To determine which ratios are equivalent to 16:20, we must first understand what it means for ratios to be equivalent. Two ratios are equivalent if they simplify to the same value.
The original ratio we are examining is 16:20. We need to simplify this ratio:
1. Simplify 16:20.
[tex]\[
\frac{16}{20} = \frac{16 \div 4}{20 \div 4} = \frac{4}{5}
\][/tex]
Next, we will simplify each given ratio and compare it to the simplified form of 16:20, which is 4:5.
1. Simplify 20:25.
[tex]\[
\frac{20}{25} = \frac{20 \div 5}{25 \div 5} = \frac{4}{5}
\][/tex]
2. Simplify 40:50.
[tex]\[
\frac{40}{50} = \frac{40 \div 10}{50 \div 10} = \frac{4}{5}
\][/tex]
3. Simplify 2:5.
[tex]\[
\frac{2}{5} \quad (\text{This ratio is already in its simplest form and is not equal to } 4:5)
\][/tex]
Now we compare each simplified ratio to [tex]\(\frac{4}{5}\)[/tex]:
- The simplified form of 20:25 is 4:5.
- The simplified form of 40:50 is 4:5.
- The simplified form of 2:5 is not equal to 4:5.
Therefore, the ratios that are equivalent to 16:20 are:
- 20:25
- 40:50
So, the final answer is:
```
['20:25', '40:50']
```
