Question

Select all ratios equivalent to 2:6.
3:9
14:42
15:8

Answer 1

To determine which ratios are equivalent to 2:6, we can simplify 2:6.

The ratio 2:6 can be simplified by dividing both numbers by their greatest common divisor, which is 2:

\[
\frac{2}{2} : \frac{6}{2} = 1:3
\]

Now, we will simplify the other ratios to see if they are also equivalent to 1:3.

1. **3:9**
- Simplifying 3:9:
\[
\frac{3}{3} : \frac{9}{3} = 1:3
\]
- This is equivalent to 2:6.

2. **14:42**
- Simplifying 14:42:
\[
\frac{14}{14} : \frac{42}{14} = 1:3
\]
- This is also equivalent to 2:6.

3. **15:8**
- Simplifying 15:8:
- This ratio cannot be simplified further to match 1:3, as 15 and 8 do not share a common factor.
- Since 15/8 does not equal 1/3, this ratio is not equivalent.

Therefore, the ratios equivalent to 2:6 are **3:9** and **14:42**.