Question

Using the suitable properties, evaluate the following:
1) \[8 \times 53 \times \left( { - 125} \right)\]
2) \[\left( { - 6} \right) \times 2 \times 8 \times 5\]
3) \[26 \times \left( { - 48} \right) + \left( { - 48} \right) \times \left( { - 36} \right)\]

Answer 1

Hint:
Here we will perform the multiplication to get the value of the expression. We will multiply those numbers which will form the numbers which are multiple of 10 which helps us to solve the expression easily.

Complete Step by Step Solution:
1) Given expression is \[8 \times 53 \times \left( { - 125} \right)\]
We will use the basic concept of the multiplication to solve this expression. We will multiply 8 with \[\left( { - 125} \right)\] to solve the expression in a more simplified way. Therefore, we get
\[8 \times 53 \times \left( { - 125} \right) = 8 \times \left( { - 125} \right) \times 53\]
Now by applying the basic multiplication we get
\[ \Rightarrow 8 \times 53 \times \left( { - 125} \right) = \left( { - 1000} \right) \times 53\]
\[ \Rightarrow 8 \times 53 \times \left( { - 125} \right) = - 53000\]
Hence the value of the given expression is equal to \[ - 53000\]

2) Given expression is \[\left( { - 6} \right) \times 2 \times 8 \times 5\]
We will use the basic concept of the multiplication to solve this expression. We will multiply \[\left( { - 6} \right)\] with 8 firstly and 2 with 5 to solve the expression in a more simplified way. Therefore, we get
\[\left( { - 6} \right) \times 2 \times 8 \times 5 = \left( { - 6} \right) \times 8 \times 2 \times 5\]
Now by applying the basic multiplication we get
\[ \Rightarrow \left( { - 6} \right) \times 2 \times 8 \times 5 = \left( { - 48} \right) \times 10\]
\[ \Rightarrow \left( { - 6} \right) \times 2 \times 8 \times 5 = - 480\]
Hence the value of the given expression is equal to \[ - 480\]

3) Given expression is \[26 \times \left( { - 48} \right) + \left( { - 48} \right) \times \left( { - 36} \right)\]
We will use the basic concept of the multiplication to solve this expression. We will take \[\left( { - 48} \right)\] common and then solve the equation in the simplified form. Therefore, we get
\[26 \times \left( { - 48} \right) + \left( { - 48} \right) \times \left( { - 36} \right) = \left( { - 48} \right)\left( {26 - 36} \right)\]
Now by applying the basic multiplication we get
\[ \Rightarrow 26 \times \left( { - 48} \right) + \left( { - 48} \right) \times \left( { - 36} \right) = \left( { - 48} \right)\left( { - 10} \right)\]
\[ \Rightarrow 26 \times \left( { - 48} \right) + \left( { - 48} \right) \times \left( { - 36} \right) = 480\]

Hence the value of the given expression is equal to \[480\].

Note:
We should also know that addition is the operation in which two numbers are combined to get the result. Here we have to note that while solving these types of equations we have to use the rule of BODMAS. We know that in mathematics, a mathematical expression is solved according to the BODMAS Rule. We should apply the mathematical operations in a particular order which is given by the letters of BODMAS and letters of BODMAS are defined as B-Brackets, O-Of, D-Division, M-Multiplication, A-Addition and S-Subtraction.