Multiplying by 11
インド式計算道
Way of Indian Math
99 × 99 in seconds.
Thirteen methods. One mental-math practice.
From Level 1 to Master 7, each rank teaches a different way to see a multiplication. No ads, no network, just ink-quiet focus.

Editorial dispatch
Why five seconds is enough.
Indian-style mental math is not a shortcut. You split the place values, find a symmetry, and rewrite the expression as something simpler. The long form disappears.
Worked example: 37 × 43
- 01
37 × 43
Long multiplication takes four lines.
- 02
= (40 − 3)(40 + 3)
Average is 40, the gap is 3.
- 03
= 40² − 3²
Sum × difference is a difference of squares.
- 04
= 1600 − 9
Squares are well within recall.
- 05
= 1591
Done. Four seconds.
Curriculum
Thirteen ways of seeing.
Each method is the shortest path through one specific pattern. You don't memorise it — you learn to see it.
Rank
Pattern
Example
- 01 / Level26 × 11 = 286
Level 1
ab × 11
Multiplying by 11
01 / LevelLevel 1ab × 11Multiplying by 1126 × 11 = 286 - 02 / Level35 × 75 = 2625
Level 2
(ab) × (cb), a+c=10
Same ones, tens sum to 10
02 / LevelLevel 2(ab) × (cb), a+c=10Same ones, tens sum to 1035 × 75 = 2625 - 03 / Level43 × 47 = 2021
Level 3
(ab) × (ac), b+c=10
Same tens, ones sum to 10
03 / LevelLevel 3(ab) × (ac), b+c=10Same tens, ones sum to 1043 × 47 = 2021 - 04 / Level13 × 14 = 182
Level 4
(1a) × (1b)
Both numbers in 11–19
04 / LevelLevel 4(1a) × (1b)Both numbers in 11–1913 × 14 = 182 - 05 / Level37 × 43 = 1591
Level 5
(N − d)(N + d)
Average is a round number
05 / LevelLevel 5(N − d)(N + d)Average is a round number37 × 43 = 1591 - 06 / Level97 × 96 = 9312
Level 6
Numbers near 100
Both numbers in the 90s
06 / LevelLevel 6Numbers near 100Both numbers in the 90s97 × 96 = 9312 - 07 / Master37 × 6 = 222
Master 1
2-digit × 1-digit
2-digit × 1-digit
07 / MasterMaster 12-digit × 1-digit2-digit × 1-digit37 × 6 = 222 - 08 / Master24 × 35 = 840
Master 2
even × ones-is-5
Even 2-digit × ones-is-5
08 / MasterMaster 2even × ones-is-5Even 2-digit × ones-is-524 × 35 = 840 - 09 / Master35 × 75 = 2625
Master 3
(a5) × (b5)
Both end in 5
09 / MasterMaster 3(a5) × (b5)Both end in 535 × 75 = 2625 - 10 / Master68 × 25 = 1700
Master 4
even × 25 / 75
Even 2-digit × 25 / 75
10 / MasterMaster 4even × 25 / 75Even 2-digit × 25 / 7568 × 25 = 1700 - 11 / Master31 × 41 = 1271
Master 5
(a1) × (b1)
Both end in 1
11 / MasterMaster 5(a1) × (b1)Both end in 131 × 41 = 1271 - 12 / Master34 × 37 = 1258
Master 6
(ab) × (ac), same tens
Same tens digit
12 / MasterMaster 6(ab) × (ac), same tensSame tens digit34 × 37 = 1258 - 13 / Master47 × 58 = 2726
Master 7
Vertical & crosswise
General 2-digit × 2-digit
13 / MasterMaster 7Vertical & crosswiseGeneral 2-digit × 2-digit47 × 58 = 2726
Ranked path
Thirteen seals, Level 1 to Master 7.
Five seconds per question, fifty for the round of twenty. Mistakes cost time. That's the price of a seal.
- 01Level 1
- 02Level 2
Same ones, tens sum to 10
- 03Level 3
Same tens, ones sum to 10
- 04Level 4
Both numbers in 11–19
- 05Level 5
Average is a round number
- 06Level 6
Both numbers in the 90s
- 07Master 1
2-digit × 1-digit
- 08Master 2
Even 2-digit × ones-is-5
- 09Master 3
Both end in 5
- 10Master 4
Even 2-digit × 25 / 75
- 11Master 5
Both end in 1
- 12Master 6
Same tens digit
- 13Master 7
General 2-digit × 2-digit
From the pages
What's inside.
37 × 43
= ?
1.9s left
Question screen
Just the time and the expression. The rest is space for thinking.
MASTER COURSE
The Path
- ✓Level 1
- ✓Level 2
- ✓Level 3
- ▶Level 4
- ·Level 5
- ·Level 6
- ·Master 1
- ·Master 2
- ·Master 3
- ·Master 4
- ·Master 5
- ·Master 6
- ·Master 7
The path
Thirteen ranks at a glance. Seals stack as you climb.
Cleared
Clear time 47.6s
Avg 2.4s per question
Pass screen
Confetti and Ganesha's blessing.
Price
¥350. Once.
One-time. No ads. No subscriptions. No accounts.
One-time
¥350
(tax incl.)
01 / 4
Zero ads
No ad SDK, no interruption to learning.
02 / 4
Fully offline
The app holds no network permission.
03 / 4
Six languages
Japanese, English, Korean, Chinese, French, Spanish.
04 / 4
iOS / Android
Both platforms covered for ¥350.
Frequently asked
What you might be wondering.
01Is it really one-time?
Yes. ¥350 unlocks all thirteen methods and all thirteen ranks. No subscriptions, no in-app purchases.
02Is it suitable for children?
Yes, from upper elementary age. The expressions are number-led, designed to work with a parent alongside.
03Does it work offline?
Yes. The app holds no network permission. All progress and best times stay on the device.
04Are there ads?
No. No ad SDK is included.
05Do I need an account?
No. There is no account system, no cloud sync. History does not transfer between devices.
06Which languages are supported?
Japanese, English, Korean, Chinese (Simplified), French, and Spanish. The app follows your OS language.
07Why five seconds per question?
Five seconds is a sane upper bound for the three steps of mental math: read, see the pattern, build the answer aloud. Beyond that, you're doing long multiplication.