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Lesson 41: Multiplying Three Digits by Two Digits
If you are in high school or college, you are probably allowed to use calculators on all of your exams. However, it is important to understand how multiplication really works. This lesson will also reinforce the concept of place value.
Take
a look at the multiplication problem at right. First we start by
multiplying 5 x 3. We get 15. The 5 of 15 goes below the line in the
ones place, and then we have to carry the one (the remaining 10) into the tens
column. No we multiply 5 x 2, but we have to remember that the 2 really
represents 20, since it's in the tens place. We get 10, but we have to add
the one that we carried into the tens place. We now have 11. The
ones place 1 goes below the line in the tens place, and tens place one gets
carried into the hundreds column. No we'll multiply 5 times the 1 in the
hundreds column. We get 5, but we must add the 1 that we carried into that
column. We get 6, and write it below the line.
Now we need to start again, but multiplying the 4 that we have in the tens place of the second number. We have to remember that this 4 actually means 40, since it's in the tens place. We'll start with 4 x 3 to get 12. We can put the 2 below the line in the tens place, and carry the 1 into the tens place, in the row above the one that we used in the first part of our multiplication. What you'll see is that since we're multiplying using a number in the tens place, everything gets shifted over one column to the left, as it should.
Continuing, we multiply 4 x 2 to get 8, and add the one that we carried to get 9. That 9 goes below the line into the hundreds column. Now we multiply 4 x 1 to get 4, and remember that even though we have a carried number in that column, that was from the first part of our multiplying, not this part. The 4 goes in the thousands column.
Now we need to add the results of the two parts of our multiplying. Everything has been entered into the correct place values, so we just add as usual. We get 5,535.
Try
this second example at right on your own for more practice.
Follow all the steps like we did above. It is done exactly the
same way, except you'll be carrying larger numbers than 1. For
example, if something multiplies to 42, write the 2 below the line
in the appropriate place, and carry the 4. The answer in this
example takes us into the ten thousands place, but don't let that
concern you.
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