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| Combining Numbers |
There are a number of different ways of combining any two given numbers. They can be added together to form their sum, subtracted to form their difference, multiplied together to form their product, and divided, provided the divisor is nonzero, to form their ratio. In fact, if we think of a − b as a + (−b) and a/b as a × (1/b) , then the only operations really involved are addition and multiplication, together with taking the reciprocal to calculate 1/b.
Addition and multiplication are said to be commutative, in that the order of the numbers involved does not matter, but for more complicated sequences, the order in which operations are performed can make a difference. To aid clarity in these cases, certain conventions have been developed. Most important, operations to be performed first are written in brackets. Multiplication and addition also satisfy some other general rules about how brackets can be reinterpreted, known as associativity and distributivity, demonstrated opposite.
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