Multiplying numbers close to 100 (base method)

If both numbers you're multiplying are close to 100, there's a shortcut that turns a messy three-digit multiplication into simple addition and a small multiplication. This is one of the most useful mental math tricks for exam quant sections, since numbers like 97, 103, or 108 show up constantly.

This method is part of the wider Vedic "Nikhilam" technique — see Vedic math tricks for fast multiplication for how it generalizes to other bases like 10 and 1000. Here, we focus specifically on 100 with more worked examples and edge cases.

The setup

For each number, find its deviation from 100 — how far above or below it is. Then:

• Cross-add or cross-subtract a deviation from the other original number to get the left part of the answer
• Multiply the two deviations together to get the right part of the answer (always written as 2 digits, since 100 has 2 zeros)

Case 1: Both numbers below 100

Example: 96 × 94.

• 96 is 4 below 100 → deviation −4
• 94 is 6 below 100 → deviation −6
• Left part: 96 − 6 = 90 (or equivalently 94 − 4 = 90)
• Right part: (−4) × (−6) = 24

Case 2: Both numbers above 100

Example: 106 × 102.

• 106 is 6 above 100 → deviation +6
• 102 is 2 above 100 → deviation +2
• Left part: 106 + 2 = 108
• Right part: 6 × 2 = 12

Case 3: One number above, one below

This is the case people find trickiest, because one deviation is negative.

Example: 108 × 94.

• 108 is 8 above 100 → deviation +8
• 94 is 6 below 100 → deviation −6
• Left part: 108 + (−6) = 102 (or 94 + 8 = 102, same result)
• Right part: (+8) × (−6) = −48

A negative right part means you borrow from the left part instead of adding directly:

The rule when the right part is negative: subtract 1 from the left part, and subtract the right part's magnitude from 100 (the base) to get the corrected right part.

Case 4: The right-part carry

If multiplying the deviations gives a number with more than 2 digits, the extra digit carries into the left part — the same idea as carrying in normal addition.

Example: 88 × 87.

• 88 is 12 below 100 → deviation −12
• 87 is 13 below 100 → deviation −13
• Left part: 88 − 13 = 75
• Right part: (−12) × (−13) = 156 — three digits, too big for the 2-digit slot
• Keep the last 2 digits (56) as the right part, carry the 1 into the left part: 75 + 1 = 76

Using a different base (200, 500, 1000)

The same method works with other round bases, not just 100 — the number of digits in the "right part" just matches the number of zeros in the base (2 digits for 100, 3 digits for 1000). For numbers like 500, it's often easier to use 100 as the base and adjust with a multiplying factor afterward, but for exam speed, sticking to numbers naturally near 100 or 1000 covers most cases you'll actually see.

Where this actually helps

Exam quant sections love numbers like 97, 98, 102, 103, and 104 in multiplication and approximation questions specifically because this shortcut applies. Recognizing "both numbers are within about 15 of 100" in half a second, then running the deviation steps, is consistently faster than standard multiplication for numbers in this range.

If you'd rather use a general-purpose method that works on any pair of two-digit numbers, regardless of how close they are to a round base, see Vedic math tricks for fast multiplication for the vertically-and-crosswise technique.