Question

The numerator of a fraction is 9 and the denominator is 6. All of the following numbers are equivalent except _____.

3/2
2/3

1 1/2
18/12

Answer 1

To determine which fraction is not equivalent to \(\frac{9}{6}\), we can simplify \(\frac{9}{6}\).

1. Simplifying \(\frac{9}{6}\):
\[\frac{9 \div 3}{6 \div 3} = \frac{3}{2}\]

Now we know that \(\frac{9}{6}\) simplifies to \(\frac{3}{2}\).

Next, we need to check the equivalence of the other fractions to \(\frac{3}{2}\):

- **Check \(\frac{3}{2}\)**: Already equivalent to \(\frac{9}{6}\).

- **Check \(\frac{2}{3}\)**:
\[\frac{2}{3} \neq \frac{3}{2}\] (Not equivalent)

- **Check \(1 \frac{1}{2}\)** (which is \( \frac{3}{2}\)):
- Converting to an improper fraction: \(1 \frac{1}{2} = \frac{3}{2}\).
- This is equivalent to \(\frac{9}{6}\).

- **Check \(\frac{18}{12}\)**:
- Simplifying \(\frac{18}{12}\):
\[\frac{18 \div 6}{12 \div 6} = \frac{3}{2}\]
- This is also equivalent to \(\frac{9}{6}\).

Thus, all options are equivalent except for \(\frac{2}{3}\).

The answer is **\(\frac{2}{3}\)**.