Question

Find the value of the following:
 \[\begin{align}
  & \left( a \right)297\times 17+297\times 3 \\
 & \left( b \right)54279\times 92+8\times 54279 \\
 & \left( c \right)81265\times 169-81265\times 69 \\
 & \left( d \right)3845\times 5\times 782+769\times 25\times 218 \\
\end{align}\]

Answer 1

Hint: First and foremost we have to apply the rule of “BODMAS” in all of the equations, i.e., the brackets are put according to ease, to make equations simpler to solve. The number common* in the brackets are taken out as common from the brackets (*if any) Then the brackets are solved in sequence of which they are put in the equation in order to simplify. Further operations (Addition, subtraction, multiplication and division) are performed to find out the final answer.

Complete step-by-step answer:
There are four types of the most basic operation in “MATHEMATICS”, i.e., addition, subtraction, multiplication and division.
The name “BODMAS” is expanded as “Bracket Order Division Multiplication Addition Subtraction”. As the name ”BODMAS” suggests , the problems in the brackets are solved by the sequence of operations, i.e., first step(operation) is division, second is multiplication, third is addition and fourth and last is subtraction.

(a) On applying the “BODMAS” rule, we get,
\[\left( 297\times 17 \right)+\left( 297\times 3 \right)\] ………. \[eq.1\]
On analyzing the above equation properly we can see that the number 297 is common in both the brackets. The number 297 is taken out as a common number from both of the brackets to make it easier to solve.
So, the equation now becomes,
\[297\times \left( 17+3 \right)\] ………. \[eq.2\]
  On solving the above equation, we get,
\[297\times 20=5940\]

(b) We apply the same rule of “BODMAS” in this part as we applied in the part above,
 \[\left( 54279\times 92 \right)+\left( 8\times 54279 \right)\] ………. \[eq.1\]
After going through the above equation, we get the number 54279 common in both the brackets. The number 54279 is taken out as a common number from both of the brackets for convenience in solving the above equation.
\[54279\times \left( 92+8 \right)\] ………. \[eq.2\]
On solving the equation further, we get,
\[54279\times 100=5427900\]

(c) In this part we will apply the same rule of “BODMAS” but for subtraction.
After applying the rule, we get,
\[\left( 81265\times 169 \right)-\left( 81265\times 69 \right)\] ………. \[eq.1\]
This equation seems easier to solve now. The above equation has the number 81265 in common in both of the brackets. The number 81265 is taken out as common from both of the brackets. The equation now becomes,
\[81265\times \left( 169-69 \right)\] ………. \[eq.2\]
Further, solving the equation gives,
\[81265\times 100=8126500\]

(d) This part seems different from all of the other three parts. Applying the same rule of “BODMAS” gives,
\[\left( 3845\times 5\times 782 \right)+\left( 769\times 25\times 218 \right)\] ………. \[eq.1\]
But, the above equation can be made easier. To make the equation easier to solve we put some more brackets in the equation as shown below,
\[\left( \left( 3845\times 5 \right)\times 782 \right)+\left( 769\times \left( 25\times 218 \right) \right)\] ……….\[eq.2\]
The above equation seems complicated, but it is easier to solve. Solving the terms in the brackets sequentially gives,
 \[\left( 19225\times 782 \right)+\left( 769\times 5450 \right)\] ………. \[eq.3\]
Now, the above equation is further solved.
\[15033950+4191050=19225000\]
So, the final answers are,
\[\begin{align}
  & \left( a \right)297\times 17+297\times 3=5940 \\
 & \left( b \right)54279\times 92+8\times 54279=5427900 \\
 & \left( c \right)81265\times 169-81265\times 69=8126500 \\
 & \left( d \right)3845\times 5\times 782+769\times 25\times 218=19225000 \\
\end{align}\]

Note: Here we solved the problems using the rule of “BODMAS”, but there are two more types that can be used to solve problems easily. The two types are namely “BIDMAS” and “PEMDAS”, “BIDMAS” and “PEMDAS” have same functionality but using different words. “BIDMAS” stands for “Brackets Indices Division Multiplication Addition Subtraction” and “PEMDAS” stands for “Parenthesis Exponents Multiplication Division Addition Subtraction”.