Quick Eleven Times (III)

The other activity children would enjoy is the following:Ask them first to find out 11 times of 11. Next they should find out 11 times of the earlier product. Let them repeat this, thus finding out 11 times of whatever product they get. Through this activity they will not only develop a number sense but also get introduced naturally to the idea of finding out square, cube etc. of the number eleven. In future, such calculations would help in solving problems related to compound interest. This exponentiation of eleven is shown in the left-hand figure.

Use the ideas related to multiplication by eleven and solve the following problems quickly :

After practicing many problems a better idea is to ask the children to express the method of multiplying by 11, in words to help memorization.

When the multiplicand consists of two digits, the sum of which is less than ten, the product is found by writing the two digits of the multiplicand with their sum between them. Thus, to multiply 42 by 11, we write 4 and 2 with the sum of 4 and 2 between these digits, obtaining 462.

When the multiplicand is larger we apply the following rule. We begin at the rightmost digit of the multiplicand. First we write this digit, then successively the units plus the tens, the tens plus the hundreds, the hundreds plus the thousands etc., carrying whenever required. We end with writing of the highest order digit of the multiplicand as it is, if there is no carrying. Otherwise we must add the carry to the highest order digit in the multiplicand then write it.

For example, we want to know the product of 11 times 5328. We begin by writing 8, then we add 2 and 8. We get 10, so we write 0 to the left of 8 and carry 1. Then we add 3 and 2 obtaining 5, to this we add the carry 1, obtaining 6. This 6 we write to the left of the digit 0. Next, we add 5 and 3 getting 8. This we write to the left of 6. Finally we write 5, which is the highest order digit of the multiplicand 5328, to the left of 8. Thus, 58608 become product of 11 times 5328.

Now, we can lead our children to think of the method we can use to find out 111 times of any number.

Most of the children will be able to do it using the method illustrated in the figure here.

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