Question

Find the product of the following numbers by using suitable properties.
(1) \[26\times \left( -48 \right)+\left( -48 \right)\times \left( -36 \right)\]
(2) \[\left( -57 \right)\times \left( -19 \right)+57\]
(3) \[7\times \left( 50-2 \right)\]

Answer 1

Hint: We solve this problem by using the BODMAS rule of binary operations.
The name BODMAS stands for “Brackets of Division, Multiplication, Addition, and Subtraction”. This means that we need to follow the order in the BODMAS in the process of applying the binary operations. The binary operations are addition, subtraction, multiplication, and division.
By using this rule we find the product of given numbers.

Complete step-by-step solution
We are asked to find the product of the given numbers
Let us solve it one by one.
(1) Let us assume that the given product as
\[\Rightarrow P=26\times \left( -48 \right)+\left( -48 \right)\times \left( -36 \right)\]
We know that the rule to be followed while applying the binary operations is the BODMAS rule.
We know that the name BODMAS stands for “Brackets of Division, Multiplication, Addition, and Subtraction”. This means that we need to follow the order in the BODMAS in the process of applying the binary operations.
By using this rule let us do the multiplication first then we get
\[\Rightarrow P=\left( -1248 \right)+\left( 1728 \right)\]
Now, by using the subtraction to the above equation we get
\[\Rightarrow P=480\]
Therefore the value of first expression can be written as
\[\therefore 26\times \left( -48 \right)+\left( -48 \right)\times \left( -36 \right)=480\]
(2) Let us assume that the given expression as
\[\Rightarrow Q=\left( -57 \right)\times \left( -19 \right)+57\]
We know that the rule to be followed while applying the binary operations is the BODMAS rule.
Now, by using the BODMAS rule let us apply the multiplication first and then add then we get
\[\begin{align}
  & \Rightarrow Q=1083+57 \\
 & \Rightarrow Q=1140 \\
\end{align}\]
Therefore the value of first expression can be written as
\[\therefore \left( -57 \right)\times \left( -19 \right)+57=1140\]
(3) Let us assume that the given expression as
\[\Rightarrow R=7\times \left( 50-2 \right)\]
We know that the rule to be followed while applying the binary operations is the BODMAS rule.
Now, by using the BODMAS rule let us solve the expression inside the brackets first and then multiplication then we get
\[\begin{align}
  & \Rightarrow R=7\times \left( 48 \right) \\
 & \Rightarrow R=336 \\
\end{align}\]
Therefore the value of first expression can be written as
\[\therefore 7\times \left( 50-2 \right)=336\]

Note: Students may make mistakes only in the application of binary operations. We need to use the BODMAS rule only in order to get the correct value of a given expression.
Now, let us find the value of first expression without using the BODMAS rule as follows
\[\begin{align}
  & \Rightarrow P=26\times \left( -48 \right)+\left( -48 \right)\times \left( -36 \right) \\
 & \Rightarrow P=-1248-48\times \left( -36 \right) \\
 & \Rightarrow P=\left( -1296 \right)\times \left( -36 \right) \\
 & \Rightarrow P=46656 \\
\end{align}\]
Here, we can see that the value of the first expression is 46656 but when we used the BODMAS rule we got the value as 480.
But the correct value is 480 as it was found by using the BODMAS rule.
It is the standard rule which we need to follow at all times while applying the binary operations.