When multiplying a multiple digit number by another multiple digit number, there are several steps involved. Before performing this operation you must know how to do
basic multiplication,
multiplication of multiple digit numbers by single digit numbers and
addition of multiple digit numbers with carrying.
The first step is to set up the problem. Like when multiplying multiple digit numbers by single digit numbers, it is best to put one number on top of the other as so:
In order to solve this problem we must break it up into two separate problems. We must break it up into multiplying by the ones portion of 34 as well as the tens portion of 34. So Essentially we are breaking it up into 27 x 3 and 27 x 4. We can then add those portions together to get our final result. This can be done due to the
distributive property which says:
27 x 34 =
27 x (30 + 4) =
(27 x 30) + (27 x 4).
Step By Step
Our first step is to start with the ones part of the problem. We can multiply the ones column to get 7 x 4 = 28. Do not forget to carry the 2 into the tens column.
We now complete this portion of the problem by multiplying the tens column in 27 by the ones column of 34. 2 x 4 + 2 = 10. We can't forget to add the carry.
We now have completed the first half of the problem and now must complete the second half of the problem (27 x 30). We start by multiplying 7 x 3 = 21. For now we can ignore the extra 0 on the thirty and just treat it as a three.
Since we are multiplying the tens column we must start writing our answer in the tens column, not the ones column. This is why we are allowed to ignore the 0 from the 30. In reality we could put an extra zero at the end of our second answer row, but it is not really needed as long as you always start writing your answer for the row starting with the column directly under the digit of the second number you are multiplying. In this case we are multiplying by the 3 in the second number so we want to start our answer for this part of the problem directly under the 3.
We must also carry the 2 from the 21 to the tens column once again.
We can now multiply 2 x 3 + 2 = 8 which we write in the hundreds column.
We are now done with the two parts of our problem 27 x 30 = 810 (don't forget the hidden zero). and 27 x 4 = 108. We now add up 108 + 810 = 918, our final answer.
