Easy Multiplication Part 3

We have seen easy multiplication with base 10 and 100, but what about numbers which are close to 20, 50, 200 .Today we will see the same. Here the base we will take is 20, 50, 200.One thing we should remember while using base any other than 10 or 100 that the real base is 10 or 100. So we need to take some more steps before we write the last answer. E5BQ8WKRNXW4

Example 1: 24 × 26 let us see how we can do this

Take base as 20 (real base is 10)

Step1: write 24 as 24 + 4

Write 26 as 26 + 6

Step2: Multiply right side digits  4× 6= 24

Right side answer = 4 and carry 2 (same like base 10).

Step3: Cross addition 24 +6 =30 or 26+ 4 = 30

Can we write 30 as it is and add carry to this?

Answer is NO. So what we do?

As we have taken base as 20 we will have to double the answer and then add carry.

30 × 2= 60 +2 = 62. This is left side answer.

Step4: So the final answer is 624.

example 2: 27× 19

Step1: Write 27 as 27 + 7

Write 19 as 19 ─ 1

Step2: Multiply right side 7× ─1 = ─7

We cannot write ─7 in the right side, let us calculate the left side.

Step3: Cross addition 27 ─ 1= 26 or 19 + 7 = 26

Double 26, 26 × 2 =52.This is left side answer.

What about -7 in the right side?

We take 1 from left side, so left side is 52− 1= 51.

As this 1 is from 10^ths position we have to write right side as 10− 7= 3.

Step4:  Answer is 513

Practice:

1) 18 × 17

2) 21 × 23

3) 27 × 28

4) 21 × 32

5) 26 × 31

Next we will take numbers near 200 .Here we will take base as 200 but the real base is 100. Let us take an example.

Example 1: 212 × 210

Step1: write 212 as 212 + 12

Write 210 as 210 + 10

Step2: For right side answer multiply 12×10 = 120.

Right side answer, write 20 and carry 1.

Step3: For left side answer, cross addition 212 + 10 = 222 or 210 + 12 = 222.

As the base is 200 and real base is 100, we will have to double this answer 222 × 2= 444.

For left side answer add the carry 444+1 = 445

Step4:  Write the answer 44520

 

Example 2:  193 × 204

Step1: Write 193 as 193 – 7

Write 204 as 204 + 4

Step2: For right side answer multiply -7× 4 = -28

We cannot write negative number in the right hand side, so let us calculate left side.

Step3: For left side answer, cross addition/ subtraction 193+ 4= 197 or 204− 7= 197

As base is 200, double this answer 197× 2= 394.

Step4: Now let us go back to right side.

Take 1 from left and pass it to right side, left side becomes 393.

This 1 is from 100^ths place so right side answer is 100 -28= 72

Step5:  Answer= 39372

 

Practice:

1) 202× 225

2) 211× 205

3) 198× 189

4) 208× 220

5)210× 196

 

Let us try numbers near 50

Example1: 57 × 58

Here both the numbers are near 50 so we have to take base as 50.

Step1: Write 57 as 57+ 7

Write 58 as 58+ 8

Step2: For the right side of answer multiply 7× 8 = 56

Step3: For the left side answer add 57+8 = 65 or 58+ 7=65

Now as I had said before real base is 100, so we have to divide left side by 2

65÷ 2 = 32.5 we cannot write left side like this so get .5 to right side as this is in the 100^ths place we will have to write as(.5 ×100) 50 and add to 56.

So right side we have 50+ 56 = 106. Bit tricky we cannot write 106 in right side so we have to carry 1 and write 06 in right side

Step4:  Left side answer 32+ 1=33

Step5: Answer 3356

The example I have taken is a bit tricky. Here one number is odd and other is even, if both the numbers are odd or even it is very easy to solve the sum.  But with practice you will be able to solve this kind of sums easily.

 

Practice:

1) 53 × 59

2) 54 × 56

3)65 × 52

4) 57 × 61

5) 71 × 52

Are you all solving practice sums? Please leave your comment to let me know how you all like these posts.