Answered

What is the relationship between the ratios?

[tex] \frac{10}{24} [/tex] and [tex] \frac{5}{12} [/tex]

Drag and drop a term to correctly complete the statement.

The ratios are [tex] \square [/tex]



Answer :

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.