Practice
Two-Digit Multiplication in Your Head: Four Methods With Worked Examples
By HumanCalc · Published · 3 min read
Multiplying two-digit numbers without paper feels hard mainly because people try to copy the written method in their head. Mental methods work differently: they break the problem into pieces that are easy to hold, then add the pieces.
Below are four methods, each with a worked example you can check. Every one of them is plain arithmetic, so you can verify the steps yourself.
Method 1: split one number into tens and ones
This works for any pair. Keep one number whole and split the other into tens and ones. Multiply each part, then add. It is the distributive rule: 14 × 17 = 14 × 10 + 14 × 7.
14 × 17
- Split 17 into 10 + 7.
- 14 × 10 = 140.
- 14 × 7 = 98.
- 140 + 98 = 238.
14 × 17 = 238
Method 2: the teens shortcut (11–19 × 11–19)
When both numbers are between 11 and 19, add the first number to the ones digit of the second, multiply by 10, then add the product of the two ones digits. It works because (10 + a)(10 + b) = 10 × (10 + a + b) + a × b.
16 × 13
- 16 + 3 = 19, so start with 190.
- Ones digits: 6 × 3 = 18.
- 190 + 18 = 208.
16 × 13 = 208
Method 3: round to a friendly number, then adjust
If one number is close to a multiple of ten, multiply by the round number and subtract (or add) the difference. This keeps the hard part to a single small correction.
19 × 6 and 48 × 7
- 19 × 6: 20 × 6 = 120, minus one 6 = 114.
- 48 × 7: 50 × 7 = 350, minus 2 × 7 = 14, gives 336.
19 × 6 = 114 and 48 × 7 = 336
Method 4: multiplying by 11
For a two-digit number, write its first digit, then the sum of its two digits, then its last digit. If the middle sum is 10 or more, carry the 1 into the first digit.
34 × 11 and 78 × 11
- 34: 3, (3 + 4 = 7), 4 → 374.
- 78: 7, (7 + 8 = 15), 8 → carry 1 → 858.
34 × 11 = 374 and 78 × 11 = 858
Which method to use
Percentages follow the same idea: 25% of 160 is 160 ÷ 4 = 40, and 75% is three times that, 120.
| Problem looks like | Try | Example |
|---|---|---|
| Any two-digit pair | Split into tens and ones | 23 × 14 = 230 + 92 = 322 |
| Both numbers 11–19 | Teens shortcut | 12 × 15 = 170 + 10 = 180 |
| One number near 20, 30, 50… | Round and adjust | 29 × 4 = 120 − 4 = 116 |
| One number is 11 | Times 11 | 52 × 11 = 572 |
Practise with real questions
The Daily Challenge includes a teens multiplication, a percentage and a two-step expression every day, so it is a short, fixed set to try these methods on. Mental Arithmetic gives longer, adaptive practice.
- Say each intermediate result quietly; it is easier to hold a number you have heard.
- Check one answer a different way, for example 14 × 17 by rounding: 14 × 20 − 14 × 3 = 280 − 42 = 238.
- Aim for accuracy first. Speed follows once the steps stop needing attention.
