Use cross products to determine which of the following pairs of ratios cannot form a proportion.

Question

(1 point)
Responses

one-third and three-ninths
Image with alt text: one-third and three-ninths

two-thirds and four-ninths
Image with alt text: two-thirds and four-ninths

two-thirds and four-sixths
Image with alt text: two-thirds and four-sixths

one-third and two-sixths

Answer 1

To determine if the pairs of ratios can form a proportion, we will use the cross product method.

For the pair one-third and three-ninths:
Cross product: 1 * 9 = 3 * 3
9 = 9
The cross products are equal, so the pair one-third and three-ninths can form a proportion.

For the pair two-thirds and four-ninths:
Cross product: 2 * 9 = 4 * 3
18 = 12
The cross products are not equal, so the pair two-thirds and four-ninths cannot form a proportion.

For the pair two-thirds and four-sixths:
Cross product: 2 * 6 = 4 * 3
12 = 12
The cross products are equal, so the pair two-thirds and four-sixths can form a proportion.

For the pair one-third and two-sixths:
Cross product: 1 * 6 = 2 * 3
6 = 6
The cross products are equal, so the pair one-third and two-sixths can form a proportion.

Therefore, the pair two-thirds and four-ninths cannot form a proportion.