Do the multiplication in easier way — lesson. Mathematics State Board, Class 7.

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Integers have five remarkable properties on multiplication operation. With the help of those properties, we can find the product value easily.

Let us see how to apply those properties to do the multiplication more easily.

Now let $a$ and $b$ are integers. Their multiplicative properties are as follows:

Integer property	Over multiplication
Closure	$a \times b \in ℤ$
Associativity	$a \times (b \times c) = (a \times b) \times c$
Identity	$a \times 1 = a = 1 \times a$
Commutativity	$a \times b = b \times a$
Distributivity	$\begin{array}{l} a (b + c) = a \times b + a \times c \\ a (b - c) = a \times b - a \times c \end{array}$