Use the standard algorithm to find the product of 355 and 893. Record the products of each multiplying through by each place value in 893 as well as the final product.(2 points)
To find the product of 355 and 893 using the standard algorithm, we multiply each digit of 355 by each digit of 893 and then add the resulting products.
First, we start by multiplying 355 by the ones digit of 893, which is 3:
355
× 3
------
1065
Next, we multiply 355 by the tens digit of 893, which is 9. However, we also need to account for the place value of this digit, so we multiply it by 10:
355
× 90
------
3195
Finally, we multiply 355 by the hundreds digit of 893, which is 8. However, we need to account for the place value of this digit, so we multiply it by 100:
355
× 800
-------
284000
Now, we add up all the products we obtained:
1065
+ 3195
+284000
-------
= 288260
Therefore, the product of 355 and 893 is 288260.
To find the product of 355 and 893 using the standard algorithm, you would follow these steps:
Step 1:
Multiply the ones place of 355 by each digit in 893:
5 * 3 = 15
5 * 9 = 45
5 * 8 = 40
Step 2:
Write down the products obtained in step 1:
15
45
40
Step 3:
Align the products obtained in step 2 vertically:
15
45
+ 40
_______
Step 4:
Add the aligned products from step 3:
15
45
+ 40
_______
1,587
Therefore, the product of 355 and 893 is 1,587.
To find the product of 355 and 893 using the standard algorithm, you need to perform a series of single-digit multiplications and then add the partial products to get the final product.
Here's how you can do it step by step:
Step 1: Write the numbers down vertically, with one number below the other. Align them according to their place values:
355 <-- This is the multiplicand
x 893 <-- This is the multiplier
__________
Step 2: Start by multiplying the units (ones) digit of the multiplicand (5) by each digit of the multiplier:
355
x 893
_________
5 × 3 = 15 <-- Write down the partial product of the units digit under the line
5 × 9 = 45 <-- Write down the partial product of the tens digit under the line
5 × 8 = 40 <-- Write down the partial product of the hundreds digit under the line
__________
Step 3: Proceed to the next place value, which is the tens digit in the multiplicand (5). Multiply it by each digit of the multiplier:
355
x 893
_________
5 × 3 = 15
5 × 9 = 45
5 × 8 = 40
_________
2,665 <-- Add up the partial products from the previous step
Write down the sum under the line as the next partial product
Step 4: Finally, multiply the hundreds digit in the multiplicand (3) by each digit of the multiplier:
355
x 893
_________
5 × 3 = 15
5 × 9 = 45
5 × 8 = 40
3 × 3 = 9 <-- Write down the partial product of the hundreds digit under the line
_________
2,665 <-- Add up the partial products from the previous step
+ 31,600 <-- Add up the partial products for the hundreds digit
_________
316,315 <-- This is the final product of 355 and 893 obtained using the standard algorithm.
So, the product of 355 and 893 is 316,315.