To determine which of the given ratios are equivalent to [tex]\(7:5\)[/tex], we will compare each given ratio to the target ratio of [tex]\(7:5\)[/tex].
First, let's express the target ratio [tex]\(7:5\)[/tex] as a fraction:
[tex]\[ \frac{7}{5} \][/tex]
Next, we will convert each given ratio to a fraction and compare it with [tex]\(\frac{7}{5}\)[/tex].
1. Ratio [tex]\(11:7\)[/tex]:
[tex]\[ \frac{11}{7} \][/tex]
We compare it to [tex]\(\frac{7}{5}\)[/tex] and see that [tex]\(\frac{11}{7}\)[/tex] is not equal to [tex]\(\frac{7}{5}\)[/tex].
2. Ratio [tex]\(77:55\)[/tex]:
[tex]\[ \frac{77}{55} \][/tex]
To simplify [tex]\(\frac{77}{55}\)[/tex]:
We find the greatest common divisor (GCD) of 77 and 55, which is 11.
So, [tex]\(\frac{77 \div 11}{55 \div 11} = \frac{7}{5}\)[/tex].
Thus, [tex]\(\frac{77}{55}\)[/tex] is equivalent to [tex]\(\frac{7}{5}\)[/tex].
3. Ratio [tex]\(28:20\)[/tex]:
[tex]\[ \frac{28}{20} \][/tex]
To simplify [tex]\(\frac{28}{20}\)[/tex]:
We find the greatest common divisor (GCD) of 28 and 20, which is 4.
So, [tex]\(\frac{28 \div 4}{20 \div 4} = \frac{7}{5}\)[/tex].
Thus, [tex]\(\frac{28}{20}\)[/tex] is equivalent to [tex]\(\frac{7}{5}\)[/tex].
Therefore, the ratios that are equivalent to [tex]\(7:5\)[/tex] are:
[tex]\[ 77:55 \quad \text{and} \quad 28:20 \][/tex]
These ratios correspond to:
[tex]\[ 77:55 = \frac{77}{55} = \frac{7}{5} \][/tex]
[tex]\[ 28:20 = \frac{28}{20} = \frac{7}{5} \][/tex]
So, the correct ratios are [tex]\(77:55\)[/tex] and [tex]\(28:20\)[/tex].
