Definition
Distributive property
The distributive property multiplies one factor by every term inside a sum or difference.
Continue from this idea into connected AXIO math.
Defining relationship
Share the outside factor with every term inside.
Multiplication distributes over addition and subtraction: a(b + c) = ab + ac and a(b − c) = ab − ac. Applying it preserves the value of the expression.
- 1
outside factor meets the whole group
- 2
share 3 with both terms
- 3
calculate both products
- 4
same value
- The 3 reaches every inside term
- The expression keeps its value
What it means
Split a difficult number into useful parts. Multiply the outside factor by each part, then combine the partial results. Every term inside the parentheses must receive the factor.
Remember it
Share the outside factor with every term inside.
Example
6 × 27 = 6 × (20 + 7) = (6 × 20) + (6 × 7) = 120 + 42 = 162.
Watch for
6(20 + 7) is not 120 + 7; the 6 must multiply both 20 and 7.
Common mix-up
Distributing changes one product into equivalent partial products; it does not change the total.
Exact meaning
Multiplication distributes over addition and subtraction: a(b + c) = ab + ac and a(b − c) = ab − ac. Applying it preserves the value of the expression.