1 · The facts, fast
Everything in this walkthrough uses the times tables to 12 × 12. Row 7, column 8: 56.
Tricks that help: × 9 is × 10 minus one group (9 × 7 = 70 − 7 = 63). × 4 is double, then double again. × 6 is × 5 plus one more group.
2 · Multiplying by 10 and 100
× 10 moves every digit one place bigger, so a 0 fills the ones: 34 × 10 = 340. × 100 adds two zeros: 34 × 100 = 3,400.
Multiples of ten: 3 × 40 is 3 × 4 tens = 12 tens = 120. 30 × 40 = 3 × 4 with two zeros = 1,200.
3 · Break apart: 2-digit × 1-digit
28 × 9: split 28 into 20 and 8. 20 × 9 = 180, 8 × 9 = 72. Add: 180 + 72 = 252.
The area model draws this: one big rectangle cut into a tens part and a ones part.
4 · The area model: 2-digit × 2-digit
23 × 14: split both numbers. 23 = 20 + 3 and 14 = 10 + 4. That makes four small rectangles.
20 × 10 = 200, 3 × 10 = 30, 20 × 4 = 80, 3 × 4 = 12. Add all four: 200 + 30 + 80 + 12 = 322.
5 · The column method
Same problem, written in columns. First multiply by the ones: 23 × 4 = 92. Then by the tens: 23 × 10 = 230. Add: 92 + 230 = 322.
The second row always ends in 0, because it is a multiple of ten.
6 · Carrying in multiplication
47 × 6: 7 × 6 = 42. Write 2, carry 4. Then 4 × 6 = 24, plus the carried 4 = 28. Answer 282.
Check with the break-apart: 40 × 6 = 240, 7 × 6 = 42, 240 + 42 = 282. Same.
7 · Estimate first
Before you multiply, round and guess: 28 × 9 is about 30 × 9 = 270. The real answer, 252, is close. If you got 2,520, something went wrong.
Tests ask "about how many" or "closest to." Round both numbers, then multiply.
8 · Rows and columns
A hall has 23 rows with 14 chairs in each row. Rows × chairs per row = 23 × 14 = 322 chairs.
An array is just a picture of rows × columns. Any "rows of" or "boxes of" problem is multiplication.
9 · Which is bigger: compare products
6 × 8 or 7 × 7? 48 vs 49: 7 × 7 by one. 12 × 5 or 10 × 6? Both 60: equal.
Work out both sides before you compare. A bigger number in the problem does not always give a bigger answer.
10 · Multiplying three numbers
4 × 7 × 5: pair up the easy ones first. 4 × 5 = 20, then 20 × 7 = 140. Order does not matter in multiplication.
Look for pairs that make 10, 100, or a multiple of ten.
11 · Doubling and halving
16 × 25: halve one, double the other. 8 × 50 = 400, or 4 × 100 = 400. The answer does not change.
This trick is very handy for × 25 and × 5: 24 × 5 = 12 × 10 = 120.
12 · Two-step multiplication stories
"A store has 28 boxes with 9 crayons in each. It sells 50 crayons. How many are left?" First 28 × 9 = 252, then 252 − 50 = 202.
Write the first answer down before the second step.
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