# Hands On: Model the Distributive Property

Distributive Property

• Demonstrate how the distributive property works

to simplify an expression containing parentheses to an expression without parentheses using multiplication

• show the partial products for each and find the sum.

• write a multiplication sentence for each.

### Comments for Hands On: Model the Distributive Property

 Oct 19, 2012 Model the Distributive Property by: Staff Answer The Distributive Property combines the following two operations in mathematics: multiplication and addition . It is formally defined as "the distribution of multiplication over addition". It is used to simplify an expression containing parentheses to an expression without parentheses. • Four examples of how the distributive property is used:          i. parentheses containing variables multiplied by a constant                   3(a + b) = 3*a + 3*b = 3a + 3b multiplication sentence: three times (a plus b).          ii. parentheses containing variables multiplied by a variable                   y = x(a + b) = x*a + x*b = ax + bx multiplication sentence: x times (a plus b).          iii. parentheses containing numbers multiplied by a number                   3(20 + 5) = 3*20 + 3*5 = 60 + 15 multiplication sentence: three times (20 plus 5).          iv. Using exponents 4m²(2m² - m³) = 4m² * 2m² - 4m² * m³) = 4*2*m⁽²⁺²⁾ - 4*m⁽²⁺³⁾ = 4*2*m⁴ - 4*m⁵ = 8m⁴ - 4m⁵ Thanks for writing. Staff www.solving-math-problems.com