Multiplication — table to 15 × 15, and a mental-math tool

Two things to learn

The memorized facts: every product a × b where a, b are integers from 2 to 15. That's 196 facts (14 × 14 grid). You already know most of them.
The breakdown trick: when one or both numbers are 2-digit, split them into tens + ones and use distribution.

The memorized table — what's worth knowing cold

Easy rows (you have these)

× 2, × 5, × 10 — instant.
× 11 for single digits: just double the digit. 11 × 7 = 77.
Squares: 7² = 49, 8² = 64, 9² = 81, 12² = 144, 13² = 169, 14² = 196, 15² = 225.

The ones people forget

6 × 7 = 42 · 6 × 8 = 48 · 6 × 9 = 54
7 × 8 = 56 · 7 × 9 = 63
8 × 9 = 72
12 × 7 = 84 · 12 × 8 = 96 · 12 × 9 = 108
13 × 11 = 143 · 13 × 12 = 156
14 × 11 = 154 · 14 × 12 = 168
15 × 11 = 165 · 15 × 12 = 180

Drill these specifically; everything else flows out.

The breakdown — distributive expansion

The rule:

(a + b) × (c + d) = a·c + a·d + b·c + b·d

You break each number into a "round" part (10, 20) and a "small" part (the ones). Then you only have to do small multiplications.

1-digit × 2-digit

17 × 8:

Split: 17 = 10 + 7.
(10 + 7) × 8 = 80 + 56 = 136.

13 × 6:

13 = 10 + 3.
(10 + 3) × 6 = 60 + 18 = 78.

2-digit × 2-digit

17 × 25:

Split: 17 = 10 + 7, 25 = 20 + 5.
(10 + 7) × (20 + 5) = 10×20 + 10×5 + 7×20 + 7×5 = 200 + 50 + 140 + 35 = 425.

23 × 14:

(20 + 3) × (10 + 4) = 200 + 80 + 30 + 12 = 322.

18 × 17:

(10 + 8) × (10 + 7) = 100 + 70 + 80 + 56 = 306.

Variations / shortcuts

Squares of two-digit ending in 5: a5 × a5 = a(a+1)·100 + 25. 15² = (1·2)·100 + 25 = 225. 25² = 625. 35² = 1225.
Difference of squares: 21 × 19 = (20+1)(20-1) = 400 - 1 = 399.

These are nice when they fit; the general (a+b)(c+d) always works.

Practice

The /fractions page has practice tools — but for plain multiplication, paper is fine. Spend 10 minutes drilling the "forgotten" facts above and 10 minutes on 2-digit × 2-digit breakdowns each morning.