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Extending Learning: Lightning Fast Multiplication by 11

Feb 19, 2018

Extending Learning: Lightning Fast Multiplication by 11

Once elementary school students master addition and subtraction, they typically move on to multiplication. For many kids, this means memoriing the times tables. Picking up patterns in multiplication by 2's, 5's, and 10's is usually picked up quickly, but when 3's, 4's, 6's, 8's etc. are added to the mix, it can be a lot for them to remember. The Mathnasium Method for multiplying is simple and based on addition; it explores the concept that multiplication is simply repeated addition. For example, 4x4 is just another way to say 4+4+4+4. To illustrate this, we teach with the language of "What is 4, 4 times?"  When kids "see behind the curtain" of multiplication like this, they understand more deeply and no longer need to memorize facts.

Another truism about mulitplication in school is that the facts after 10 may not be emphasized. 11 and 12 are important numbers to include, considering that 11 is actually fun and easy for students to pick up on the pattern, and 12 is the base for our systems of time and measurement. (a dozen, a foot, etc.) With 11, kids pickup on the pattern of 11, 22, 33, 44, 55, etc. quickly, but happens when the numbers get bigger? Here's a great way to easily multiply two, three, and four digit numbers by 11 mentally.


Multiplying a 2-Digit Number by 11

Example: 47 x 11 =

1. The digit in the ten's place of the multiplier (4) becomes the hundreds place digit of the answer.

Ex. 47 X 11 = 4 _ _

2. The digit in the ones place of the multiplier (7) becomes the ones place digit of the answer.

Ex. 47 x 11 = 4 _ 7

3. Add the multiplier's digits together:

Ex. 4+7=11

4. The 1 in the ones place of 11 goes to the tens place of the answer, and you carry the 1 from the tens place to the hundreds place of the answer:

Ex. 47 x 11 = (4+1) 1 7

Answer 47 X 11 = 517


Multiplying a 3-Digit Number by 11

Example: 218 x 11 = 

1. The digit in the hundreds place of the multiplier (2) becomes the thousands place digit of the answer.

Ex. 218 X 11 = 2 _ _ _

2. The digit in the ones place of the multiplier (8) becomes the ones place digit of the answer.

Ex. 218 x 11 = 2 _ _ 8

3. Add the multiplier's digits together:

Ex. hundreds plus tens (2+1) and tens plus ones (1+8)

4. The 'hundreds+tens" sum goes to the hundreds place of the answer, and the "tens plus ones" sum goes to the ones place of the answer:

Ex. 218 x 11 = 2 3 9 8

Answer 218x11=2,398.

Multiplying a 4-Digit Number by 11

Example: 4533 x 11 = 

1. The digit in the thousands place of the multiplier (4) becomes the ten thousands place digit of the answer.

Ex. 4533 X 11 = 4 _ _ _ _

2. The digit in the ones place of the multiplier (3) becomes the ones place digit of the answer.

Ex. 4533 x 11 = 4 _ _ _ 3

3. Add the multiplier's digits together:

Ex. Thousand plus hundreds (4+5), hundreds plus tens (5+3) and tens plus ones (3+3)

4. The 'thousands plus hundreds' sum goes to the thousands place, the 'hundreds+tens" sum goes to the hundreds place of the answer, and the "tens plus ones" sum goes to the ones place of the answer:

Ex. 4533 x 11 = 4 9 8 6 3

Answer 4533x11=49,863.


Remember in step 3 that if the digits sum over 10, you'll have to carry that over to the next larger place. Beyond that, you've got a rock solid method to solve multiplication by 11 fast with large numbers!