Multiplying by 11 in your head
This is the first trick most people learn, and it is still the one I use most often.
For a two-digit number, write its two digits apart and put their sum in the middle:
11 × 43 → 4 _ 3 → 4 (4+3) 3 = 473
If the middle sum is 10 or more, keep the last digit and carry the one to the left:
11 × 87 → 8 (15) 7 → (8+1) 5 7 = 957
Why it works
Multiplying by 11 is multiplying by 10 and adding the number once more.
For 10a + b that gives 100a + 10(a + b) + b: the first digit stays,
the last digit stays, and the tens place collects a + b. The carry is just ordinary addition.
Longer numbers
The same idea extends: keep the outer digits and replace every inner position with the sum of neighbouring pairs, working right to left and carrying as you go.
11 × 2,413 → 2 (2+4) (4+1) (1+3) 3 = 26,543
After a week of practice it becomes faster than reaching for a phone.