This document provides steps to multiply a two-digit number by 11 or 12. For 11, the first and last digits are the same, and the middle digits are found by adding the digits. For 12, each digit is multiplied by 2 and added to the next digit. This process is extended to multiplying by higher single-digit numbers like 13 by multiplying each digit by 3 instead of 2.

2. Step 1: First and last digits will be same as the first and last digit of the number Step 2: Add both the digits and place the answer in between Example: 62 X 11 So the answer is 682 6 2 6 8 2

3. Step 1: First and last digits will be same as the first and last digit of the number Step 2: Add the digits next to each other to get middle numbers as shown in the figure 4 5 3 4 So the Answer is - 4 9 8 7 4 Adding to the neighbour 4 9 8 7 4 E.g. – 4534 X 11

4. Step 1 & 2: Same as in earlier slide Step 2: Add the carry over number to the number on the left hand side as shown. 4 9 3 4 So the Answer is - 5 4 2 7 4 Adding to the neighbour 4 1 3 1 2 7 4 5 4 2 7 4 E.g. – 4934 X 11

5. Multiply each digit by 2 and add the digit on the right hand side. Assume a Zero at the end and beginning of the number In the example: (4 X 2) + 0 = 8 (2 X 2) + 4 = 8 (0 X 2) + 2 = 2 Example: 24 X 12 So the answer is 288 2 4 2 8 8 Multiply and Add to the neighbour

6. Multiply each digit by 2 and add to the digit on right hand side. In the example: (3 X 2) + 0 = 6 (4 X 2) + 3 = 11 (4 X 2) + 4 = 12 (0 X 2) + 4 = 4 Add the carry over's as shown 4 4 3 So the Answer is - 5 3 1 6 Multiply and Add to the neighbour 4 1 2 1 1 6 E.g. – 443 X 12 5 3 1 6

7. Just as we multiplied each digit by 2 for multiplying by 12, For 13 we will multiply each digit by 3 and add the neighbour. Similarly for 14 multiply by 4, for 15 multiply by 5 and so on.

8. Maths is now simpler. isn't it? To learn more Call: Abhishek – 9820155871 Neha – 9619313066 OR Send a mail on nehaakabra@gmail.com