Process for easy Multiplication with 11

Let us consider an example, 18 × 11

Step 1: Write the first and last digit of the given number as it is.

Step 2: write the sum of the digits of the given number in between the digits of step 1.

1 (1+8) 8

Hence, 198 is the required result of the given multiplication 18 × 11

Let us make our concepts more clear with more examples.

Q 2. Check if 105875 is divisible by 11 or not?

Solution: Sum of digits at odd places = 5+8+0 = 13

Sum of digits at even places = 7+5+1 = 13

Difference = 13 – 13 => 0

Hence, 105875 is divisible by 11.

Q 3. When 121011 is divided by 11, the remainder we get is ?

Solution : Let us follow the simple trick,

Hence remainder = 0

Q 4. Check if the number 1001011 is divisible by 11 or not?

Solution: on following the method2 as said above, we have

sum = -1 + 0+ 0+ 1+ 0 +1 -1 => 0 Hence, given number is divisible by 11.

Q 5. The smallest number which should be added to 3428 so as to obtain a multiple of 11, is?

Solution : Let us first divide the given number by 11.

3428 ÷ 11

remainder = 7

If remainder becomes 11, then the number would have exactly divisible by 11. So, the remainder, in order to become 11, we must add 4 to it. So, here the least number to be added to make the number divisible by 11 is 4.

Q 6. Find the value of x , in 4321×8 in order to make it completely divisible by 11?

Solution : Sum of digits at odd places = 8+1+3 = 12

sum of digits at even places = x+2+4 = 6+x

now, 12-(6+x)=0 or 12 -(6+x)=11

on solving both, 12-6-x=0 or 12-6-x = 11

x=6 or x=-5(Impossible)

so, value of x = 6

The divisibility rule is a basic concept in mathematics that would determine if a given number is divided by a particular divisor or not without actually performing the entire division process. Let us understand the divisibility rule of 11 and some easy tricks to solve problems related to 11 in this article.