Mental Multiplication Tricks: How to Multiply in Your Head
Mental multiplication gets easy once you stop multiplying the hard way. Break a number into parts, work left to right, and lean on a few patterns: ×11 by adding the digits, ×9 as ×10 minus one, and squaring numbers ending in 5 with a quick shortcut. A few minutes of practice a day makes them automatic.
Why Multiplication Feels Hard in Your Head (and the One Habit That Fixes It)
You learned the times tables up to 12. Then school ended, the calculator moved into your pocket, and the muscle quietly went soft. Now, when someone asks "what's 17 times 8?" your mind goes blank — not because you forgot math, but because you never had a method for anything outside the grid.
The fix is one foundational habit: break the number apart before you multiply.
It sounds obvious, but most people were never shown how to do it systematically in their head. The formal name is the distributive property — the rule that says multiplying a number by a group of numbers added together is the same as doing each multiplication separately. In practice it looks like this:
17 × 8. Split 17 into 10 and 7. Multiply each part by 8, then add:
- 10 × 8 = 80
- 7 × 8 = 56
- 80 + 56 = 136
That's it. You've just done a multiplication problem that would have stumped you before — not with a trick, but with a method. Every other shortcut in this article is built on this same move. If you want a deeper look at the underlying principles and how to build from here, the pillar post How to Improve Your Mental Math covers the full picture.
Work left to right, break numbers into friendly chunks, and the carrying disappears. Now layer the patterns on top.
The ×11 Trick (Add the Digits)
This is the one that makes people say "why didn't school teach it this way?" Multiplying any two-digit number by 11 is almost instant once you see the pattern.
The rule: write the first digit, write the sum of both digits in the middle, write the last digit.
25 × 11:
- First digit: 2
- Middle: 2 + 5 = 7
- Last digit: 5
- Result: 275
Simple. But what happens when the middle sum is 10 or more? You carry — and it only takes one extra step.
57 × 11:
- First digit: 5
- Middle: 5 + 7 = 12 — write the 2, carry the 1
- Add the carry to the first digit: 5 + 1 = 6
- Last digit: 7
- Result: 627
Try a few in your head right now: 43 × 11 (answer: 473), 36 × 11 (answer: 396), 84 × 11 (answer: 924). The pattern clicks within minutes.
Why does it work? Multiplying by 11 is the same as multiplying by 10 and adding the original number once — which is just the break-apart method again. 57 × 11 = (57 × 10) + (57 × 1) = 570 + 57 = 627. The digit-sum trick is just a fast way to run that calculation in your head without holding as many numbers.
×9 and ×5 the Easy Way
These two are closely related to the break-apart method, and they cover a surprisingly large slice of everyday multiplication.
Multiplying by 9: use ×10 then subtract once
Any multiplication by 9 is just ×10 with one quick correction.
9 × 7: 10 × 7 = 70, then subtract 7 once: 70 − 7 = 63.
9 × 13: 10 × 13 = 130, then subtract 13: 130 − 13 = 117.
The same idea scales to 99 and 999. A $7.99 price? Treat it as $8.00 and subtract one cent — you're already doing this instinctively; now it's on purpose. For the full "minus one" rounding logic, see How to Improve Your Mental Math.
Multiplying by 5: halve the ×10 result
Multiplying by 5 is just multiplying by 10 and cutting the answer in half.
48 × 5: 48 × 10 = 480, then 480 ÷ 2 = 240.
37 × 5: 37 × 10 = 370, then 370 ÷ 2 = 185.
If the number is odd, the halving lands on a .5 — that's fine: 37 × 5 = 18.5 × 10 = 185. Either route works; the key is to anchor on ×10 first, not to try to multiply by 5 directly.
Squaring Numbers That End in 5
This one feels like a magic trick the first time you see it.
The rule for a number ending in 5: multiply the leading part n by (n + 1), then stick 25 on the end.
35²: n = 3, so 3 × 4 = 12. Append 25: 1225.
75²: n = 7, so 7 × 8 = 56. Append 25: 5625.
