Fast Multiplication Tricks

Multiplication by 11

Multiplying by 11 is easy because $11 = 10 + 1$. $N \times 11 = N(10 + 1) = 10N + N$

Visual Trick: To multiply a number like 3874 by 11:

1. Write down the last digit (4).
2. Add pairs of adjacent digits from right to left.
3. Write down the first digit (plus any carry).

Example: $3874 \times 11$

• Last digit: 4
• $7+4 = 11$ (Write 1, Carry 1)
• $8+7+1(\text{carry}) = 16$ (Write 6, Carry 1)
• $3+8+1(\text{carry}) = 12$ (Write 2, Carry 1)
• First digit: $3+1(\text{carry}) = 4$
• Result: 42614

Using Difference of Squares

Calculate $45 \times 55$. Notice that these numbers are centered around 50. $45 = 50 - 5$ $55 = 50 + 5$

Using Identity 1C: $(50 - 5)(50 + 5) = 50^2 - 5^2$ $= 2500 - 25$ $= 2475$

Calculating Squares near Base

Calculate $99^2$. $99 = 100 - 1$ $(100 - 1)^2 = 100^2 - 2(100)(1) + 1^2$ $= 10000 - 200 + 1$ $= 9801$