Answer :
To determine which of the given equations is a proportion, we need to check if the fractions on either side of each equation are equal.
Let's step through each option:
### Option 1:
[tex]\(\frac{5}{8} = \frac{16}{26}\)[/tex]
Calculate:
[tex]\[ \frac{5}{8} \approx 0.625 \][/tex]
[tex]\[ \frac{16}{26} \approx 0.615 \][/tex]
Since [tex]\(0.625 \neq 0.615\)[/tex], the fractions are not equal.
### Option 2:
[tex]\(\frac{22}{33} = \frac{3}{2}\)[/tex]
Calculate:
[tex]\[ \frac{22}{33} \approx 0.6667 \][/tex]
[tex]\[ \frac{3}{2} = 1.5 \][/tex]
Since [tex]\(0.6667 \neq 1.5\)[/tex], the fractions are not equal.
### Option 3:
[tex]\(\frac{10}{18} = \frac{25}{45}\)[/tex]
Calculate:
[tex]\[ \frac{10}{18} \approx 0.5556 \][/tex]
[tex]\[ \frac{25}{45} \approx 0.5556 \][/tex]
Since [tex]\(0.5556 = 0.5556\)[/tex], the fractions are equal, thus this is a proportion.
### Option 4:
[tex]\(\frac{19}{3} = \frac{76}{16}\)[/tex]
Calculate:
[tex]\[ \frac{19}{3} \approx 6.3333 \][/tex]
[tex]\[ \frac{76}{16} = 4.75 \][/tex]
Since [tex]\(6.3333 \neq 4.75\)[/tex], the fractions are not equal.
Therefore, the correct proportion is given in Option 3:
[tex]\[ \frac{10}{18} = \frac{25}{45} \][/tex]
So, the proportion holds true for the third option.
Let's step through each option:
### Option 1:
[tex]\(\frac{5}{8} = \frac{16}{26}\)[/tex]
Calculate:
[tex]\[ \frac{5}{8} \approx 0.625 \][/tex]
[tex]\[ \frac{16}{26} \approx 0.615 \][/tex]
Since [tex]\(0.625 \neq 0.615\)[/tex], the fractions are not equal.
### Option 2:
[tex]\(\frac{22}{33} = \frac{3}{2}\)[/tex]
Calculate:
[tex]\[ \frac{22}{33} \approx 0.6667 \][/tex]
[tex]\[ \frac{3}{2} = 1.5 \][/tex]
Since [tex]\(0.6667 \neq 1.5\)[/tex], the fractions are not equal.
### Option 3:
[tex]\(\frac{10}{18} = \frac{25}{45}\)[/tex]
Calculate:
[tex]\[ \frac{10}{18} \approx 0.5556 \][/tex]
[tex]\[ \frac{25}{45} \approx 0.5556 \][/tex]
Since [tex]\(0.5556 = 0.5556\)[/tex], the fractions are equal, thus this is a proportion.
### Option 4:
[tex]\(\frac{19}{3} = \frac{76}{16}\)[/tex]
Calculate:
[tex]\[ \frac{19}{3} \approx 6.3333 \][/tex]
[tex]\[ \frac{76}{16} = 4.75 \][/tex]
Since [tex]\(6.3333 \neq 4.75\)[/tex], the fractions are not equal.
Therefore, the correct proportion is given in Option 3:
[tex]\[ \frac{10}{18} = \frac{25}{45} \][/tex]
So, the proportion holds true for the third option.
