To find the missing number that makes the fractions equal, we set up the equation:
\[ \frac{3}{x} + \frac{9}{15} = 1 \]
First, simplify \(\frac{9}{15}\):
\[ \frac{9}{15} = \frac{3}{5} \]
Now the equation becomes:
\[ \frac{3}{x} + \frac{3}{5} = 1 \]
Next, isolate \(\frac{3}{x}\):
\[ \frac{3}{x} = 1 - \frac{3}{5} \]
Finding a common denominator (which is 5):
\[ 1 = \frac{5}{5} \]
Thus, we have:
\[ \frac{3}{x} = \frac{5}{5} - \frac{3}{5} = \frac{2}{5} \]
Now, cross-multiply:
\[ 3 \cdot 5 = 2 \cdot x \]
So:
\[ 15 = 2x \]
Now, solve for \(x\):
\[ x = \frac{15}{2} = 7.5 \]
Thus, the missing number is 7.5.
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