#### Which Expression is Equivalent to the Following Complex Fraction?

Which expression is equivalent to the subsequent complicated fraction? :complicated fractions can be intimidating, however with a clear expertise of equivalent expressions, they come to be a lot greater plausible. In this article, we can discover a way to discover an expression this is equal to a given complicated fraction. With the aid of breaking down the stairs and providing examples, we hope to simplify this process and raise your self belief in dealing with complicated fractions.

1. Information complicated Fractions: complicated fractions are fractions in which both the numerator, denominator, or both contain fractions. They frequently contain operations including addition, subtraction, multiplication, and department. Fixing complicated fractions calls for simplifying them into an equal expression that is simpler to paintings with.
1. Simplifying complex Fractions: To simplify a complex fraction, comply with these steps: a) pick out the numerator and denominator. B) If the numerator or denominator contains a fraction, simplify it first. C) Multiply the numerator and denominator by the least not unusual a couple of (LCM) of the denominators involved. D) Simplify the resulting expression.
2. Finding an equivalent Expression: To discover an expression equivalent to a complex fraction, you could multiply both the numerator and denominator by way of a appropriate expression that gets rid of the fraction within the complicated fraction. With the aid of doing this, the ensuing expression can be equivalent to the unique complicated fraction.
3. Examples of equivalent Expressions: let’s discover a few examples to illustrate the way to discover equal expressions for complex fractions.

Example 1: Given complex fraction: (2/3) / (4/5)

Step 1: Identify the numerator and denominator. Numerator: 2/3 Denominator: 4/5

Step 2: Simplify the numerator and denominator. Numerator: 2/3 Denominator: 4/5

Step 3: Multiply the numerator and denominator by the LCM of the denominators. Numerator: (2/3) * 5 = 10/3 Denominator: (4/5) * 5 = 4

Step 4: Simplify the resulting expression. Equivalent expression: (10/3) / 4

Example 2:

Given complex fraction: (3/4) / [(1/2) + (1/3)] Step 1: Identify the numerator and denominator. Numerator: 3/4 Denominator: [(1/2) + (1/3)]

Step 2: Simplify the numerator and denominator. Numerator: 3/4 Denominator: (3/6) + (2/6) = 5/6

Step 3: Multiply the numerator and denominator by the LCM of the denominators. Numerator: (3/4) * 6 = 18/4 = 9/2 Denominator: (5/6) * 6 = 5

Step 4: Simplify the resulting expression. Equivalent expression: (9/2) / 5

1. Frequently Asked Questions (FAQs): Q1: Can I simplify the numerator and denominator separately? A1: Yes, it is often easier to simplify the numerator and denominator before finding an equivalent expression for the complex fraction.

Q2: What if the complex fraction has multiple fractions in the numerator or denominator? A2: You can apply the same steps of simplification and finding an equivalent expression to each fraction individually.

Q3: Are there any shortcuts for finding equivalent expressions for complex fractions? A3: While there are no universal shortcuts, familiarity with common fraction operations and simplification techniques can help you streamline the process.

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Solving complicated fractions turns into less complicated while you recognize how to find equivalent expressions. By means of following the steps mentioned in this text and training with examples, you could optimistically simplify complex fractions and find their equal expressions. Take into account to continually simplify the numerator and denominator earlier than multiplying through the LCM to make certain accuracy. With exercise, you will come to be talented in handling complicated fractions and overcome even the maximum challenging problems.