**Properties of Equality**

Let a, b, and c be real numbers.

### Addition Property of Equality

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

i.e. When two quantities
are equal, if you add the same number to both quantities, the sums
will also be equal.

### Subtraction Property of Equality

If a = b, then a - c = b - c.

i.e. When two
quantities are equal, if you subtract the same number from both
quantities, the differences will also be equal.

### Multiplication Property of Equality

If a = b, then ac = bc
and ca = ba.

i.e. When two
quantities are equal, if you multiply them by the same number, the
products will also be equal.

### Division Property of Equality

If a = b and c does NOT
equal 0, then a/c = b/c.

i.e. When two
quantities are equal, if they are divided by the same non-zero number,
the quotients are also equal.

### Reflexive Property of Equality

a = a

i.e. Any number is
equal to itself.

### Symmetric Property of Equality

If a = b, then b = a.

### Transitive Property of Equality

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

##### "Structures are the weapons of the
mathematician."

Bourbaki