To determine the relationship between the ratios \(\frac{10}{24}\) and \(\frac{5}{12}\), we need to simplify both ratios to their simplest form and then compare them.
Step 1: Simplify the first ratio \(\frac{10}{24}\).
- Find the greatest common divisor (GCD) of 10 and 24. The GCD of 10 and 24 is 2.
- Divide the numerator and the denominator by the GCD to simplify:
[tex]\[
\frac{10}{24} = \frac{10 \div 2}{24 \div 2} = \frac{5}{12}
\][/tex]
Step 2: Simplify the second ratio \(\frac{5}{12}\).
- Find the greatest common divisor (GCD) of 5 and 12. The GCD of 5 and 12 is 1.
- Divide the numerator and the denominator by the GCD to simplify:
[tex]\[
\frac{5}{12} = \frac{5 \div 1}{12 \div 1} = \frac{5}{12}
\][/tex]
Step 3: Compare the simplified ratios.
- After simplification, both ratios \(\frac{10}{24}\) and \(\frac{5}{12}\) are equivalent to \(\frac{5}{12}\).
Therefore, the statement can be completed as follows:
The ratios are equivalent.
