Box 3–1 Properties of the Arithmetic Operations

Commutativity of addition. The order of the two numbers does not affect their sum: 3+5=8=5+3. In general, m+n=n+m.

Associativity of addition. When adding three (or more) numbers, it does not matter whether the first pair or the last pair is added first: (3+5)+4=8+4=12=3+ 9=3+(5+4). In general, (m+n)+p=m+(n+p).

Commutativity of multiplication. The order of the two numbers does not affect their product: 5×8 produces the same answer as 8×5. In general, m×n=m×n.

Associativity of multiplication. When multiplying three or more numbers, it does not matter whether the first pair or the last pair is multiplied first: 3×(5×4) is the same as (3×5)×4. In general, (m×n)×p=m×(n×p).



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