How to Multiply Two-Digit Numbers in Your Head
Four ways to multiply two-digit numbers mentally, from splitting to cross multiplication and the near-100 shortcut, with worked examples and practice problems.
On this page
Multiplying two two-digit numbers is where most people reach for a calculator. But you don’t need to hold a whole paper calculation in your head. Each method below breaks the problem into a few small steps, and with practice you’ll know at a glance which one to use.
You only need one thing first: the times tables up to 10 × 10, by heart.
Method 1: Split one number
This is the method to learn first because it works for everything. Break one number into tens and ones, multiply each part, then add.
34 × 12
- 34 × 10 = 340
- 34 × 2 = 68
- 340 + 68 = 408
Split whichever number makes the steps easier. For 47 × 21, split the 21:
47 × 21
- 47 × 20 = 940
- 47 × 1 = 47
- 940 + 47 = 987
Sometimes splitting by subtraction is easier. 19 is 20 − 1:
19 × 34
- 20 × 34 = 680
- 680 − 34 = 646
Method 2: Cross multiply
For two numbers with no easy split, cross multiplication gives the answer one place at a time, right to left. Write the numbers as tens and ones:
23 × 41
- ones: 3 × 1 = 3
- tens: 2 × 1 + 3 × 4 = 2 + 12 = 14 → write 4, carry 1
- hundreds: 2 × 4 = 8, plus the carry = 9
- 943
The middle step is the cross: the outer pair (2 × 1) plus the inner pair (3 × 4). It takes a few days of practice to keep the carries straight, but after that it works for any pair of two-digit numbers.
Method 3: Numbers near 100
When both numbers are just under 100, use how far each is from 100.
97 × 94
- 97 is 3 under 100, 94 is 6 under
- 97 − 6 = 91
- 3 × 6 = 18
- write them together: 9118
It also works just over 100. For 103 × 107: 103 + 7 = 110, and 3 × 7 = 21, so the answer is 11021.
Method 4: The difference of squares
If the two numbers are the same distance either side of a round number, there’s a beautiful shortcut: square the middle, then subtract the square of the distance.
48 × 52
- both are 2 from 50
- 50² = 2500
- 2² = 4
- 2500 − 4 = 2496
That’s the calculation in the background of Mathlite’s welcome screen. It works for 39 × 41 (1600 − 1 = 1599) and 67 × 73 (4900 − 9 = 4891) too.
Which method should you use?
| The numbers look like… | Use | Example |
|---|---|---|
| One is small or near a round number | Split | 19 × 34 |
| Both just under or over 100 | Near 100 | 97 × 94 |
| Same distance from a round number | Difference of squares | 48 × 52 |
| Anything else | Cross multiply | 23 × 41 |
Choosing quickly is a skill in itself. When you practise, mix the problems so you have to decide each time.
Try it
- 26 × 11
Answer
286 - 43 × 21
Answer
903 - 29 × 15
Answer
435 - 95 × 98
Answer
9310 - 58 × 62
Answer
3596 - 32 × 24
Answer
768
Tips for doing it fast
- Say the steps quietly. Saying “340, plus 68” keeps the numbers in your working memory.
- Keep the big part first. Do the tens before the ones so you always have an estimate.
- Estimate before you start. 47 × 21 is about 50 × 20 = 1000, so an answer of 987 makes sense and 9870 doesn’t.
- Practise each method on its own, then mix them.
The bottom line
You don’t need a calculator for two-digit multiplication. Split when the numbers allow it, use the near-100 trick and the difference of squares when they fit, and cross multiply for everything else. Ten minutes of practice on each method is enough to start using it.
Mathlite has lessons for each of these, from splitting and multiplying in columns to cross multiplication, numbers near 100 and squares, all with worked examples and practice at your level.
Practise this in Mathlite
Every trick in this article is a lesson in Mathlite, with worked examples and practice that adapts to you.
Frequently asked questions
What is the easiest way to multiply two-digit numbers in your head?
Splitting one number into tens and ones, multiplying each part, then adding. For 34 × 12 that is 34 × 10 = 340 plus 34 × 2 = 68, which makes 408.
How do you multiply 2-digit numbers quickly?
Pick the method that fits the numbers: split when one number is small or round, use the near-100 trick when both are close to 100, use the difference of squares when both are the same distance from a round number, and cross multiply otherwise.
Do I need to memorise anything first?
The times tables up to 10 × 10. Every method here breaks a big multiplication into small ones you should know instantly.
How long does it take to learn?
Splitting can be learned in a single session. Cross multiplication usually takes a few days of short practice before it feels comfortable.