What is Multiplication? — Mathematics

Definition 10.1 Primary & Middle School Mathematics · Chapter 10 — Multiplication: First Steps

$4 \times 3$ means “four times three”:

4 \times 3 = 3 + 3 + 3 + 3 = 12 .

The sign is $\times$ , read “times”. The answer is the product (multiplication grows up in Chapter 16).

An array: 4 rows of 3. Counting by rows gives 4 × 3; the same dots by columns give 3 × 4 — so the order does not matter. — An *array*: $4$ rows of $3$ . Counting by rows gives $4 \times 3$ ; the same dots by columns give $3 \times 4$ — so the order does not matter.

Examples

Example 10.2 (Order does not matter)

$4 \times 3$ and $3 \times 4$ count the same $12$ dots, one by rows, one by columns. Turning the array on its side proves it. So learning one product gives its twin for free.

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Definition 16.1 Primary & Middle School Mathematics · Chapter 16 — Multiplication

The product $3 \times 7$ means “three times seven”:

3 \times 7 = 7 + 7 + 7 = 21 .

On a picture, $3 \times 7$ is a rectangle of dots: $3$ rows of $7$ dots.

The same 21 dots, counted by rows or by columns: the order of a product does not matter. Knowing 3 × 7 gives 7 × 3 for free — half the tables to learn! — The same $21$ dots, counted by rows or by columns: the order of a product does not matter. Knowing $3 \times 7$ gives $7 \times 3$ for free — half the tables to learn!

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