Question

018
Verify the following
3/7× (5/6+12/13)= (3/7×5/6) + (3/7× 12/13)​

Answer 1

Step-by-step explanation:

Given :

$\rm{\dfrac{3}{7}\times(\dfrac{5}{6}+\dfrac{12}{13})=(\dfrac{3}{7}\times\dfrac{5}{6})+(\dfrac{3}{7}\times\dfrac{12}{13})}$

To find :

To verify the equation

Concept :

First , find the value of LHS (Left hand side) and then find the value of RHS (Right hand side) .

If the value of both hand side will come same then the equation will be verified .

Solution :

LHS -:

$:\Rightarrow\rm{LHS=\dfrac{3}{7}\times(\dfrac{5}{6}+\dfrac{12}{13})}$

So , the L.C.M. of 6 and 13 is 78 .

$:\Rightarrow\rm{LHS=\dfrac{3}{7}\times(\dfrac{65+72}{78})}$

$:\Rightarrow\rm{LHS=\dfrac{3}{7}\times(\dfrac{137}{78})}$

$:\Rightarrow\rm{LHS=\dfrac{\cancel{3}}{7}\times\dfrac{137}{\cancel{78}}}$

$:\Rightarrow\rm{LHS=\dfrac{137}{182}}$

RHS -:

$:\Rightarrow\rm{RHS=(\dfrac{\cancel{3}}{7}\times\dfrac{5}{\cancel{6}})+(\dfrac{3}{7}\times\dfrac{12}{13})}$

$:\Rightarrow\rm{RHS=\dfrac{5}{14}+\dfrac{36}{91}}$

L.C.M. of 14 and 91 is 182

$:\Rightarrow\rm{RHS=\dfrac{65+72}{182}}$

$:\Rightarrow\rm{RHS=\dfrac{137}{182}}$

Hence , verified ...

Answer 2

The answer to the question could be:-

The question has asked if the 3/7 * (5/6 + 12/13) = (3/7 * 5/6) + (3/7 * 12/13) and theoretically, it is correct for this comes under the Distributive Property of Multiplication. Yet let's mathematically solve the verify the answer and also verify the Distributive Property of Multiplication.

The solution to the question is:-

Left Hand Side = 3/7 * (5/6 + 12/13)

                         = 3/7 * 137/78

                         = 137/182

Right Hand Side = (3/7 * 5/6) + (3/7 * 12/13)

                           = 5/14 + 36/91

                           = 137/182

Because L.H.S or Left Hand Side = R.H.S or Right Hand Side

That is, L.H.S = 137/182 and R.H.S is also equal to = 137/182;

The question is verified and so is the Distributive Property of Multiplication.