Arithmetic. Mental calculation, etc.

Arithmetic involves the use of the four basic operations on integers, fractions, and decimals. Mental calculation relies on understanding properties like associativity, commutativity, and distributivity to simplify calculations without written work.

Important properties

• Commutative property: $a + b = b + a$, $a \times b = b \times a$

• Associative property: $(a + b) + c = a + (b + c)$, $(a \times b) \times c = a \times (b \times c)$

• Distributive property: $a \times (b + c) = a \times b + a \times c$

• Breaking numbers into factors or parts can simplify calculations.

• Estimation and rounding can help check mental calculations.