Double-Digit Multiplication
We cheated a bit by introducing some two- and three-digit multiplication in our carrying section. We were working with easy numbers, though. Rules are easy if you are multiplying a two-digit number by a one-digit number. Multiply the ones value and then multiply the tens value.Example:
32 x 3 = ?
Multiply the ones: 3 x 2 = 6
Multiply the tens: 3 x 3 = 9
32 x 3 = 96
That example didn't have any carrying/regrouping. If you have some carrying, you will need to do the "Multiply—Carry—Multiply—Add" pattern.
Example:
96 x 8 = ?
MULTIPLY ONES: 6 x 8 = 48
WRITE AND CARRY: Write the "8" and carry the "4"
MULTIPLY TENS: 8 x 9 = 72
ADD: Add the carried amount. 72 + 4 = 76
WRITE: Write down the "76"
Answer: 96 x 8 = 768
Two Multiplication Problems in One
So what happens if you have two two-digit numbers for your factors? Although it will take a little longer, it's an easy process to solve the problem. You just need to do two multiplication problems and then add up the answers. What? How could it be so simple? Let's watch.Example:
96 x 28 = ?
Part 1: Multiply 8 x 96.
Answer: From the example above we know that the answer is 768.
Part 2: Multiply 2 x 96.
(1) 6 x 2 = 12
(2) Write "2" and carry "1"
(3) 2 x 9 = 18
(4) Add. 18 + 1 = 19
(5) Write "19"
Answer: 96 x 2 = 192
Part 3: Add your two answers.
Do you think you can just add the two values now? No! There is one trick. When you multiply the second part, add a "0" to that answer, because you are multiplying the value from the tens column (the 2). If it's from the tens, add a zero. If it's from the hundreds, you would add two zeros.
768 + 1920 = 2,688 (See how we added a "0" to the "192" value?)
Let's write it out in a vertical (up and down) format. It will be easier for you to see the setup.
|
96 x 28 768 + 1920 2668 |
Sum It Up
It might be hard to understand when this idea is written out in words, but the concept is a simple one. If your second factor (or the bottom one) has two-digits, you do two multiplication problems. You will quickly see in the next section that if your second factor has three digits, you will complete three multiplication problems.The second idea to know is that before you add the answers, you need to add some zeros. When you multiply the first value, don't add any zeros. When you multiply the tens value, add one zero to the end of the answer. Add two zeros if there is a hundreds value and three zeros for a value from the thousands place. Do you see a pattern with the zeros? See how quickly numbers can get really big when you multiply?
Example:
|
352 x 231 352 10560 + 70400 81,312 |
Sorry about using such big numbers. We need to show you a pattern. All of the multiplication was very easy. The most difficult multiplication problem we did was 5x3. When you have big problems, just be patient and follow all of the steps.
Useful Reference Materials
Wikipedia:https://en.wikipedia.org/wiki/Arithmetic
Encyclopædia Britannica:
http://www.britannica.com/topic/arithmetic
Encyclopedia.com:
http://www.encyclopedia.com/topic/arithmetic.aspx
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