Evaluating Expressions After Number Interchange

The problem asks us to interchange the given two numbers, 4 and 6, in two different mathematical expressions and then evaluate the resulting expressions. We need to find the new values of Expression (I) and Expression (II) respectively after performing the interchange.

Step 1: Understanding the Number Interchange

We are given two numbers: 4 and 6. The instruction is to interchange these numbers. This means wherever the number 4 appears in the original expressions, we will replace it with 6, and wherever the number 6 appears, we will replace it with 4. We will then evaluate the new expressions using the standard order of operations (BODMAS/PEMDAS).

Step 2: Evaluating Expression (I) After Interchange

The original Expression (I) is: $8 – 4 × 3 + 6 ÷ 2$

After interchanging 4 and 6, the new Expression (I) becomes:

$8 – \mathbf{6} × 3 + \mathbf{4} ÷ 2$

Now, let's evaluate this new expression using the order of operations (Division and Multiplication first, then Addition and Subtraction from left to right).

• First, perform the division: $4 ÷ 2 = 2$
• The expression is now: $8 – 6 × 3 + 2$
• Next, perform the multiplication: $6 × 3 = 18$
• The expression is now: $8 – 18 + 2$
• Finally, perform addition and subtraction from left to right: $8 – 18 = -10$
• Then: $-10 + 2 = -8$

So, the value of Expression (I) after interchanging the numbers is -8.

Step 3: Evaluating Expression (II) After Interchange

The original Expression (II) is: $4 + 3 × 6 – 8 ÷ 2$

After interchanging 4 and 6, the new Expression (II) becomes:

$\mathbf{6} + 3 × \mathbf{4} – 8 ÷ 2$

Now, let's evaluate this new expression using the order of operations.

• First, perform the division: $8 ÷ 2 = 4$
• The expression is now: $6 + 3 × 4 – 4$
• Next, perform the multiplication: $3 × 4 = 12$
• The expression is now: $6 + 12 – 4$
• Finally, perform addition and subtraction from left to right: $6 + 12 = 18$
• Then: $18 – 4 = 14$

So, the value of Expression (II) after interchanging the numbers is 14.

Conclusion

After interchanging the numbers 4 and 6, the value of Expression (I) is -8 and the value of Expression (II) is 14. The values of the expressions are -8 and 14 respectively.

Revision Table: Expression Evaluation

Additional Information: Order of Operations

When evaluating mathematical expressions involving multiple operations, we follow a specific order to ensure a consistent result. This order is commonly known as BODMAS or PEMDAS.

• BODMAS: Brackets, Orders (powers/roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
• PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

In this problem, we used Division and Multiplication before Addition and Subtraction. When operations of the same priority level (like Division and Multiplication, or Addition and Subtraction) appear, we perform them from left to right in the expression.