Question

Which of the following sets of the numbers will make the number sentence true?
\[\dfrac{\,\,\,\,\,\,}{\,\,\,\,}\div \,\,\dfrac{\,\,\,\,\,\,}{\,\,\,\,}+\dfrac{\,\,\,\,\,\,}{\,\,\,\,}=12\]
(a) \[(6,8,12)\]
(b) \[(6,8,16)\]
(c) \[(16,8,10)\]
(d) \[(6,8,10)\]

Answer 1

Hint: In order to solve the expression we need to use the concept of the addition and the concept of the division with the help of BODMAS rule in a proper way. We need to check all the options and find the best fit for our question.

Complete step-by-step answer:
Solve for the given options as
\[(i)6\div 8+12\ \ldots \ldots (1)\]
Rewrite the equation after simplification by using BODMAS rule
Firstly solved the division part of the expression and then addition
\[6\div 8=0.75\]
Substitute the value of \[6\div 8\] in the equation \[(1)\]
\[\Rightarrow 0.75+12\]
Use the concept of the addition
\[\Rightarrow 12.75\]
Therefore
\[12.75\ne 12\]
Hence, option (a) is not the correct answer.
\[(ii)\]\[6\div 8+16\,\,\,\,\,\,\,\,\,........(2)\]
Rewrite the equation after simplification by using BODMAS rule
\[6\div 8+16\]
Then
\[6\div 8=0.75\]
Substitute the value of \[6\div 8\]in the equation \[(2)\]
\[\Rightarrow 0.75+16\]
Simplify the expression
\[\Rightarrow 16.75\]
Therefore
\[16.75\ne 12\]
Hence, option (b) is not the correct answer.
\[(iii)\]\[16\div 8+10\,\,\,\,\,\,\,\,\,\,..........(iii)\]
Use the concept of the division
\[16\div 8\]
Rewrite the equation after simplification by using BODMAS rule
\[\Rightarrow 16\div 8=2\]
Substitute the value of \[16\div 8\]in the equation\[(iii)\]
\[\Rightarrow 2+10\]
Use the concept of the addition
\[\Rightarrow 12\]
\[\Rightarrow 12=12\]
Hence, option (c) is the correct answer.
\[(iv)\]\[6\div 8+10\]
Use the concept of the division
\[6\div 8\]
Rewrite the equation after simplification by using BODMAS rule
\[\Rightarrow 0.75\]
Substitute the value of \[6\div 8\]in the equation\[(iv)\]
\[\Rightarrow 0.75+10\]
Use the concept of the addition
\[\Rightarrow 10.75\]
Therefore
\[\Rightarrow 10.75\ne 12\]
Hence, option (d) is not the correct answer.

Thus, option (c) is the correct answer.

Note: The BODMAS rules apply in this way:
B = Bracket
O = of
D = Division
M = Multiplication
A = Addition
S = Subtraction
Whenever we are operating on integers with multiple operations, we must follow the above order.