Question

Which of the following fractions are equivalent to 15/21
? Select all that apply.

(1 point)
Responses

5/7


30/42

21/15



25/31


45/84

Answer 1

To determine which fractions are equivalent to \( \frac{15}{21} \), we can simplify \( \frac{15}{21} \) and check the other fractions against the simplified form.

First, let's simplify \( \frac{15}{21} \):
- The greatest common divisor (GCD) of 15 and 21 is 3.
- Dividing both the numerator and denominator by 3 gives:
\[
\frac{15 \div 3}{21 \div 3} = \frac{5}{7}
\]

Now, we have \( \frac{15}{21} \) simplified to \( \frac{5}{7} \).

Next, we will check each of the given fractions:

1. **\( \frac{5}{7} \)**: This is already the simplified form, so it is equivalent.

2. **\( \frac{30}{42} \)**: Simplifying:
- GCD of 30 and 42 is 6:
\[
\frac{30 \div 6}{42 \div 6} = \frac{5}{7}
\]
So, it is equivalent.

3. **\( \frac{21}{15} \)**: To see if this is equivalent, we can find its simplified form:
- GCD of 21 and 15 is 3:
\[
\frac{21 \div 3}{15 \div 3} = \frac{7}{5}
\]
This is not equivalent to \( \frac{5}{7} \).

4. **\( \frac{25}{31} \)**: Since 25 and 31 share no common factors (31 is prime), this fraction cannot simplify to \( \frac{5}{7} \) and is not equivalent.

5. **\( \frac{45}{84} \)**: Simplifying:
- GCD of 45 and 84 is 3:
\[
\frac{45 \div 3}{84 \div 3} = \frac{15}{28}
\]
This also does not equal \( \frac{5}{7} \).

Therefore, the fractions equivalent to \( \frac{15}{21} \) are:

- \( \frac{5}{7} \)
- \( \frac{30}{42} \)

So, the correct choices are:
- **\( \frac{5}{7} \)**
- **\( \frac{30}{42} \)**