Figure It Out: Fast Multiplication

Multiplying by 11

Evaluate: (i) $94 \times 11$ $4 \rightarrow (9+4=13) \rightarrow (9+1=10)$ $1034$

(ii) $495 \times 11$ $5 \rightarrow (9+5=14) \rightarrow (4+9+1=14) \rightarrow (4+1=5)$ $5445$

(iii) $3279 \times 11$ $9 \rightarrow (7+9=16) \rightarrow (2+7+1=10) \rightarrow (3+2+1=6) \rightarrow 3$ $36069$

Multiplying by 101

General Rule: Multiply by 100 then add the number itself. $N \times 101 = N(100+1) = 100N + N$ For a 2-digit number $ab$, $ab \times 101 = abab$.

(i) $89 \times 101 = 8989$

(ii) $949 \times 101$ $= 94900 + 949 = 95849$

Multiplying by 1001

(iii) $265831 \times 1001$ $= 265831000 + 265831 = 266096831$

(iv) $1111 \times 1001$ $= 1111000 + 1111 = 1112111$

Multiplying by 99

(v) $9734 \times 99$ $= 9734(100 - 1) = 973400 - 9734$ $= 963666$