Unit Rates & Proportions Unit Test 6 of 156 of 15 Items Question Use the table to answer the question. # of Trees # of Apples 2 26 3 39 6 78 10 130 12 156 Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio between the number of trees and the number of apples remains constant.
Ratio for the first pair: 26/2 = 13
Ratio for the second pair: 39/3 = 13
Ratio for the third pair: 78/6 = 13
Ratio for the fourth pair: 130/10 = 13
Ratio for the fifth pair: 156/12 = 13
Since the ratio between the number of trees and the number of apples remains constant at 13, the quantities in the data table are in a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio between the number of trees and the number of apples is the same for each row.
Let's calculate the ratios for each row:
- For the first row (2 trees and 26 apples), the ratio is 26/2 = 13.
- For the second row (3 trees and 39 apples), the ratio is 39/3 = 13.
- For the third row (6 trees and 78 apples), the ratio is 78/6 = 13.
- For the fourth row (10 trees and 130 apples), the ratio is 130/10 = 13.
- For the fifth row (12 trees and 156 apples), the ratio is 156/12 = 1/13.
Since the ratios in the table are not the same for each row, the quantities in the data table are not in a proportional relationship.
To determine if the quantities in the data table are in a proportional relationship, we need to check if the ratio between the number of trees and the number of apples remains constant.
To do this, we can calculate the unit rate for each pair of values, which represents the number of apples per tree. If the unit rate remains the same for all pairs, then the quantities are in a proportional relationship.
Let's calculate the unit rates for each pair of values:
For the first pair (2 trees, 26 apples), the unit rate is 26/2 = 13 apples per tree.
For the second pair (3 trees, 39 apples), the unit rate is 39/3 = 13 apples per tree.
For the third pair (6 trees, 78 apples), the unit rate is 78/6 = 13 apples per tree.
For the fourth pair (10 trees, 130 apples), the unit rate is 130/10 = 13 apples per tree.
For the fifth pair (12 trees, 156 apples), the unit rate is 156/12 = 13 apples per tree.
Since the unit rate remains the same (13 apples per tree) for all pairs, we can conclude that the quantities in the data table are in a proportional relationship.