This lesson gives you a list of nine important properties for simplifying algebraic expressions.

Let a,b,and c represent real numbers.

**Definition of subtraction **: a - b = a + (-b)

**Definition of division **: a ÷ b = a/b = a × 1/b, b ≠ 0

**Multiplication by zero** : 0 × a = 0

**Multiplication by -1** : -1 × a = -a

**Distributive property for subtraction** : a(b - c) = ab - ac

**Opposite of a difference** : -(a - b) = b - a

**Opposite of a sum** : -(a + b) = -a + -b

**Opposite of a product** : -(ab) = -a × b = a × -b

**Opposite of an opposite** : -(-a) = a

Match the equation with the appropriate property name

**A.** 4(x - y) = 4x - 4y **B.** (x - 2) ÷ 5z = (x - 2) / 5z

**C.** -(t-1) = -1(t-1)

**D.** 2d - 7 = 2d + (-7)

**E.** -( 2d - 7) = 7 - 2d

**F.** -[-(8 + s)] = 8 + s

**G.** -(12xy) = 12(-xy)

**H.** -[3 + (-a)] = -3 + [-(-a)]

**I.** (10x^{2} - 15y)(0) + -x = 0 + -x

**1.** Definition of division

**2.** Opposite of a sum

**3.** Opposite of an opposite

**4.** Opposite of a product

**5.** Multiplication by zero

**6.** Multiplication by -1

**7.** Opposite of a difference

**8.** Distributive property for subtraction

**9.** Definition of subtraction