# Distributive property

**Distributive property**: Named the 'Distributive law' because in essence, you are distributing something as you separate or break it into parts. The distributive law makes numbers easier to work with. In algebra when we use the distributive law, we're expanding (distributing).

The distributive law of multiplication over addition / subtraction: multiplication may be distributed over addition / subtraction.

For any three whole numbers a, b and c,a x (b + c) = (a x b) + ( a x c ) a x ( b - c ) = a x b - a x c OR (a x b ) + ( a x c ) = a x ( b + c) ( a x b ) - ( a x c) = a x ( b - c) This is called the Distributive law of Addition over multiplication for the set of W. |

**Some solved examples :**

1) 125 x 8 + 125 x 92

= 125 x( 8 + 92 )

= 125 x 100

= 12,500

2) 3 × (1 + 99) = (3 × 1) + (3 × 99)

= 3 + 297

= 300

3) 4 ( a + 5 )

= 4 x a + 4 x 5

= 4a + 20

4) Solve using distributive law :

250 x 998

= 250 x ( 1000 - 2)

= 250 x 1000 - 250 x 2

= 250,000 - 500

= 249,500

5) Solve using distributive law :

94 x 123 + 6 x 123

= 123 x ( 94 + 6 )

= 123 x 100

= 12,300

6) Solve using distributive law :

5(b -4)= 12

5 x b - 5 x 4 = 12

5b - 20 = 12

5b = 12 + 20

5b = 22

∴ b = 22/5 = 4.4

**Whole numbers**

• Closure property

• Commutative property

• Associative property

• Additive Identity

• Distributive property

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