Multiplication

Terms · Repeated Addition · Grid Method · Practice

Multiplication is repeated addition — watch each group appear, then all apples merge into the product.

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What is Multiplication?
Multiplication is fast repeated addition. 4×3 = 4+4+4 = 12 (add 4 exactly 3 times)
First
6
Factor
Second
7
Factor
Result
42
Product
Quick Mental Tricks
1
× 2 — Double itDoubling is fastest: 2×13=26 (13+13).
2
× 4 — Double twice4×8: double 8=16, double again=32.
3
× 5 — Halve then × 105×14: half of 14=7, ×10=70.
4
× 10 — Shift digits leftAdd a zero: 6×10=60, 45×10=450.
5
× 9 — Use × 10 then −9×7 = 10×7−7 = 70−7 = 63.
6
× 11 (2-digit)Sum the two digits and put in middle: 11×13 = 1_(1+3)_3 = 143.
Grid Method (Partitioning)

Break numbers into tens and ones, multiply each part, then add. Great for 2-digit × 1-digit.

Example: 47 × 6

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40
7
6
240
42
240 + 42 = 282
Properties
Commutative
6×7 = 7×6 — order does not matter
Associative
(2×3)×4 = 2×(3×4) — grouping does not matter
Identity
n×1 = n — multiplying by 1 changes nothing
Zero
n×0 = 0 — multiplying by 0 always gives 0
Distributive
6×(4+3) = 6×4+6×3 = 42