Algorithm
This approach is similar to the standard algorithm for multiplication, where you break down numbers into their place values, multiply each part, and then combine the results. This method clearly shows how each part contributes to the final product while enforcing the connection between place value and multiplication, just as in the column method where you would perform multiplication in stages and combine them at the end.
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