Meg mixes 3 parts silver paint with 4 parts green paint to get a specific color. Is the ratio 5:6 equivalent to 3:4? (1 point) Responses No, because there cannot be more than 4 green parts. No, because there cannot be more than 4 green parts. No, because the numbers in the given ratio must be multiplied by the same number. No, because the numbers in the given ratio must be multiplied by the same number. Yes, because any combination of silver and green will work. Yes, because any combination of silver and green will work. Yes, because both ratios show a pair of numbers that have a difference of 1.

Answer 1

To determine if the ratios 5:6 and 3:4 are equivalent, we can compare them by looking for a common factor.

1. Convert the ratios to fractions:

   • 3:4 can be expressed as \( \frac{3}{4} \).
   • 5:6 can be expressed as \( \frac{5}{6} \).

2. Cross-multiply to check for equivalence:

   • Multiply the numerator of the first ratio by the denominator of the second ratio: \( 3 \times 6 = 18 \).
   • Multiply the numerator of the second ratio by the denominator of the first ratio: \( 5 \times 4 = 20 \).

Since \( 18 \neq 20 \), the two ratios are NOT equivalent.

Thus, the correct response is: No, because the numbers in the given ratio must be multiplied by the same number.