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Near-Base Multiplication (Base 100)आधार 100 के पास गुणा

Multiply two numbers in 90–99 using base-100 deficits, a two-digit right block, and carry when needed.

Popularised in modern Vedic Mathematics teaching as near-base multiplication; this lab locks Base 100 Model A only (both factors in 90–99). Always verify with ordinary multiplication.

Recognition signal

Both factors are integers from 90 to 99 inclusive (both below base 100). Model A only — no above-base or mixed cases in this lab.

When to use

  • You need the exact product of two integers both in 90–99.
  • You can form deficits from 100 and will verify with ordinary multiplication.

When not to use

  • Either factor is below 90 or above 99 (including 100).
  • Above-base or mixed above/below pairs (Model B/C and scaled bases are excluded).
  • Bases other than 100 (10, 50, 200, 1000) or scaled-base shortcuts.

Ordinary method

Multiply the two numbers: n × m.

Rapid method

  1. Confirm both numbers are integers in 90–99.
  2. Compute deficits: d1 = 100 − n and d2 = 100 − m.
  3. Left raw: n − d2 (same as m − d1).
  4. Right raw: d1 × d2.
  5. Write the right block as exactly two digits (zero-pad if rightRaw < 100).
  6. If rightRaw ≥ 100, carry floor(rightRaw / 100) into the left part; right = rightRaw % 100.
  7. Final answer = left × 100 + right. Verify with ordinary multiplication.

Identity: n × m = 100(n − d2) + d1 × d2 (Model A)

Identity: n times m equals 100 times open parenthesis n minus d 2 close parenthesis plus d 1 times d 2, Model A base 100

Guided examples

98 × 97
  1. Confirm both 98 and 97 are in 90–99.
  2. Deficits: d1 = 100 − 98 = 2; d2 = 100 − 97 = 3.
  3. Left raw: 98 − 3 = 95 (also 97 − 2).
  4. Right raw: 2 × 3 = 6.
  5. Right block (two digits): 06 (zero-pad if needed).
  6. Final rapid answer: 9506 = 9506.
  7. Ordinary check: 98 × 97 = 9506.

Ordinary verification: Ordinary: 98 × 97 = 9506. Rapid: deficits 2 and 3; right block 06; product 9506.

96 × 94
  1. Confirm both 96 and 94 are in 90–99.
  2. Deficits: d1 = 100 − 96 = 4; d2 = 100 − 94 = 6.
  3. Left raw: 96 − 6 = 90 (also 94 − 4).
  4. Right raw: 4 × 6 = 24.
  5. Right block (two digits): 24 (zero-pad if needed).
  6. Final rapid answer: 9024 = 9024.
  7. Ordinary check: 96 × 94 = 9024.

Ordinary verification: Ordinary: 96 × 94 = 9024. Rapid: deficits 4 and 6; right block 24; product 9024.

90 × 90 (carry into left; right block 00)
  1. Confirm both 90 and 90 are in 90–99.
  2. Deficits: d1 = 100 − 90 = 10; d2 = 100 − 90 = 10.
  3. Left raw: 90 − 10 = 80 (also 90 − 10).
  4. Right raw: 10 × 10 = 100.
  5. Carry: floor(100/100) = 1 adds to left → 81; right block = 00.
  6. Final rapid answer: 8100 = 8100.
  7. Ordinary check: 90 × 90 = 8100.

Ordinary verification: Ordinary: 90 × 90 = 8100. Rapid: deficits 10 and 10; rightRaw = 100; carry 1; right block 00; product 8100.

When the rapid rule does not apply

88 × 97

88 is below 90, so the first operand is outside the locked Model A range 90–99. Do not apply this T03 method.

103 × 97

103 is above base 100 while 97 is below — a mixed above/below case excluded from Model A in the current supported practice set.

Common errors

  • Error reference T03-ERR-WRONG-DEFICIT.

    Computing the wrong deficit from 100 for either factor.

  • Error reference T03-ERR-NO-LEADING-ZERO.

    Dropping a leading zero in the two-digit right block (for example writing 6 instead of 06).

  • Error reference T03-ERR-NO-CARRY.

    Forgetting carry when rightRaw ≥ 100, especially for 90 × 90 where rightRaw = 100.

  • Error reference T03-ERR-RANGE.

    Using the method when either factor is outside 90–99.

  • Error reference T03-ERR-BASE-50.

    Applying a base-50 or other scaled-base shortcut instead of locked Model A base 100.

Verification

Always check that the rapid result equals ordinary n × m.

Direct practice

12 exact-integer questions in fixed order. Accuracy only; no timer.

Start direct practice

Basic progress summary

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