15²: n = 1, so 1 × 2 = 2. Append 25: 225. (Check: 15 × 15 = 225. That's right.)
Why does it work? A number ending in 5 can be written as (10n + 5). Squaring it gives 100n² + 100n + 25 = 100·n(n+1) + 25. In plain terms: the last two digits are always 25, and the digits before them are always n × (n+1). The algebra just confirms the pattern — you don't need to follow it to use the trick. This shortcut comes up more often than you'd expect, and once you know it, you'll never reach for a calculator to square a number ending in 5.
Doubling and Halving (the ×4, ×6, ×8 Shortcut)
The most flexible tool in mental multiplication is simple doubling. Once you can double quickly, you can handle ×4, ×8, and a lot of ×6 problems without much strain.
×4 = double, then double again. 23 × 4: double 23 = 46, double again = 92.
×8 = double three times. 12 × 8: 12 → 24 → 48 → 96.
These are fast because doubling a number is one of the most natural mental operations we have — it doesn't require breaking apart or carrying in the same way.
The halve-and-double swap is an extension: if one number is even, you can halve it and double the other, and the product stays the same.
16 × 35: halve 16 to get 8, double 35 to get 70, then 8 × 70 = 560. That's a lot easier than multiplying 16 × 35 directly. It works because halving one factor and doubling the other keeps the area constant — the same rectangle, just reshaped.
When to use it: look for an even number in the problem. If one factor is divisible by 2, try halving it. If the resulting pair is friendlier (like 8 × 70 versus 16 × 35), you've found a shortcut.
How to Make These Automatic
Reading six tricks won't make them stick. Using them will.
- Start with one. Pick the ×11 trick or break-apart first. Use it in real life for a week, then add another.
- Use real moments. Unit prices, tips, splitting costs — real stakes make patterns stick faster than worksheets.
- Keep sessions short. Five minutes daily beats an hour on the weekend. Reflexes come from frequency, not marathon sessions.
- Work at the edge. Easy problems confirm what you know; slightly harder ones build speed.
The game below rebuilds the underlying number sense. Fast, free, no sign-up.
Ready to put it into practice?
Make 10 is a free number puzzle — drop blocks so rows or columns sum to ten. It's the same number-sense work that makes mental math feel natural, in a format that takes about 30 seconds to learn. Play a few rounds, then come back to the tricks.
Want to sharpen your multiplication speed right now?
30 seconds. Multiply as many pairs as you can. No leaderboard, no judgment — just a speed score for you, just for fun.
Frequently Asked Questions
What's the easiest multiplication trick to learn first?
The break-apart method (partial products). It works on any problem, not just special cases. Once you can split "17 × 8" into "10 × 8 + 7 × 8" mentally, everything else builds on that. The ×11 trick is a close second — fast, satisfying, with an instant "aha."
How do I get faster at multiplication in my head?
Short daily sessions beat occasional long study. Use tricks in real situations — unit prices, tips, splitting bills — not just worksheets. Real context consolidates patterns. A timed quiz (like the one above) adds mild pressure that builds retrieval speed.
Why does the ×11 trick work?
11 = 10 + 1, so ×11 is ×10 plus the number once. For 57 × 11: 570 + 57 = 627. The digit-sum shortcut is a compressed way to run that addition — the middle digit is the digit-sum because that's where the carry from adding tens and ones lands.
Do I need to memorize times tables to do mental math?
Knowing them up to 12 helps, but you don't need them to start. The break-apart method reduces any multiplication to simpler parts. If you know 2 × 8 = 16 and 10 × 8 = 80, you can reach 12 × 8 = 96 without memorizing it. Use both — but don't let table gaps stop you from starting.
These tricks aren't shortcuts around understanding — they're the understanding itself, stripped down to what you actually need in your head. Pick one, use it this week, and add another when it feels automatic. A few minutes a day is enough. Start with Make 10 to warm up the number sense, or go back to How to Improve Your Mental Math if you want to see the full picture.
Source: Distributive Law — Math is Fun