Algebra and General Mathematics: Basic Rules of Algebra

Review notes in Basic Rules of Algebra. This will help you prepare in taking the Engineering Board Exam or simply reviewing for your Algebra subject.

Algebra and General Mathematics: Basic Rules of Algebra

PROPERTIES OF REAL NUMBERS

1. Closure Property

Addition           :      a + b
Multiplication          :      a · b

2. Commutative Property

Addition          :      a + b = b + a
                                     :      4m + n2 = n2 + 4m
Multiplication          :      ab = ba
                                                         :      (m – 3)n2 = n2(m – 3)

3. Associative Property of Addition

Addition          :      (a + b) + c = a + (b + c)
                                        :      (m + 12) + 3n2 = m + (12 + 3n2)
Multiplication          :      (ab)c = a(bc)
                                                    :      (4m · 3n)6 = 4m(3n · 6)

4. Distributive Property

Right Distributive          :      a(b + c) = ab + ac
                                           :     n(m + 9) = mn + 9n
Left Distributive          :      (a + b)c = ac + bc
                                          :      (m + 9)n = mn + 9n

5. Additive Identity Property

a + 0 = a           :      4m2 + 0 = 4m2

6. Multiplicative Identity Property

a · 1 = 1 · a = a           :      (5m2)(1) = (1)(5m2) = 5m2

7. Additive Inverse Property

a + (-a) = 0           :      7m2 + (-7m2) = 0

8. Multiplicative Inverse Property

a · 1/a = 1,  a ≠ 0           :      (3m2 + 4) [1 / (3m2 + 4)] = 1

PROPERTIES OF EQUALITY

1. Reflexive Property

a = a

2. Symmetric Property

If a = b, then b = a

3. Transitive Property

If a = b, and b = c, then a = c

4. Addition Property

If a = b, then a + c = b + c

5. Subtraction Property

If a = b, then a – c = = b – c

6. Substitution Property

If a = b, then a can be replaced by b in any expression involving a.

7. Multiplicative Property

If a = b, then ac = bc

8. Division Property

If a = b, then a/c = b/c, with c ≠ 0

9. Cancellation Property

If a + c = b + c, then a = b
If ac = bc, then a = b, provided c ≠ 0

OPERATIONS WITH ZERO AND INFINITY

1. a + 0 = a
2. a – 0 = a
3. a(0) = 0
4. 0/a = 0
5. a/∞ = 0
6. 0a = 0
7. a(∞) =
8. a/0 = undefined
9. ∞/a = ∞
10. a0 = 1, a ≠ 0

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