Numihana98 × 97
Base 100; signed differences -2 and -3. Raw left: 95; raw right: 6. Carry/borrow: 0.
Normalised parts: 95 × 100 + 6 = 9506. The right part must be between 0 and 99.
Partial products give the same result: 98 × 90 + 98 × 7 = 8820 + 686 = 9506.
MATHS METHOD LAB
Near-base multiplication.
Multiply numbers close to ten, one hundred or one thousand using their signed differences from that base. Normalise the right-hand part with a carry or borrow before combining the parts.
When this helps
Optional enrichment when both numbers are near the same power of ten. For other numbers, compare with partial products or long multiplication.
A common slip
A negative right-hand part needs a borrow; a part as large as the base needs a carry. Never concatenate signed differences directly.
Worked example
10 × 13 =
Answer: 130
What is the difference 10 − 10?
Keep its sign: below the base gives a negative difference.
0What is the difference 13 − 10?
Keep its sign.
3What is the unnormalised left part?
Add the base and both differences.
13What is the unnormalised right part?
Multiply the signed differences.
0What carry or borrow goes into the left part?
Use floor(right ÷ base). A negative right part borrows one or more.
0What is the normalised right part?
Subtract carry × base from the raw right part. It must be between zero and base minus one.
0What is the normalised left part?
Add the carry (or negative borrow) to the raw left part.
13What is the final answer?
Recombine your working and check it against the original question.
130
Compare near-base with partial products
This technique is often called Nikhilam in modern Vedic Maths materials. It is optional enrichment. It helps when both numbers are close to the same power of ten.
103 × 97
Base 100; signed differences 3 and -3. Raw left: 100; raw right: -9. Carry/borrow: -1.
Normalised parts: 99 × 100 + 91 = 9991. The right part must be between 0 and 99.
Partial products give the same result: 103 × 90 + 103 × 7 = 9270 + 721 = 9991.
104 × 103
Base 100; signed differences 4 and 3. Raw left: 107; raw right: 12. Carry/borrow: 0.
Normalised parts: 107 × 100 + 12 = 10712. The right part must be between 0 and 99.
Partial products give the same result: 104 × 100 + 104 × 3 = 10400 + 312 = 10712.
With a negative right part, borrow from the left before combining. With a right part at least as large as the base, carry into the left. Choose the method that you can explain and check reliably.
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Teaching context
This lesson practises mathematical representations and calculations. The displayed practice uses selected England Year 6 skills; the strategy can also help learners in other years.
Curriculum alignment describes the mathematical skill. It does not mean this is the only required teaching method.
Department for Education: mathematics programmes of study ↗Original method lesson v1.
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