Question

1. \frac{3}{12y} + \frac{9}{24}

Explanation:

Step1: Find a common denominator

The denominators are \(12y\) and \(24\). The least common denominator (LCD) of \(12y\) and \(24\) is \(24y\).

Step2: Rewrite each fraction with the LCD

For \(\frac{3}{12y}\), multiply numerator and denominator by \(2\):
\(\frac{3\times2}{12y\times2}=\frac{6}{24y}\)
For \(\frac{9}{24}\), multiply numerator and denominator by \(y\):
\(\frac{9\times y}{24\times y}=\frac{9y}{24y}\)

Step3: Add the fractions

Now that both fractions have the same denominator, we add the numerators:
\(\frac{6}{24y}+\frac{9y}{24y}=\frac{6 + 9y}{24y}\)

Step4: Simplify the numerator (if possible)

Factor out a \(3\) from the numerator:
\(\frac{3(2 + 3y)}{24y}\)
Then simplify the fraction by dividing numerator and denominator by \(3\):
\(\frac{2 + 3y}{8y}\)

Answer:

\(\frac{3y + 2}{8y}\) (or \(\frac{2 + 3y}{8y}\))