Which pair of ratios does NOT form a proportion?
A. three over five and twenty-four over forty
B. thirty over ten and fifteen over five
C. nine over fourteen and three over four
D. seven over twelve and fourteen over twenty-four
B. thirty over ten and fifteen over five does not form a proportion because both ratios reduce to 3/1.
To determine which pair of ratios does not form a proportion, we need to compare the ratios and check if they are equivalent.
Let's compare each pair of ratios:
A. three over five and twenty-four over forty
To check if these ratios are equivalent, we can cross-multiply and check if the products are equal:
3 * 40 = 5 * 24
120 = 120
Since the products are equal, the pair of ratios A does form a proportion.
B. thirty over ten and fifteen over five
Cross-multiply:
30 * 5 = 10 * 15
150 = 150
The pair of ratios B also forms a proportion.
C. nine over fourteen and three over four
Cross-multiply:
9 * 4 = 14 * 3
36 ≠ 42
The product on the left side (36) is not equal to the product on the right side (42). Therefore, the pair of ratios C does not form a proportion.
D. seven over twelve and fourteen over twenty-four
Cross-multiply:
7 * 24 = 12 * 14
168 = 168
The pair of ratios D forms a proportion.
Based on our analysis, the pair of ratios that does not form a proportion is C. Therefore, the answer is C. nine over fourteen and three over four.
To determine which pair of ratios does NOT form a proportion, we need to check if the ratios are equal.
A. three over five and twenty-four over forty:
To check if they are equal, we can cross-multiply:
(3 * 40) = (5 * 24)
120 = 120
Since the cross-products are equal, the pair of ratios does form a proportion.
B. thirty over ten and fifteen over five:
To check if they are equal, we can cross-multiply:
(30 * 5) = (10 * 15)
150 = 150
Since the cross-products are equal, the pair of ratios does form a proportion.
C. nine over fourteen and three over four:
To check if they are equal, we can cross-multiply:
(9 * 4) = (14 * 3)
36 = 42
Since the cross-products are not equal, the pair of ratios does NOT form a proportion.
D. seven over twelve and fourteen over twenty-four:
To check if they are equal, we can cross-multiply:
(7 * 24) = (12 * 14)
168 = 168
Since the cross-products are equal, the pair of ratios does form a proportion.
Therefore, the answer is C. nine over fourteen and three over four.