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Multiplication Facts - 11 and 12 Dont let eleven and twelve timetables frighten you. They are full of patterns which make mental math and memorization easier than you think. Eleven Timetables Pattern One The eleven timetables are neat to learn because the products results in a double reflection of the number multiplied by eleven. 11 x 1 =11 11 x 2 = 22 11 x 3 = 33 11 x 4 = 44 . . .11 x 9 = 99 This pattern is true for 11 x 1 through 11 x 9. Pattern Two This multiplication pattern and strategy applies to all two digit numbers multiplied by eleven. 11 x 11 = 121 11 x 12 = 132 11 x 13 = 143 11 x 14 = 154 11 x 15 = 165 Did you notice? First, the middle number in the product is the sum of the numbers beside it. Secondly, the outer digits in the product are the second factor. So, the following strategy can apply when multiplying 11 x 11 thru 11 x 99. Example: 11 x 21 = Steps: 1. Write the second factor as the product but leave a space between the numbers.11 x 21 = 2 1 (notice the space between the numbers) 2. **Add the digits of the second factor and place the sum between the two numbers in step one. (The second factor is 21, so 2 + 1 = 3; Thus 11 x 21 = 231. **When the sum is larger than 9. Example 11 x 39 = 1. Separate digits of second factor: 11 x 39 = 3 9 2a. Add digits of second factor (3 + 9 =12) 2b. Place the ones digit of the sum in the space, meaning 2 : 2c. Add the tens place digit of the sum,1 to the hundred place of the product, 3. Thus, 11 x 39 = 429 Twelve Timetables Wow, youve made it to the twelve timetables! Dont stop practicing all the other timetables. Well use them to learn the 12s. Lets start with finding patterns. Patterns are helpful when you take the initiative to write the timetables on an assignment or test before you begin to work any problems. Then, use the patterns to check for accuracy. 12 x 1 = 12 12 x 2 = 24 12 x 3 = 36 12 x 4 = 48 12 x 5 = 60 12 x 6 =72 12 x 7 = 84 12 x 8 = 96 12 x 9 = 108 12 x 10 =120 Pattern One: Look at 12 x 1 through 12 x 4. The tens digit in the product is the same as the number multiplied by twelve. Thereafter, the tens digit in the product / answer is one more than the 2nd factor or number multiplied by twelve. Pattern Two: The digit in the ones place of the product skip counts by 2 and starts over after the count reaches 8. Pattern Three: The first digit(s) in the product are in numerical order with the exception 5 and 11 are skipped. Mental Strategy for 12 x12 thru 12 x 19 12 x 12 = 144 12 x 13 = 156 12 x 14 = 168 Example: 12 x 13 = Steps: 1. To get the first two numbers of the answer: Add 12 and the ones digit of the other number. 12 + 3 = 15 **2. To get the last digit of the answer: Multiply 2 which is the tens digit of 12 and the ones digit of the other number. In this case, 3. 2 x 3 = 6 3. Thus, the answer is 156. **When the sum in step two is larger than nine. . . Example: 12 x 15 = Step 1) To get the first two numbers of the answer: Add 12 and the ones digit of the other number. 12 + 5 =17 Step 2) To get the last digit of the answer: Multiply 2 which is the tens digit of 12 and the ones digit of the other number. In this case, 5. 2 x 5 = 10 (The zero is the last digit of the answer. The 1 is added to the 17....thus the answer is 180) Try it and check your answer below. 12 x 16 = 192 12 x 17 = 204 12 x 18 = 216 12 x 19 = 228 Did you notice the previous patterns still apply?
Content copyright © 2008 by Beverly Mackie. All rights reserved.
This content was written by Beverly Mackie. If you wish to use this content in any manner, you need written permission. Contact Beverly Mackie for details.
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