Question

which fractions are equivalent to 24/26
hint there may be more than one
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 compare it to the other fractions provided.

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

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

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

Now that we have simplified \( \frac{24}{26} \) to \( \frac{12}{13} \), we can compare this to the other fractions provided:

1. **\( \frac{36}{39} \)**:
- Simplify: The GCD of 36 and 39 is 3.
- \( \frac{36 \div 3}{39 \div 3} = \frac{12}{13} \) (Equivalent)

2. **\( \frac{12}{13} \)**:
- This is already simplified and is equivalent to \( \frac{12}{13} \) (Equivalent)

3. **\( \frac{43}{46} \)**:
- Simplify: The GCD of 43 and 46 is 1.
- \( \frac{43}{46} \) is already in simplest form and does not simplify to \( \frac{12}{13} \) (Not Equivalent)

4. **\( \frac{29}{38} \)**:
- Simplify: The GCD of 29 and 38 is 1.
- \( \frac{29}{38} \) is already in simplest form and does not simplify to \( \frac{12}{13} \) (Not Equivalent)

The fractions that are equivalent to \( \frac{24}{26} \) are:

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