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Double-Digit MultiplicationWe cheated a bit by introducing some two-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.
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. If you have some carrying you will need to do the "Multiply -- Carry -- Multiply -- Add" pattern.
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 OneSo what happens if you have two two-digit numbers for your factors? Although it will take a little longer, its 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.
96 x 28 = ?
Part 1: Multiply 8 x 96.
Answer: From the example above we know 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
Do you think you can just add the two values now? No! there is one trick. When you multiplied the second part, add a "0" to that answer because you were multiplying the value from the tens column. 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?)
Sum it UpIt might be hard to understand when this idea is written out in words. The concept is a simple one. If your second number has two-digits, you do two multiplication problems. You will quickly see in the next section that if your second value has three digits you will complete three multiplication problems.
The other idea 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 are using the tens value, add one zero to the end of the answer. Two zeros if it were a hundred and three zeros for a value from the thousands place. See a pattern?
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