To determine which ratios are equivalent to 4:8, we'll compare each given ratio to 4:8.
1. Check if 2:5 is equivalent to 4:8
- A ratio [tex]\( a:b \)[/tex] is equivalent to [tex]\( c:d \)[/tex] if [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex].
- Comparing 2:5 with 4:8, we can convert the ratio 4:8 to its simplest form:
- [tex]\( \frac{4}{8} = \frac{1}{2} \)[/tex]
- Now, check if [tex]\( \frac{2}{5} = \frac{1}{2} \)[/tex]:
- [tex]\( \frac{2}{5} \)[/tex] is not equal to [tex]\( \frac{1}{2} \)[/tex]
- Therefore, 2:5 is not equivalent to 4:8.
2. Check if 7:14 is equivalent to 4:8
- Convert 7:14 to its simplest form:
- [tex]\( \frac{7}{14} = \frac{1}{2} \)[/tex]
- Now, compare [tex]\( \frac{1}{2} \)[/tex] with [tex]\( \frac{1}{2} \)[/tex]:
- They are equal.
- Therefore, 7:14 is equivalent to 4:8.
3. Check if 12:24 is equivalent to 4:8
- Convert 12:24 to its simplest form:
- [tex]\( \frac{12}{24} = \frac{1}{2} \)[/tex]
- Now, compare [tex]\( \frac{1}{2} \)[/tex] with [tex]\( \frac{1}{2} \)[/tex]:
- They are equal.
- Therefore, 12:24 is equivalent to 4:8.
### Conclusion
- The ratios equivalent to 4:8 are:
- 7:14
- 12:24
