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When we set up our problem it doesn't matter which number is on top and which is below, you'll still get the same answer in the end. But I find it easier to put the larger number on top, and it makes the final addition easier, as you'll see later in the lesson.
Like addition and subtraction, we work from right to left. We are going to take the 7 on the bottom and multiply it by each digit on top, from right to left. This means our first step is to multiply 7 * 4, which equals 28. The 8 goes underneath below the first column. The 2 gets written above the next column.
Next we need to multiply 7 * 3, then add the 2 that was carried over from the last column. 7 * 3 + 2 = 23. We put the 23 underneath because this is the last column, and our final answer is 168.
This next example will cover anything we didn't cover above. Now we have 3 digits on the bottom instead of one. Thats okay, we work right to left so we start with the 7 and multiply it by each digit in the top number, as we did above, right to left. The first step is to multiply 7 * 6, which is 42. The 2 goes underneath and the 4 goes to the top of the next column.
Next we multiply 7 * 8, then add the 4 from above, so 7 * 8 + 4 = 60. We write the 0 underneath and carry the 6 to the top of the next column.
7 * 4 + 6 = 34. We write the whole number 34 underneath because there are no more columns to carry the 3 to.
Now we will move to the 8 on the bottom and multiply it by each digit in the top number, right to left. But first there are two things we must do. We must erase all of the numbers that we carried on top and we need to add a zero under the first (rightmost) column.
Now we will multiply 8 * 6, which is 48. The 8 goes down in front of the zero we just added, and the 4 goes to the top of the next column.
8 * 8 + 4 = 68. 8 goes down bottom, 6 goes up top.
8 * 4 + 6 = 38. Both digits go underneath.
As we prepare to multiply the 3 by each digit in the top number, we must again erase all the numbers we carried to the top. This time we have to add 2 zeros underneath.
6 * 3 = 18. 1 up top, 8 down below.
3 * 8 + 1 = 25
3 * 4 + 2 = 14
Now all of our multiplication is done. Our final step is to add all the results from the multiplication together. This gives us a final answer of 188,082!
