How to do three digit by two digit multiplication:
How to do three digit by two digit multiplication:
Three-digit by two-digit multiplication can be broken down into a series of smaller steps to make the process easier. Here’s a step-by-step explanation:
1. Write the numbers: Place the three-digit number (multiplicand) above the two-digit number (multiplier). Align them to the right.
123
x 45
2. Multiply the ones place of the multiplier by each digit of the multiplicand: Start by multiplying the digit in the ones place of the multiplier (5) by each digit of the multiplicand (123).
123
x 45
-----
615 (123 x 5)
3. Multiply the tens place of the multiplier by each digit of the multiplicand: Now, multiply the digit in the tens place of the multiplier (4) by each digit of the multiplicand (123). Since it is in the tens place, write the result one place to the left (add a zero to the right).
123
x 45
-----
615 (123 x 5)
4920 (123 x 40, shifted one place to the left)
4. Add the two results: Finally, add the results of the two multiplications together to get the final answer.
123
x 45
-----
615
4920
-----
5535
So, 123 multiplied by 45 equals 5535.
Example
Let's multiply 346 by 27 using the same steps:
1. Write the numbers:
346
x 27
2. Multiply the ones place of the multiplier by each digit of the multiplicand:
346
x 27
-----
2422 (346 x 7)
3. Multiply the tens place of the multiplier by each digit of the multiplicand:
346
x 27
-----
2422 (346 x 7)
6920 (346 x 20, shifted one place to the left)
4. Add the two results:
346
x 27
-----
2422
6920
-----
9342
So, 346 multiplied by 27 equals 9342.
This method can be used for any three-digit by two-digit multiplication, breaking the problem into manageable steps.
How to do three digit by three digit multiplication:
Three-digit by three-digit multiplication can be tackled by breaking it down into simpler, more manageable steps. Here’s a step-by-step guide:
1. Write the numbers: Place the three-digit multiplicand above the three-digit multiplier. Align them to the right.
234
x 456
2. Multiply the ones place of the multiplier by each digit of the multiplicand: Start by multiplying the digit in the ones place of the multiplier (6) by each digit of the multiplicand (234).
234
x 456
-----
1404 (234 x 6)
3. Multiply the tens place of the multiplier by each digit of the multiplicand: Next, multiply the digit in the tens place of the multiplier (5) by each digit of the multiplicand (234). Write the result one place to the left (add a zero to the right).
234
x 456
-----
1404 (234 x 6)
11700 (234 x 50, shifted one place to the left)
4. Multiply the hundreds place of the multiplier by each digit of the multiplicand: Finally, multiply the digit in the hundreds place of the multiplier (4) by each digit of the multiplicand (234). Write the result two places to the left (add two zeros to the right).
234
x 456
-----
1404 (234 x 6)
11700 (234 x 50, shifted one place to the left)
93600 (234 x 400, shifted two places to the left)
5. Add the three results: Finally, add all the partial results together to get the final product.
234
x 456
-----
1404
11700
93600
-----
106704
So, 234 multiplied by 456 equals 106,704.
Example
Let's multiply 321 by 123 using the same steps:
1. Write the numbers:
321
x 123
2. Multiply the ones place of the multiplier by each digit of the multiplicand:
321
x 123
-----
963 (321 x 3)
3. Multiply the tens place of the multiplier by each digit of the multiplicand:
321
x 123
-----
963 (321 x 3)
6420 (321 x 20, shifted one place to the left)
4. Multiply the hundreds place of the multiplier by each digit of the multiplicand:
321
x 123
-----
963 (321 x 3)
6420 (321 x 20, shifted one place to the left)
32100 (321 x 100, shifted two places to the left)
5. Add the three results:
321
x 123
-----
963
6420
32100
-----
39483
So, 321 multiplied by 123 equals 39,483.
This method can be used for any three-digit by three-digit multiplication, breaking the problem into smaller, more manageable steps.
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