Shortcut to multiply two two digit numbers

Shortcut to multiply two, two digit numbers

By asha gauri shankar

Let us see how we can multiply two, 2 digit numbers.

consider the numbers 23 and 46​

By asha gauri shankar

​

​

23 x 46​

Step 1 Multiply the units digit of both the numbers, ie 3 and 6.

3 x 6 is 18. write 8 and carry 1. So

​23 x 46​ = -------8, carry 1

​

By asha gauri shankar

By asha gauri shankar

​

​

23 x 46​

Step 2 Multiply the units digit of one of the numbers, with the tens digit of the other number and add them. Thus we multiply 3 and 4; 2 and 6 and add the products. 3x 4 = 12, 2 x 6 = 12. 12 + 12 = 24. to this we add the carry from step 1. So, 24 + 1 = 25.Write the 5 and carry 2, as we normally do

So

​23 x 46​ = ----58, carry 2

​

We can also say that "multiply the near neighbors and the far neighbors of the two numbers and add them​. Then add the carry.

23 x 46​. Here 3, 4 are the near neighbors and 2, 6 are the far neighbors.

​

​

​

23 x 46​

Step 3 Multiply the tens digit of one of the two numbers. Thus we multiply 2 and 4; and to this we add the carry from step 2. So, 8 + 2 = 10.

​Thus, 23 x 46​ = 1058

​

By asha gauri shankar

​

​

Now let us see how to multiply a number with itself, ie to find the square of a number.

We can use the above method, but there is a shorter way also.

Let's see this with an example.​

Let's calculate​ 38 x 38 or 38²

​Step 1 Multiply the unit digit with itself. That is, 8 x 8 = 64. Write the unit's digit 4 and carry 6.

so ​38² = ----4, carry 6.

Step 2 Multiply the unit digit with the ten's digit. That is, 8 x 3 = 24. Now multiply this by 2. So, 24 x 2 = 48. Add the carry 6. 48 + 6 = 54.

Write the unit's digit 4 and carry 5.

so ​48² = ---44, carry 5.​

(in short, multiply the unit and ten's digit and double it. Add the carry)

​

By asha gauri shankar

By asha gauri shankar

​

​

​

​Step 3 Multiply the ten's digit with itself. That is, 3 x 3 = 9. Add the carry from step 2 which is 5. So 9 + 5 = 14.

so ​38² = 1444,

Thus 338² = 1444.

​

​

By asha gauri shankar

By asha gauri shankar