what is the definition of distributive property
Solution
Suppose we have three whole numbers a, b, and c.
Distributive property:
a × (b + c) = a × b + a × c (Distributive property for multiplication over addition)
a × (b + c) means that first of all we need to add b and c, then this result is multiplied with a.
Multiply a with b and a with c. The sum of the products, a × b + a × c is same as the a × (b + c).
a × (b – c) = a × b – a × c (Distributive property for multiplication over subtraction)
a × (b – c) means that first of all we need to subtract c from b, then this result is multiplied with a. Multiply a with b and a with c. The difference of the products, a × b – a × c is same as the a × (b – c).
Example:
Let us take a = 5, b = 19 and c = 27.
According to distributive property, the value of the expression 5 × (19 + 27) must be equal to the expression 5 × 19 + 5 × 27 and the value of the expression 5 × (27 – 19) must be equal to the value of the expression 5 × 27 – 5 × 19.
These can be verified as,
5 × (19 + 27) = 5 × 46 = 230
5 × 19 = 95 and 5 × 27 = 135
∴ 5 × 19 + 5 × 27 = 95 + 135 = 230
Thus, 5 × (19 + 27) = 5 × 19 + 5 × 27
In the similar manner, it can be verified that 5 × (27 – 19) = 5 × 27 – 5 × 19.