Question

which ratios are equivalent to the ratio \\(\frac{120 \text{ applications}}{36 \text{ openings}}\\)? (select all that apply.)\\(\frac{60 \text{ applications}}{18 \text{ openings}}\\) \\(\frac{30 \text{ applications}}{9 \text{ openings}}\\) \\(\frac{40 \text{ applications}}{15 \text{ openings}}\\) \\(\frac{10 \text{ applications}}{3 \text{ openings}}\\)

Explanation:

To determine if a ratio is equivalent to \(\frac{120}{36}\), we simplify \(\frac{120}{36}\) by dividing numerator and denominator by their greatest common divisor (GCD). The GCD of 120 and 36 is 12. So, \(\frac{120\div12}{36\div12}=\frac{10}{3}\). Now we check each option:

Step 1: Check \(\frac{60}{18}\)

Simplify by dividing numerator and denominator by 6: \(\frac{60\div6}{18\div6}=\frac{10}{3}\). So, it is equivalent.

Step 2: Check \(\frac{30}{9}\)

Simplify by dividing numerator and denominator by 3: \(\frac{30\div3}{9\div3}=\frac{10}{3}\). So, it is equivalent.

Step 3: Check \(\frac{40}{15}\)

Simplify by dividing numerator and denominator by 5: \(\frac{40\div5}{15\div5}=\frac{8}{3}\), which is not equal to \(\frac{10}{3}\). So, it is not equivalent.

Step 4: Check \(\frac{10}{3}\)

This is the simplified form of \(\frac{120}{36}\), so it is equivalent.

Answer:

A. \(\frac{60 \text{ applications}}{18 \text{ openings}}\)
B. \(\frac{30 \text{ applications}}{9 \text{ openings}}\)
D. \(\frac{10 \text{ applications}}{3 \text{ openings}}\)