Question

Select all the fractions that are equivalent to 812 (1 point)
Responses

1624
16 over 24

23
2 thirds

1014
10 over 14

46

Answer 1

To determine which fractions are equivalent to \( \frac{8}{12} \), we first simplify the fraction.

The fraction \( \frac{8}{12} \) can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4:

\[
\frac{8 \div 4}{12 \div 4} = \frac{2}{3}
\]

Now we can check each response to see which fractions are equivalent to \( \frac{2}{3} \):

1. **\( \frac{16}{24} \)** - This can be simplified by dividing both the numerator and the denominator by 8:
\[
\frac{16 \div 8}{24 \div 8} = \frac{2}{3}
\]
So, \( \frac{16}{24} \) is equivalent to \( \frac{8}{12} \).

2. **\( \frac{2}{3} \)** - This is already in its simplest form and is equivalent to \( \frac{8}{12} \).

3. **\( \frac{10}{14} \)** - This can be simplified by dividing both the numerator and the denominator by 2:
\[
\frac{10 \div 2}{14 \div 2} = \frac{5}{7}
\]
So, \( \frac{10}{14} \) is **not** equivalent to \( \frac{8}{12} \).

4. **\( 4 \times 6 \)** - This seems to be an oversight as "46" does not represent a fraction, thus it cannot be equivalent to \( \frac{8}{12} \).

Based on this analysis, the fractions equivalent to \( \frac{8}{12} \) are:
- \( \frac{16}{24} \)
- \( \frac{2}{3} \)

The correct responses are **\( \frac{16}{24} \)** and **\( \frac{2}{3} \)**.