Solving the Mathematical Expression 1/2a - a/b with Given Values

In this tutorial, we will solve the mathematical expression 1/2a - a/b given the values a 4, b 3, c -2. This problem is a great example to demonstrate the principles of algebra and basic arithmetic operations. Let's break it down step by step.

Step 1: Calculate 1/2a

Given that a 4, we can substitute this value into the expression 1/2a.

1/2a 1/2 * 4 1/2 * 4 2.

Step 2: Calculate a/b

Given that a 4 and b 3, we can substitute these values into the expression a/b.

a/b 4/3.

Step 3: Subtract the Two Results

Now we need to subtract the two results obtained from step 1 and step 2:

1/2a - a/b 2 - 4/3.

To perform this subtraction, we need to have a common denominator. The least common multiple (LCM) of 1 and 3 is 3. We will convert 2 to a fraction with a denominator of 3.

2 2 * (3/3) 6/3.

Now, we can easily subtract the fractions:

2 - 4/3 6/3 - 4/3 (6 - 4)/3 2/3.

Final Answer

The value of the expression 1/2a - a/b is 2/3. The value of c -2 does not affect this result because it is not involved in the given expression.

Conclusion

This problem demonstrates the importance of correctly applying arithmetic operations and the concept of common denominators. Understanding these principles is crucial for solving more complex mathematical problems. If you have any questions or need further assistance, feel free to reach out in the comments section below.

Related Keywords

mathematical expression: A combination of numbers and symbols that represents a quantity or a relationship between quantities.

algebra: A branch of mathematics dealing with symbols and the rules for manipulating these symbols.

problem solving: The process of finding solutions to problems, particularly through the use of logical reasoning and mathematical skills.