How to multiply numbers close to 100 in your head — the Vedic near-base method
97 × 98. Most people write out the full long multiplication — 6 lines, 30 seconds, good chance of an error. The Vedic near-base method produces 9,506 in two steps. This is the technique Gaurav Tekriwal demonstrated in his TED-Ed lesson viewed by millions.
97 × 98. Set up long multiplication and you're looking at 6 lines of working and 30 seconds, with at least one carry to track across. The Vedic near-base method produces 9,506 in two steps and about 4 seconds.
The technique applies to any two numbers close to the same base — 10, 100, or 1,000. Because these numbers sit just below a round number, each one has a small "deficiency." The method uses those deficiencies instead of the full numbers. Small numbers are faster than large ones. That's the whole idea behind near-base multiplication.
Vedic Math calls this the Nikhilam sutra — "all from 9, the last from 10." It's the technique Gaurav Tekriwal demonstrated in his TED-Ed lesson on Vedic Math, which has been viewed millions of times. The visual elegance of watching 97 × 98 collapse into two single-digit operations tends to stop people mid-scroll.
The rule for numbers near 100
Find each number's deficiency from 100. Cross-subtract one deficiency from the other number. Multiply the deficiencies. Write the two parts together.
97 × 98 → deficiencies: 3 and 2
Cross: 97 − 2 = 95 | Product: 3 × 2 = 06
Answer: 9506
Near 100
Both numbers just below 100. Deficiencies are small, so the multiplication is trivial.
97 × 98
Deficiencies: 3 and 2
Cross-subtract: 97 − 2 = 95
Multiply deficiencies: 3 × 2 = 06 (2 digits)
Answer: 9,506
96 × 99
Deficiencies: 4 and 1
Cross-subtract: 96 − 1 = 95
Multiply deficiencies: 4 × 1 = 04
Answer: 9,504
Check: 96 × 99 = 96 × 100 − 96 = 9,600 − 96 = 9,504 ✓
Larger deficiency
When the deficiency product has more than 2 digits, carry into the left part.
93 × 97
Deficiencies: 7 and 3
Cross-subtract: 93 − 3 = 90
Multiply deficiencies: 7 × 3 = 21
Answer: 9,021
88 × 95
Deficiencies: 12 and 5
Cross-subtract: 88 − 5 = 83
Multiply deficiencies: 12 × 5 = 60
Answer: 8,360
Right part stays at 2 digits — 60 fits.
Near 10
Same method, base is 10 instead of 100. Right part is 1 digit.
7 × 8
Deficiencies: 3 and 2
Cross-subtract: 7 − 2 = 5
Multiply deficiencies: 3 × 2 = 6
Answer: 56
6 × 9
Deficiencies: 4 and 1
Cross-subtract: 6 − 1 = 5
Multiply deficiencies: 4 × 1 = 4
Answer: 54
Challenge
Near 1,000 — the method scales directly. Right part is 3 digits.
994 × 998
Deficiencies: 6 and 2
Cross-subtract: 994 − 2 = 992
Multiply deficiencies: 6 × 2 = 012 (3 digits)
Answer: 992,012
Try it: 996 × 997. Two deficiencies, one cross-subtract, one product. You should have the answer in under 10 seconds.
See the method in motion
The diagram below shows how 97 × 98 breaks into the cross-subtract and deficiency product — one step at a time.
[Interactive visual flow available at https://www.thevedicmind.com/blog/near-base-multiplication-vedic.]
How Vedic Math reduces 6-step multiplication to 2 steps — the algebra
The cross-subtract and deficiency product aren't arbitrary steps. They follow directly from the distributive law. Write 97 as (100 − 3) and 98 as (100 − 2):
(100−3)(100−2) = 10,000 − 200 − 300 + 6
= 100(100 − 3 − 2) + 3×2
= 100 × 95 + 6 = 9,506
The cross-subtract (100 − 3 − 2 = 95) is the left part. The deficiency product (3 × 2 = 06) is the right part. The long multiplication does the same computation across 6 steps because it doesn't see the (100 − d) structure. The Vedic method does.
The same logic applies at base 10 and base 1,000. The numbers change; the structure doesn't. That's what makes this a sutra — a thread that runs through the whole system. For the squaring version of the same pattern, see squaring numbers ending in 5.
Stump someone with this
Ask someone to multiply 97 × 98. When they reach for a calculator or start writing, say 9,506. Then ask them to give you two numbers near 100 and race you. They pick 93 × 96. You say 8,928 before they finish typing.
93 − 4 = 89 (cross-subtract). 7 × 4 = 28 (deficiency product). Answer: 8,928. Two steps. Under 5 seconds. Every time.
Try the Nikhilam lesson free → — No signup required. Takes about 3 minutes.
https://www.thevedicmind.com/learn/lesson/l1-nikhilam