Prerequisites
Arithmetic | 4 of 17
Prerequisites: Addition. Enables: Division, Fractions.
Multiplication represents repeated addition, scaling, or area.
For two numbers:
$$
a \times b = c
$$
where:
$a$ and $b$ are factors
$c$ is the product
Equivalent notation:
$$
a \times b = a \cdot b = ab
$$
Properties of multiplication
| Property | Rule |
|---|---|
| Commutative property | $ab = ba$ |
| Associative property | $(ab)c = a(bc)$ |
| Multiplicative identity | $a \cdot 1 = a$ |
| Multiplicative property of zero | $a \cdot 0 = 0$ |
| Distributive property | $a(b+c)=ab+ac$ |
Repeated addition
For a whole number $n$:
$$
a \times n = \underbrace{a + a + \cdots + a}_{n\text{ times}}
$$
Example:
$$
6 \times 4 = 6 + 6 + 6 + 6 = 24
$$
Multiplying by powers of ten
Multiplying by $10^n$ shifts the decimal point $n$ places to the right.
Examples:
$$
4.37 \times 10 = 43.7
$$
$$
4.37 \times 100 = 437
$$
$$
4.37 \times 1000 = 4370
$$
Area interpretation
The area of a rectangle is:
$$
A = lw
$$
where:
$l$ = length
$w$ = width
Example:
$$
A = 7 \cdot 5 = 35
$$
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