# Basic calculations

The order of operations is always from left to right. Brackets are calculated first, followed by power calculations. Then multiplication and division from left to right and finally addition and subtraction.

**E****xample**** 1**

2 - 5·3 + 2 = 2 - 15 + 2 = -13 + 2 = -11

**E****xample**** 2**

(10 - 5)·3 + 2·2 - 2·(-2) = 5·3 + 4 + 4 = 15 + 4 + 4 = 23

**Properties of Real Numbers**

**Properties of Real Numbers**

For all real numbers** *** a* and

**b**1. *Associative laws* **a + b = b + a, ab = ba**

2. *Commutative laws* **a + (b + c) = (a + b) + c, a (bc) = (ab) c**

3. *Distributive laws* **a (b + c) = ab + ac**

4. *Identity elements* * 0 + a = a , 1a = a* (

*a*is arbitrary)

5. *Inverse elements* * x + a = 0* (denoted by x = -

*a*)

6. *M**ultiplicative inverse* ** ****xa**** = 1** (denotes *x* = 1 /* a, a* ≠ 0)

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