Q1.
Use the following multiplications to find the product of a number with 11 in a single step. (a) 3874 × 11 (b) 5678 × 11
Answer
Split 11 as 10 + 1 and distribute.
(a) 3874 × 11 = 3874 (10 + 1) = 38740 + 3874 = 42614
(b) 5678 × 11 = 5678 (10 + 1) = 56780 + 5678 = 62458
Watch the digits in (a). Writing the number as dcba = 3874:
| 38740 | d c b a 0 |
| + 3874 | + d c b a |
| 42614 | d, (c + d), (b + c), (a + b), a |
Why it happens: multiplying by 10 shifts every digit one place to the left. Adding the original number back therefore lands digit a under digit b, digit b under digit c, and so on — so each column of the sum is a pair of neighbouring digits. For 3874: 4, 7 + 4 = 11, 8 + 7 = 15, 3 + 8 = 11, 3, which after carrying gives 42614.