# Math Properties

## 35 terms

a - b = a + (-b)

### Definition of Division

a ÷ b = a/b = a x 1/b, b≠ 0

### Distributive Property for Subtraction

a(b - c) = ab - ac

0 x a = 0

-1 x a = -a

### Opposite of a Sum

-(a + b) = -a + (-b)

-(a - b) = b - a

### Opposite of a Product

- (ab) = -a x b = a x (-b)

- (-a) = a

a = a

### Symmetric Property

If a = b, then b = a

### Transitive Property

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

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

### Subtraction Property

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

### Multiplication Property

If a = b, then ac = bc

### Division Property

If a = b and c ≠ 0, then a/c = b/c

### Substitution Property

If a = b, then b may be substituted for a in any expression to obtain an equivalent expression.

### Transitive Property

If a ≤ b and b ≤ c, then a ≤ c.

If a ≤ b, then a + c ≤ b + c

### Subtraction Property

If a ≤ b, then a - c ≤ b - c

### Multiplication Property

If a ≤ b and c > 0, then ac ≤ bc. If a ≤ b and c < 0, then ac ≥ bc. ( REVERSE INEQAULITY WHEN X or ÷ by a NEGATIVE)

### Division Property

If a ≤ b and c > 0, then a/c ≤ b/c. If a ≤ b and c < 0, then a/c ≥ b/c.

### Identity Property of Addition

7 + 0 = 7 ( Identity Element = 0)

### Inverse Property of Addition

3 + -3 = 0 (Identity Element = the opposite)

### Inverse Property for Multiplication

(Identity Element = reciprocal)

### Identity Property of Multiplication

(Identity element = 1) 10 x 1 = 10

a + b = b + a

ab = ba

### Associative Property of Addition

(a + b) + c = a + (b + c)

ab(c) = a(bc)

### Identity Property of Addition

a + 0 =a, 0+a = a

### Identity Property of Multiplication

a x 1 = a, 1 x a = a

a + (-a) = 0

### Inverse Property of Multiplication

a x 1/a = , a ≠ 0

### Distributive Property

a( b + c) = ab + ac