Multiplication of any number can be done very easily using the base-complement concept in less than 10 seconds.

**Case 1: Multiplication of numbers below the base. **

The answer comes in two parts. LHS and RHS.

**Example 1:**

**What is 96 x 95? **

The nearest base for both numbers is 100. 96 is less than 100 by 4. 95 is less than 100 by 5.

Step 1: (LHS)

96 – 4

95 – 5

————–

(96-5) or (95-4) = 91

————–

Step 2: (RHS)

Multiplying the difference of numbers from the base.

(-4)(-5) = 20.

Answer – 91/20

**Answer is 9120**

**Example 2:**

**What is 99 x 91?**

The nearest base for both numbers is 100. 99 is less than 100 by 1 and 91 is less than 100 by 9.

**Step 1: (LHS)**

99 – 1

91 – 9

————————-

(99 – 9) or (91 – 1) = 90

————————-

**Step 2: (RHS)**

(-1) (-9) = 9.

Answer – 90/9

( **NOTE: The number of digits in the RHS should be equal to the number of Zeros in the nearest base. When the number of digits are not equal, we should add enough Zeros to make sure that they are equal**).

So it becomes 90/09

**Answer is 9009.**

**Example 3:**

**What is 87 x 89?**

The nearest base for both numbers is 100. 87 is less than 100 by 13 and 89 is less than 100 by 11.

**Step 1 : (LHS)**

87 – 13

89 – 11

———————–

(87 – 11) or (89 – 13) = 76

———————–

**Step 2: (RHS)**

(-13) (-11) = 143

Answer – 76/143. (Number of digits in RHS is not equal to the number of Zeroes in the base. So we have to carry over the number).

**The Answer is 7743.**

**Example 4:**

**What is 995 x 993?**

The nearest base for both numbers is 1000. 995 is less than 1000 by 5 and 993 is less than 1000 by 7.

**Step 1 (LHS)**

995 – 5

993 – 7

———————–

(995 – 7) or (993 – 5) = 988

————————

**Step 2: (RHS)**

(-5) (-7) = 35

Answer – 988/35 (Digits in RHS are less than the Zeros in base).

So, 988/035.

**The Answer is 988035.**

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