Question

Fill in the missing value in the table

1/2 3/6 9/?

Answer 1

To find the missing value in the sequence \( \frac{1}{2}, \frac{3}{6}, \frac{9}{?} \), we can start by simplifying the fractions we already have.

1. The first fraction \( \frac{1}{2} \) is already simplified.
2. The second fraction \( \frac{3}{6} \) can be simplified to \( \frac{1}{2} \) as well.

Now both fractions \( \frac{1}{2} \) and \( \frac{3}{6} \) are equal to \( \frac{1}{2} \).

Looking at the pattern, we can see that the numerators seem to be related by multiplication. Notice that:

- From \( 1 \) to \( 3 \) (numerators) is \( 1 \times 3 = 3 \).
- Thus, if we continue the pattern, from \( 3 \) to \( 9 \) (next numerator), we see that \( 3 \times 3 = 9 \).

Now, we need to find the denominator that will keep the fractions consistent. Since \( \frac{3}{6} \) simplifies to \( \frac{1}{2} \), we want \( \frac{9}{?} = \frac{1}{2} \).

We set up the equation:

\[
\frac{9}{?} = \frac{1}{2}
\]

Cross-multiplying gives:

\[
9 \times 2 = 1 \times ?
\]

This simplifies to:

\[
18 = ?
\]

So the missing value is \( 18 \).

Therefore, the complete sequence is:

\[
\frac{1}{2}, \frac{3}{6}, \frac{9}{18}
\]

Thus, the missing value is \( \boxed{18} \).