Question

Which fractions are equivalent to 24/26?
36/39
12/13
43/46
29/38

Answer 1

To determine which fractions are equivalent to \( \frac{24}{26} \), we can simplify \( \frac{24}{26} \) and then check if the other fractions simplify to the same value.

First, simplify \( \frac{24}{26} \):

1. Find the greatest common divisor (GCD) of the numerator (24) and the denominator (26). The GCD is 2.
2. Divide both the numerator and the denominator by their GCD.

\[
\frac{24 \div 2}{26 \div 2} = \frac{12}{13}
\]

Now, let's check the other fractions to see which ones simplify to \( \frac{12}{13} \):

1. **For \( \frac{36}{39} \)**:
- GCD of 36 and 39 is 3.
- Simplifying:

\[
\frac{36 \div 3}{39 \div 3} = \frac{12}{13}
\]

2. **For \( \frac{12}{13} \)**:
- This fraction is already simplified and is equal to \( \frac{12}{13} \).

3. **For \( \frac{43}{46} \)**:
- GCD of 43 and 46 is 1 (since 43 is prime).
- This fraction cannot be simplified further:

\[
\frac{43}{46}
\]

4. **For \( \frac{29}{38} \)**:
- GCD of 29 and 38 is 1 (since 29 is prime).
- This fraction cannot be simplified further:

\[
\frac{29}{38}
\]

Finally, the equivalent fractions to \( \frac{24}{26} \) are:

- \( \frac{36}{39} \)
- \( \frac{12}{13} \)

So, the equivalent fractions to \( \frac{24}{26} \) from the given options are:

- \( \frac{36}{39} \)
- \( \frac{12}{13} \)