Working with fractions can often be daunting, especially when it comes to solving expressions involving them. However, with the right approach and a clear understanding of the rules, solving these expressions can become much simpler. In this blog post, we will explore step-by-step how to solve an expression with fractions.

Step 1: Find a Common Denominator

The first step in solving an expression with fractions is to find a common denominator. This involves identifying a least common multiple of all the denominators in the expression. Once you have determined the common denominator, you can proceed to the next step.

Step 2: Rewrite the Fractions

After finding the common denominator, rewrite each fraction in the expression using the common denominator. This will allow you to perform operations on the fractions more easily. Be sure to adjust the numerators accordingly.

Step 3: Perform the Necessary Operations

Once all the fractions have been rewritten, you can perform the required operations, such as addition, subtraction, multiplication, or division. Remember to apply the operations to both the numerators and denominators separately.

Step 4: Simplify the Resulting Fraction

After performing the operations, you may end up with a fraction that can be simplified further. To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. This will give you the most simplified form of the fraction.

Step 5: Check for Extraneous Solutions

Sometimes, while solving an expression with fractions, you may end up with solutions that do not satisfy the original problem or introduce undefined values (e.g., division by zero). It is crucial to double-check your final solution and make sure it is valid in the context of the problem.

Example:

Let’s solve the expression (1/2) + (3/4) – (1/8):

  • Step 1: The common denominator is 8, as it is the least common multiple of 2, 4, and 8.
  • Step 2: Rewriting the fractions using the common denominator, we have: (4/8) + (6/8) – (1/8).
  • Step 3: Performing the addition and subtraction, we get: 9/8.
  • Step 4: Since 9 and 8 have no common divisor other than 1, the fraction 9/8 is already in its simplified form.
  • Step 5: The solution 9/8 is valid and does not introduce any extraneous solutions.

By following these steps, you can confidently solve expressions with fractions, making the process much more manageable. Remember to always double-check your solutions to ensure accuracy. With practice, you will become more proficient in solving these types of expressions.

Stay tuned for more helpful tips and strategies for working with fractions!

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