Question

Use the correct set of symbol in the $\underline{{}}$ to make the equation \[8\underline{{}}8\underline{{}}8\underline{{}}8=65\] true
\[\begin{align}
  & A.+,\text{ }\div ,\text{ }\times \\
 & B.\times ,\text{ }-,\text{ }\div \\
 & C.-,\text{ }+,\text{ }\times \\
 & D.\times ,\text{ }+,\text{ }\div \\
\end{align}\]

Answer 1

Hint: We are given \[8\underline{{}}8\underline{{}}8\underline{{}}8=65\] we have to fill those $\underline{{}}$ such that equation holds true. To do that, we will check each option one by one, the option for which equation holds true will become our required answer. We use BODMAS rule about the order of application of $+,\text{ }-,\text{ }\times \text{ and }\div $

Complete step by step answer:
We are asked to fill $\underline{{}}$ so that our equation \[8\underline{{}}8\underline{{}}8\underline{{}}8=65\] holds true.
To do so, we will check each option one by one.
Option A: \[+,\text{ }\div ,\text{ }\times \]
If we will apply in our box with $+,\text{ }\div ,\text{ }\times $ we will get:
\[8+8\div 8\times 8\]
To simplify this, we use the BODMAS rule, which says first we divide then multiply and lastly we add. So,
\[\begin{align}
  & 8+8\div 8\times 8=8+1\times 8\left( \text{as }8\div 8=1 \right) \\
 & \Rightarrow 8+8\left( \text{as }8\times 1=8 \right) \\
 & \Rightarrow 16\left( \text{as }8+8=16 \right) \\
\end{align}\]
So, we get \[8+8\div 8\times 8=16\ne 65\]
So, $+,\text{ }\div ,\text{ }\times $ is an incorrect option.
Option B: \[\times ,\text{ }-,\text{ }\div \]
Applying this we get:
\[8\times 8-8\div 8\]
We apply BODMAS again. So, first we divide then multiply and lastly subtract. So,
\[\begin{align}
  & 8\times 8-8\div 8=8\times 8-1\left( \text{as }8\div 8=1 \right) \\
 & \Rightarrow 64-1\left( \text{as }8\times 8=64 \right) \\
 & \Rightarrow 63 \\
\end{align}\]
So, we get \[8\times 8-8\div 8=63\ne 65\]
Hence, $\times ,\text{ }-,\text{ }\div $ is an incorrect option.
Option C: \[-,\text{ }+,\text{ }\times \]
Applying this we get:
\[8-8+8\times 8\]
Again, using BODMAS we first multiply then add and lastly subtract. So,
\[\begin{align}
  & 8-8+8\times 8=8-8+64\left( \text{as }8\times 8=64 \right) \\
 & \Rightarrow 72-8\left( \text{as }8+64=72 \right) \\
 & \Rightarrow 64 \\
\end{align}\]
So, we get \[8-8+8\times 8=64\ne 65\]
Hence, $-,\text{ }+,\text{ }\times $ is an incorrect option.
Option D: \[\times ,\text{ }+,\text{ }\div \]
Applying this, we get:
\[8\times 8+8\div 8\]
Using BODMAS, we get:
\[\begin{align}
  & 8\times 8+8\div 8=8\times 8+1\left( \text{as }8\div 8=1 \right) \\
 & \Rightarrow 64+1\left( \text{as }8\times 8=64 \right) \\
 & \Rightarrow 65 \\
\end{align}\]
So, we get \[8\times 8+8\div 8=65\]
Hence, equation holds true so our correct option is $\times ,\text{ }+,\text{ }\div $
Therefore, option D is correct.

Note:
If we don't apply the BODMAS rule then calculations will not be considered correct. BODMAS tells us about the sequence of the application of all the arithmetic tools. It will help us always to reach the correct calculation. In BODMAS, we first divide then multiply then add and lastly subtract, we always follow this rule while solving arithmetic questions. In these types of questions, the best way to solve is using options since it is going to be hectic, time consuming to guess the right operation at the right place in the expression.