Sure, let's break down the multiplication of 48 by 71 into partial products and then add those partial products together to find the final result.
### Step-by-Step Solution:
#### 1. Break the Numbers into Place Values
First, we break each number into its tens and ones place:
- [tex]\(48\)[/tex] is [tex]\(40 + 8\)[/tex]
- [tex]\(71\)[/tex] is [tex]\(70 + 1\)[/tex]
#### 2. Calculate the Partial Products
Next, we multiply each part of one number by each part of the other number. This will result in four partial products:
- Partial Product 1: Tens place of 48 with the tens place of 71
[tex]\[
40 \times 70 = 2800
\][/tex]
- Partial Product 2: Tens place of 48 with the ones place of 71
[tex]\[
40 \times 1 = 40
\][/tex]
- Partial Product 3: Ones place of 48 with the tens place of 71
[tex]\[
8 \times 70 = 560
\][/tex]
- Partial Product 4: Ones place of 48 with the ones place of 71
[tex]\[
8 \times 1 = 8
\][/tex]
#### 3. Add the Partial Products
Finally, we add all the partial products together to get the final product:
[tex]\[
2800 + 40 + 560 + 8 = 3408
\][/tex]
### Summary
By breaking the numbers into their place values and calculating the partial products, we've established that:
- Partial Product 1 = 2800
- Partial Product 2 = 40
- Partial Product 3 = 560
- Partial Product 4 = 8
Adding these partial products together gives us the final product:
[tex]\[
48 \times 71 = 3408
\][/tex]
Therefore, the final product of [tex]\(48\)[/tex] multiplied by [tex]\(71\)[/tex] is [tex]\(3408\)[/tex].
