Split one factor into friendly parts, compensate around a round number, or double one factor while halving the other. Estimate first and check that the final product is plausible.
Split an awkward factor into tens and units
For 23 × 7, split 23 into 20 + 3. Calculate 20 × 7 = 140 and 3 × 7 = 21, then add them: 161. This works because multiplication distributes across addition.
The same method handles 14 × 12: (14 × 10) + (14 × 2) = 140 + 28 = 168. Keep both products visible mentally or on paper so you do not accidentally add the unused factor rather than its product.
These are practice examples for this guide. Moocsoft’s Math Riddles / Math Puzzles app provides separate number challenges when you want to use the method in a game.
Multiply by 9 or 11 using a nearby ten
To multiply a number by 9, multiply by 10 and subtract the original number. For 46 × 9: 460 − 46 = 414. You are removing one group of 46 from ten groups.
For ×11, add that group instead: 46 × 11 = 460 + 46 = 506. This approach handles carries naturally and does not depend on a digit trick that may fail when the digits sum above nine.
For ×99, use 100 groups minus one: 37 × 99 = 3,700 − 37 = 3,663. Choose this only when the subtraction is easier for you than splitting the product another way.
Multiply by 25 as one quarter of 100
Because 25 = 100 ÷ 4, multiplying by 25 is equivalent to multiplying by 100 and dividing by 4. With 28 × 25, it is easier to divide 28 first: 28 ÷ 4 = 7, then 7 × 100 = 700.
If the number is not divisible by four, keep the remainder or use another method. For 18 × 25, 18 × 100 ÷ 4 = 1,800 ÷ 4 = 450. Do not round 18 ÷ 4 down to 4; that would discard part of the product.
Double one factor and halve the other
For 16 × 35, halve 16 and double 35 to get 8 × 70 = 560. The product is unchanged because the factor of two cancels: (16 ÷ 2) × (35 × 2) = 16 × 35.
You can repeat the move while it helps. With 32 × 125, use 16 × 250, then 8 × 500 = 4,000. Stop when the next step is less convenient; a shortcut is useful only if you can follow it reliably.
Do not halve both factors. That makes the product one quarter of the original rather than keeping it unchanged.
Use a nearby round number and compensate
For 19 × 6, calculate 20 × 6 = 120 and subtract one group of 6: 114. For 51 × 8, calculate 50 × 8 = 400 and add one group of 8: 408.
Pay attention to the size of the adjustment. In 98 × 7, you moved up by two groups to reach 100 × 7. Subtract 2 × 7 = 14, not just 2: 700 − 14 = 686.
Try a six-question practice round
| Question | Suggested starting point |
|---|---|
| 34 × 6 | Split 34 into 30 + 4 |
| 27 × 9 | Ten groups minus one |
| 58 × 11 | Ten groups plus one |
| 36 × 25 | Divide by four, multiply by 100 |
| 24 × 15 | Halve and double |
| 49 × 8 | Use 50 groups, subtract one |
Reveal the six worked answers
34 × 6 = 204: 180 + 24. 27 × 9 = 243: 270 − 27. 58 × 11 = 638: 580 + 58. 36 × 25 = 900: 9 × 100. 24 × 15 = 360: 12 × 30. 49 × 8 = 392: 400 − 8.
If your answer differs, check the intermediate step before starting again. For 49 × 8, an estimate of about 400 is a useful warning if your final answer has an extra zero.
Choose a small challenge for your next session
Pick one method and solve three new examples before mixing methods. Once the steps feel clear, try the app’s number challenges and see which shortcut you actually recognize while playing. This is arithmetic practice, not a promise of an IQ increase or a measured cognitive benefit.
For a broader routine, use mental math games for adults. To avoid losing an otherwise correct calculation to grouping, review order of operations. If you prefer competition, read the friendly 1v1 setup guide and check the app’s current room options.
Common questions
Which multiplication shortcut should I learn first?
Start by splitting a factor into tens and units. It applies widely and makes the reasoning visible. Add the other methods when they simplify a particular product.
Does doubling and halving always preserve the product?
Yes, when you double one factor and halve the other exactly. Rounding during the step changes the result.
Should I start with timed multiplication practice?
You can start without a timer and add time pressure only when you can explain and check the method. Speed is not a substitute for correct steps.
Published by Moocsoft, the independent studio behind Math Riddles. Examples and worksheets are illustrative. App features can vary by platform and version; see the store listing for current availability and in-app purchases.