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Lesson 40: Multiplying Two Digits by One Digit
Although an exam may allow you to use a calculator, it's very important to understand the procedure for multiplying, both how it works, and why it works.
Don't forget to watch the embedded video clip for this lesson at the bottom of the page. Please be sure to read the embedded video information and disclaimer.
Take a look at problem 1 below. To do a multiplication problem like this, we always start by multiplying the second number times the digit in the ones place of the first number. Stated another way, we're multiplying ones times ones. 4 x 2 is 8, so we'll write 8 below the line in the ones place.
Now we have to multiply the second number times the tens digit in the first number. Let's look at what is really happening. The tens place has a 3, and that really represents 30. So we're multiplying 2 x 30 to get 60. 60 is 6 tens, so we'll write 6 below the line in the tens place, giving us a final answer of 68.
Here is what really happened. We broke up the 34 into 30 (the tens value) and 4 (the ones value). Then we multiplied each part separately, and then added the results back together. This is allowed in math, and later you'll learn more about this property of multiplication. Try to experiment on your own to convince yourself that this works.
Look at problem 2. Again, we start by multiplying the digits in the ones place. 6 x 4 is 24. Like we've seen before, we can only fit one digit into the ones place. So we'll write the 4 below the line, and then we have to write the 2 at the top of the tens place, since it represents 2 tens (which is the 20 part of 24). Now we'll multiply 4 times 7 to get 28, and we have to add the 2 which we placed in the tens place. Don't get confused. We add it by doing 28 + 2 = 30. We're increasing the value of the tens multiplication by 2. Instead of 28 tens, it's actually 30 tens. What we can do is just write the 30 below the line as shown, but what we really have is 30 tens, which is 3 hundreds, so that's why we have a 3 in the hundreds place.
Look at problem 3. Like before, we'll multiply 9 x 9 in the ones place, to get 81. The 1 goes below the line, and the 8 goes into the tens column to be added in after the next step. Now we'll multiply 9 times the 9 in the tens place to again get 81, but we have to remember to add the 9 that we placed at the top. That gives us 89, which we can write below the line as shown. Again, understand that 89 tens is really 8 hundreds, and 9 tens, so that's why it's written as shown. In later lessons you'll have some practice multiplying larger numbers.
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