What is the common denominator of $y+\frac{y-3}{3}$ in the complex fraction $\frac{y+\frac{y-3}{3}}{\frac{5}{9}+\frac{2}{3 y}}$?
Answer (2)
Rewrite the term y as 3 3 y .
Combine the terms in the numerator: 3 3 y + 3 y − 3 = 3 3 y + y − 3 = 3 4 y − 3 .
Identify the common denominator of the numerator as 3.
The common denominator of y + 3 y − 3 is 3 .
Explanation
Problem Analysis We are given the complex fraction 9 5 + 3 y 2 y + 3 y − 3 . We need to find the common denominator of the numerator y + 3 y − 3 .
Rewriting the Numerator The numerator is y + 3 y − 3 . We can rewrite y as 3 3 y . Thus, the numerator becomes 3 3 y + 3 y − 3 .
Finding the Common Denominator of the Numerator Combining the terms in the numerator, we have 3 3 y + ( y − 3 ) = 3 4 y − 3 . The common denominator of the numerator y + 3 y − 3 is 3.
Conclusion Therefore, the common denominator of y + 3 y − 3 is 3.
Examples
Understanding common denominators is crucial when combining fractions in various fields, such as cooking, where you might need to adjust ingredient quantities proportionally. For instance, if a recipe calls for 2 1 cup of flour and you want to add another 4 1 cup, finding the common denominator (4) allows you to easily add the fractions: 4 2 + 4 1 = 4 3 cup of flour. This ensures accurate measurements and consistent results in your culinary creations.
The common denominator of the expression y + 3 y − 3 is 3. We rewrite y as 3 3 y , combine the fractions, and determine that the common denominator is 3. Thus, the answer is 3 .
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