We have seen multiplication of two-digit numbers where the tens digit is the same and the sum of the units digits is 10. Number pairs like 11 and 19, 12 and 18, 23 and 27 are examples. Today let us look at pairs of numbers whose units digits are the same and the sum of the tens digits is 10; pairs like 13 and 93, 25 and 85, 34 and 74. The rule followed in this type of multiplication is:
The first by the first and the last by the last.
The steps are:
Multiply the tens digits of the two numbers.
To the product obtained, add the units digit. The sum is the first part of the answer.
Multiply the units digits. This is the second part of the answer.
Example: 27 × 87
The conditions are satisfied here as 2 + 8 = 10 (sum of the tens digits). Units digit is the same – 7.
Multiply the tens digits. 2 x 8 = 16.
To 16 add the units digit. 16 + 7 = 23. This is the first part of the number.
Multiply the units digits. 7 x 7 = 49. This is the second part of the answer.
Answer: 2349
Example: 69 × 49
Multiply 6 x 4 = 24.
24 + 9 = 33. This is the first part of the answer.
Multiply 9 x 9 = 81. This is the second part of the answer.
Answer: 3381
This problem can be done directly so that it remains in our mind.
6 9
4 9
6 x 4 + 9 9 x 9
3381
Answer: 69 x 49 = 3381
Example: 31 x 71
3 1
7 1
(3 x 7+1) 1x1
22 01
Answer: 2201
Remember we must have two digits in the second part of the answer. So 1 x 1 is written as 01. We can also see that in this type of multiplication the answer always ends in a square number like 4, 16, 25.
Now for you to try:
1) 16 x 96
2) 27 x 87
3) 73 x33
4) 42 x 62
5) 59 x 59