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In this article, we are going to talk about Base Method. In this method, we identify a ‘base’. Base is a number that is a simple number (usually multiples of 10) and must be close to both the numbers given. For example, 13 x 14 – In this, the base will be 10.

Now let’s try to solve some problems using the base method.

Ex 1: Multiply 14 by 16

Step 1:

Identify the base. Since 10 is close, this will be the base.

Step 2:

The difference between number 14 and base is (+4). Since the difference is positive, we call it surplus (the negative difference is called deficit).

Similarly, the difference between number 16 and base is (+6).

Step 3:

Add either (+4) to 16 or (+6) to 14. This process is called cross addition. Either way, we get 20 as answer.

Now, multiply 20 with base, i.e, 20 x 10 = 200

Step 4:

Now multiply the surpluses, i.e, 4 and 6 in this example.

(+4) x (+6) = (+24)

Step 5:

200 + 24 = 224

Simple! Isn’t it?

Now let’s try one more.

Example 2:

Multiply 32 x 36

Step 1: Base will be 30

Step 2: 32 – 30 = (+2)

36 – 30 = (+6)

Hence, surpluses are (+2) and (+6)

Step 3: Cross addition gives us 38. By multiplying 38 with 30, we get 1140

Step 4: (+2) x (+6) = (+12)

Step 5: 1140 + (+12) = 1152. This is our answer.

Example 3:

Now let’s try this when we have deficits.

Multiply 28 x 27

Step 1: Since 20 will not be close to the numbers, we will choose 30 as our base.

Step 2: 28 – 30 = (-2)

27 – 30 = (-3)

Step 3: Cross addition gives us 25 (28 – 3) and (27 – 2)

25 x 30 = 750

Step 4: (-2) x (-3) = (+6)

Step 5: 750 + (+6) = 756

Hence, 28 x 27 = 756

NB:

1. If the numbers are in 80s or 90s, it is better to have 100 as base for easier calculations.

2. Base method is useful where the two numbers to be multiplied are close in the number series. What if the numbers are 38 x 74 or 43 x 168. We will deal with that in our next part. Till then, practice and master the base method.