Question

(i) With the help of an example explain the distributive property.
(ii) Check the distributive property of division over addition is true or false.

Answer 1

(i) Distributive property: When you distribute something, you are dividing it into parts. In math, the distributive property helps simplify difficult problems because it breaks down expressions into the sum or difference of two numbers.
Let A, B and C are the variable, then
$A(B\pm C)=AB\pm AC$
For exmaple: let $5(2+7)=(5\times 2)+(5\times 7)$
L.H.S $=5(2+7)=5\times \left(9\right)=45$
R.H.S $=(5\times 2)+\left(\right(5\times 7)=10+35=45$

(ii) Let $A,B$ and $C$ are the variabel, than
\(A$÷$(B+C)=(A$÷$B)+(A$÷$C)\)
let $A=3,B=2$ and $C=1$
L.H.S \(=3$÷$(2+1)=3/3=1\)
R.H.S \(=(3$÷$2)+(3$÷$1)=1.5+3=4.5\)
Therefore, L.H.S$\ne$ R.H.S
\(A$÷$(B+C)\neq(A$÷$B)+(A$÷$C)\)
Hence, Distributive property (division over addition) is false.