Axioms of equality are basic rules for using the equals sign…

**The Additive Axiom Of Equality:**

If a=b and c=d, then a+c=b+d.

**The Additive Axiom Of Inequality:**

If a>b, then a+c>b+c.

**Identity Element For Addition:**

Any number added to 0 gives the original number, for instance, n+0=n.

**Identity Element For Multiplication:**

Any number multiplied by 1 gives the original number, for instance, n*1=n.

**Multiplicative Axiom Of Equality:**

If a=b and c=d, then ac=bd.

**Negative Multiplication Property Of Inequality:**

You must reverse the inequality sign when multiplying or dividing by a negative number.