Question

Observe the following pattern and fill in the blanks
$\begin{align}
  & 9\times 9+7=88 \\
 & 98\times 9+6=888 \\
 & 987\times 9+5=8888 \\
 & 9876\times 9+4=........ \\
 & 98765\times 9+3=........... \\
\end{align}$

Answer 1

Hint: Observe the pattern you will find out a way to get to your answer. We get $88$ in first when we multiply $9$ with $9$ then add $7$ to it.

Complete step by step solution:
Looking at the question we find out that it’s a BODMAS calculation.
BODMAS is the rule for calculation. “BODMAS is an acronym and it stands for Bracket, Order, Division, Multiplication, Addition, and Subtraction”.
The BODMAS rule states that we should calculate the brackets first, then the orders, then any division or multiplication, and finally any addition or subtraction.
In this question also BODMAS rule is applicable and helpful to get to your answer.
In the question we have only two operations, multiplication and additions. So, according to BODMAS we will do multiplication first followed by addition.
Using BODMAS in first equation:
LHS:- $9\times 9+7$
Step-1 (Multiplication):- $9\times 9=81$
Step-2 (Addition):- $81+7=88$
Therefore, we get LHS=RHS , so our observation was correct
Using BODMAS in second equation:-
LHS:-$98\times 9+6$
$\begin{align}
  & 98\times 9=882 \\
 & 882+6=888 \\
\end{align}$
LHS=RHS
Following the same pattern let us jump to fourth equation.
$\begin{align}
  & 9876\times 9+4 \\
 & \to 9876\times 9=88884 \\
 & \to 88884+4=88888 \\
\end{align}$
Fifth equation:-
$\begin{align}
  & 98765\times 9+3 \\
 & \to 98765\times 9=888885 \\
 & \to 888885+3=888888 \\
\end{align}$
Therefore, the correct answer is $88888$ and $888888$.

Note:
Shortcut to this problem is just observing the pattern. In the first equation, we have $88$ then $888$ followed by $8888$. Therefore next we will have $88888$ and $888888$