Sandra used partial prouducts to find the product of 438x17 by multiplying 438 by 1 and 438 by 7 to get 3,066. Find the product of 438x17 by using partial proudocts. Is sandra correct? Compare your answer to sandra's and explain why it is or is not the same.
To find the product of 438x17 using partial products, we can break down the multiplication as follows:
438
x 17
_________
Let's first multiply 438 by 7:
438
x 7
_________
3066
Now, let's multiply 438 by 10 (which is equivalent to multiplying by 1 and adding a zero at the end):
438
x 10
_________
4380
Finally, we add the two products together:
3066
+ 4380
_________
7446
Therefore, the correct product of 438x17 using partial products is 7446.
Sandra's product is not the same as the correct answer. She only multiplied 438 by 1 and by 7 separately, which gave her the partial products of 3066. However, the whole multiplication involves adding those partial products together, which Sandra did not do. Hence, her answer is incorrect.
To find the product of 438 x 17 using partial products, we can multiply each digit of the multiplicand (438) with each digit of the multiplier (17) and then add the partial products together.
Let's break it down step-by-step:
Step 1: Calculate the partial product for the units digit of the multiplier (7):
438 x 7 = 3,066
Step 2: Calculate the partial product for the tens digit of the multiplier (1):
438 x 10 = 4,380
Step 3: Multiply the multiplicand by the sum of the partial products from Step 1 and Step 2:
438 x (7 + 10) = 438 x 17 = 7,446
So, the product of 438 x 17 using partial products is 7,446.
Now, let's compare this to Sandra's calculation:
Sandra's calculation: 438 x 1 = 438 and 438 x 7 = 3,066.
Sandra added the partial products (438 and 3,066) together to get a total of 3,504 (438 + 3,066 = 3,504).
As we calculated earlier, the correct product using partial products is 7,446.
Therefore, Sandra's calculation is incorrect. She should have added the partial products (438 and 3,066) together to get a total of 3,504, not 7,446.
In conclusion, Sandra's answer is not the same as the correct answer because she incorrectly added the partial products together.
To find the product of 438x17 using partial products, you break down the multiplication into smaller steps.
First, write down the numbers 438 and 17 vertically:
438
x 17
______
Now, multiply each digit of the top number (438) by each digit of the bottom number (17) and write the results below:
7 1 (17 times 8, which is 136)
+ 30 )
+ 400 ) (17 times 30, which is 510)
____________
7446
Finally, add up the results from each row to get the final product, which is 7446.
Now, let's compare Sandra's answer of 3066 to the correct answer of 7446.
Sandra is not correct. The correct answer is 7446, which is different from Sandra's answer of 3066. The reason is that Sandra made a mistake by only multiplying 438 by 1 and 438 by 7, but there are more partial products to consider. In the correct process, we multiply each digit of 438 by each digit of 17 and add up the results to obtain the correct product.