Question

1. add \\(\frac{9}{16} + \frac{5}{12}\\). \\(\frac{47}{48}\\) \\(\frac{35}{36}\\) \\(\frac{1}{2}\\) \\(\frac{17}{18}\\)

Explanation:

Step1: Find the least common denominator (LCD) of 16 and 12.

The prime factorization of 16 is \(2^4\) and of 12 is \(2^2\times3\). So, LCD is \(2^4\times3 = 48\).

Step2: Rewrite the fractions with the LCD.

For \(\frac{9}{16}\), multiply numerator and denominator by 3: \(\frac{9\times3}{16\times3}=\frac{27}{48}\).
For \(\frac{5}{12}\), multiply numerator and denominator by 4: \(\frac{5\times4}{12\times4}=\frac{20}{48}\).

Step3: Add the fractions.

\(\frac{27}{48}+\frac{20}{48}=\frac{27 + 20}{48}=\frac{47}{48}\).

Answer:

\(\frac{47}{48}\) (corresponding to the first option among the choices, likely labeled with \(\frac{47}{48}\))