Sandra used partial products to find the product of 438 × 17 438×17 by multiplying 438 by 1 and 438 by 7 to get 3,066. Find the product of 438 × 17 438×17 by using partial products. Is Sandra correct? Compare your answer to Sandra's and explain why it is or is not the same.
I know the answer but I don't know what the partial products are.
Well, if I were to use partial products to find the product of 438 × 17, I would break it down into smaller, more manageable steps. Let's take a look:
First, let's multiply 438 by 7. This gives us a partial product of 3,066, just like Sandra found. Good job, Sandra!
Next, let's multiply 438 by 1. This gives us another partial product of 438.
To find the final product, we add up these two partial products: 3,066 + 438 = 3,504.
So, according to my calculations, the product of 438 × 17 is 3,504. If Sandra's answer matches mine, then she is absolutely correct!
To find the product of 438 × 17 using partial products, you need to multiply each digit of one number by each digit of the other number and then add the individual products. Let's break it down step-by-step:
Step 1: Multiply the ones digit (8) of 438 by the ones digit (7) of 17:
8 × 7 = 56
Step 2: Multiply the tens digit (3) of 438 by the ones digit (7) of 17:
3 × 7 = 21
Step 3: Multiply the hundreds digit (4) of 438 by the ones digit (7) of 17:
4 × 7 = 28
Step 4: Multiply the ones digit (8) of 438 by the tens digit (1) of 17:
8 × 1 = 8
Step 5: Multiply the tens digit (3) of 438 by the tens digit (1) of 17:
3 × 1 = 3
Step 6: Multiply the hundreds digit (4) of 438 by the tens digit (1) of 17:
4 × 1 = 4
Step 7: Multiply the ones digit (8) of 438 by the hundreds digit (1) of 17:
8 × 1 = 8
Step 8: Multiply the tens digit (3) of 438 by the hundreds digit (1) of 17:
3 × 1 = 3
Step 9: Multiply the hundreds digit (4) of 438 by the hundreds digit (1) of 17:
4 × 1 = 4
Now, add up all the partial products:
56 + 21 + 28 + 8 + 3 + 4 + 8 + 3 + 4 = 135
Therefore, the product of 438 × 17 using partial products is 135.
Now let's compare it to Sandra's result of 3,066. It is clear that Sandra's result is not the same as the correct answer, 135. It seems that Sandra has made an error in her calculation or misunderstood how to use partial products.
Partial products are a multiplication method where each digit of one factor is multiplied separately by each digit of the other factor. You then add up all the partial products to find the final product.
To find the product of 438 × 17 using partial products, you would multiply each digit of 438 by each digit of 17 and then add up the partial products. Here's how it would look:
4 3 8 (4 hundreds, 3 tens, 8 ones)
× 1 7 (1 tens, 7 ones)
________________
7 4 4 6 (7 thousands, 4 hundreds, 4 tens, 6 ones)
Breaking it down step by step:
- Multiply 8 (the ones digit of 438) by 7 (the ones digit of 17) to get 56.
- Multiply 8 (the ones digit of 438) by 1 (the tens digit of 17) to get 8 (which you write as 08).
- Multiply 3 (the tens digit of 438) by 7 (the ones digit of 17) to get 21 (which you write as 21).
- Multiply 3 (the tens digit of 438) by 1 (the tens digit of 17) to get 3 (which you write as 03).
- Multiply 4 (the hundreds digit of 438) by 7 (the ones digit of 17) to get 28 (which you write as 28).
- Multiply 4 (the hundreds digit of 438) by 1 (the tens digit of 17) to get 4 (which you write as 04).
- Multiply each of these partial products and add them up: 56 + 8 + 21 + 3 + 28 + 4 = 120
Therefore, the correct product of 438 × 17 using partial products is 120, which is different from Sandra's answer of 3,066.
Sandra's answer is incorrect because she only multiplied the last digit of 438 (which is 8) with both digits of 17 (which are 1 and 7 separately), instead of multiplying each digit of 438 with each digit of 17 using partial products.