Question

distributive property equations & expressions
vocabulary
distributive property of multiplication over addition: multiplying a _ by a number is the same as multiplying each number in the _ by that number and _ the products.
distributive property of multiplication over subtraction: multiplying a _ by a number is the same as multiplying each number in the _ by that number and _ the products.
guided notes:
what does the word \distribute\ mean?
numerical example of the distributive property:
3(4 + 6)=
3×4+3×6=
2(8 - 3)=
2×8 - 2×3=
algebraic example of the distributive property:
a(b + c)=
a(b - c)=
the distributive property can be used to _ algebraic expressions.

Explanation:

Step1: Define distributive property over addition

Multiply a sum by a number = multiply each addend by the number and add products.

Step2: Define distributive property over subtraction

Multiply a difference by a number = multiply each number in the difference by the number and subtract products.

Step3: Answer what "distribute" means

To give out or spread.

Step4: Solve numerical example 1

$3(4 + 6)=3\times4+3\times6 = 12 + 18=30$.

Step5: Solve numerical example 2

$2(8 - 3)=2\times8-2\times3=16 - 6 = 10$.

Step6: Write algebraic example 1

$a(b + c)=ab+ac$.

Step7: Write algebraic example 2

$a(b - c)=ab - ac$.

Step8: State use of distributive property

Simplify algebraic expressions.

Answer:

• Distributive Property of Multiplication Over Addition: Multiply a sum by a number is the same as multiplying each number in the sum by that number and adding the products.
• Distributive Property of Multiplication Over Subtraction: Multiply a difference by a number is the same as multiplying each number in the difference by that number and subtracting the products.
• What "distribute" means: To give out or spread.
• Numerical example 1: $3(4 + 6)=30$, $3\times4+3\times6 = 30$.
• Numerical example 2: $2(8 - 3)=10$, $2\times8-2\times3 = 10$.
• Algebraic example 1: $a(b + c)=ab + ac$.
• Algebraic example 2: $a(b - c)=ab - ac$.
• Use of distributive property: Simplify algebraic expressions.