Final answer:
To change a 1:3 ratio to a 3:1 ratio, 8 more counters need to be added to the first position.
Step-by-step explanation:
- The question "1:3 how many more counters need to be added to make 3:1" involves understanding and creating ratios.
- To make a 1:3 ratio change to a 3:1 ratio, we need to consider how many counters form the current ratio and how many additional counters would create the inverse ratio.
- To begin with, if we have 1 counter to every 3 counters, that's a total of 1 + 3 = 4 counters. To change this ratio to 3:1, we want to have three times as many counters in the first position as in the second.
- This means we need 3 counters in the second position, giving us a total of 3 x 3 = 9 counters required in the first.
- Since there is already 1 counter in the first position, we need to add 9 - 1 = 8 more counters to the first position.