Question

Select all the fractions that are equivalent to 6/9
(1 point)
Responses

36/54

2/3

12/14

4/6

Answer 1

To determine which fractions are equivalent to \( \frac{6}{9} \), we can simplify \( \frac{6}{9} \).

1. **Simplifying \( \frac{6}{9} \)**:
- The greatest common divisor (GCD) of 6 and 9 is 3.
- Dividing both the numerator and the denominator by 3, we get:
\[
\frac{6 \div 3}{9 \div 3} = \frac{2}{3}
\]

Now let's check each of the given options to see which are equivalent to \( \frac{2}{3} \):

1. **Check \( \frac{36}{54} \)**:
- GCD of 36 and 54 is 18.
- Simplifying:
\[
\frac{36 \div 18}{54 \div 18} = \frac{2}{3}
\]
- **Equivalent**.

2. **Check \( \frac{2}{3} \)**:
- This is already \( \frac{2}{3} \).
- **Equivalent**.

3. **Check \( \frac{12}{14} \)**:
- GCD of 12 and 14 is 2.
- Simplifying:
\[
\frac{12 \div 2}{14 \div 2} = \frac{6}{7}
\]
- **Not equivalent**.

4. **Check \( \frac{4}{6} \)**:
- GCD of 4 and 6 is 2.
- Simplifying:
\[
\frac{4 \div 2}{6 \div 2} = \frac{2}{3}
\]
- **Equivalent**.

Hence, the fractions equivalent to \( \frac{6}{9} \) are:
- \( \frac{36}{54} \)
- \( \frac{2}{3} \)
- \( \frac{4}{6} \)

The final answer is: **36/54, 2/3, 4/6**.