Exploring the Value of ab × cd with Given Variables a2, b3, c4, d5

Understanding how to solve expressions involving variables is a fundamental concept in algebra. This article will guide you through the process of finding the value of ab × cd given the variables a2, b3, c4, and d5. We will use the BODMAS rule to ensure that the calculation is performed correctly.

Introduction to BODMAS Rule

BODMAS stands for Bracket, Orders, Division and Multiplication, Addition, and Subtraction. This rule dictates the order in which operations should be performed in an arithmetic expression to get the correct result.

Substitution and Application of BODMAS

Given the expression ab × cd with the values a2, b3, c4, and d5, let's apply the BODMAS rule step by step.

Step 1: Substitute the Values

Let's substitute the given values into the expression:

ab × cd 2 × 3 × 4 × 5

Step 2: Solve within Brackets (if applicable)

In this particular problem, there are no brackets, orders (exponents), or division and multiplication operations to solve within brackets first. However, we will follow the rule strictly and handle each step in the correct order.

Step 3: Perform Multiplications

The next step is to perform the multiplications. We can group the multiplications in any order as multiplication is both associative and commutative. Grouping them as 5 × 9 (from (2 × 3) × (4 × 5)) will simplify the calculation:

2 × 3 6

4 × 5 20

6 × 20 120 / 2.5 5 × 9

5 × 9 45

Conclusion and Importance of BODMAS

The value of ab × cd when a2, b3, c4, and d5 is 45. By following the BODMAS rule, we ensure that our calculations are both accurate and consistent.

Key Takeaways

The BODMAS rule is crucial for solving mathematical expressions correctly. Substituting values into variables and then performing operations in the correct order is essential for solving algebraic expressions. Multiplication can be performed in any order, but understanding the rule helps in breaking down complex expressions into simpler steps.

By mastering the BODMAS rule and understanding variable substitution, you can effectively solve a wide range of mathematical problems. This skill is not only important for academic pursuits but also in various real-world applications where mathematical calculations are needed.