To determine which ratios are equivalent to [tex]\( 24:18 \)[/tex], we first simplify the given ratio.
[tex]\[ 24:18 \][/tex]
We can simplify this ratio by dividing both numbers by their greatest common divisor (GCD), which is 6.
[tex]\[ \frac{24 \div 6}{18 \div 6} = \frac{4}{3} \][/tex]
So, the ratio [tex]\( 24:18\)[/tex] simplifies to [tex]\( 4:3 \)[/tex].
Next, we need to check each provided ratio to see if they are equivalent to the simplified ratio [tex]\( 4:3 \)[/tex].
1. [tex]\( 18:9 \)[/tex]
We simplify this ratio by dividing both numbers by their GCD, which is 9.
[tex]\[ \frac{18 \div 9}{9 \div 9} = \frac{2}{1} \][/tex]
So, [tex]\( 18:9 \)[/tex] simplifies to [tex]\( 2:1 \)[/tex], which is not equivalent to [tex]\( 4:3 \)[/tex].
2. [tex]\( 35:27 \)[/tex]
We simplify this ratio by dividing both numbers by their GCD. The GCD of 35 and 27 is 1.
[tex]\[ \frac{35 \div 1}{27 \div 1} = \frac{35}{27} \][/tex]
So, [tex]\( 35:27 \)[/tex] cannot be simplified further and remains [tex]\( 35:27 \)[/tex], which is not equivalent to [tex]\( 4:3 \)[/tex].
3. [tex]\( 20:15 \)[/tex]
We simplify this ratio by dividing both numbers by their GCD, which is 5.
[tex]\[ \frac{20 \div 5}{15 \div 5} = \frac{4}{3} \][/tex]
So, [tex]\( 20:15 \)[/tex] simplifies to [tex]\( 4:3 \)[/tex], which is equivalent to [tex]\( 4:3 \)[/tex].
After checking all the ratios, we find that the equivalent ratio to [tex]\( 24:18 \)[/tex] is:
[tex]\[ \boxed{20:15} \][/tex]
