Question

Examine the ratios to find the one that is not equivalent to the others.

StartFraction 2 Over 5 EndFraction = StartFraction 6 Over 10 EndFraction = StartFraction 8 Over 20 EndFraction = StartFraction 12 Over 30 EndFraction

Which ratio is different from the other three?
StartFraction 8 Over 20 EndFraction
StartFraction 12 Over 30 EndFraction
StartFraction 6 Over 10 EndFraction
StartFraction 14 Over 35 EndFraction

Answer 1

To determine which ratio is not equivalent to the others, we'll convert each fraction to its simplest form and see if they yield the same value.

1. **StartFraction 2 Over 5 EndFraction**:
This is already in simplest form: \( \frac{2}{5} \).

2. **StartFraction 6 Over 10 EndFraction**:
Simplifying gives \( \frac{6 \div 2}{10 \div 2} = \frac{3}{5} \).

3. **StartFraction 8 Over 20 EndFraction**:
Simplifying gives \( \frac{8 \div 4}{20 \div 4} = \frac{2}{5} \).

4. **StartFraction 12 Over 30 EndFraction**:
Simplifying gives \( \frac{12 \div 6}{30 \div 6} = \frac{2}{5} \).

5. **StartFraction 14 Over 35 EndFraction**:
Simplifying gives \( \frac{14 \div 7}{35 \div 7} = \frac{2}{5} \).

Now we can summarize the simplified values:
- \( \frac{2}{5} = \frac{2}{5} \)
- \( \frac{6}{10} = \frac{3}{5} \) (not equivalent)
- \( \frac{8}{20} = \frac{2}{5} \)
- \( \frac{12}{30} = \frac{2}{5} \)
- \( \frac{14}{35} = \frac{2}{5} \)

The only ratio that is not equivalent to the others is:

**StartFraction 6 Over 10 EndFraction**.