Use cross products to determine which of the following pairs of ratios cannot form a proportion.
A. 1/3*3/9
B. 2/3*4/9
C. 2/3*4/6
D. 1/3*2/6
Is the answer B?
Yes B.
1/3 * 3/9 = 1*9 and 3*3 = 9 and 9
2/3 * 4/9 = 2*9 and 3*4 = 18 and 12
2/3 * 4/6 = 2*6 and 3*4 = 12 and 12
1/3 * 2/6 = 1*6 and 3*2 = 6 and 6
So B is the correct answer.
I hope this helps! :)
Thank you
You're welcome, Callie.
Well, I must say, these ratios definitely need to get their proportions in order! Let me help you figure this out.
To determine whether two ratios form a proportion, we can use the cross products. The cross products of a proportion should be equal.
Let's take a look at the options:
A. 1/3 * 3/9
Cross products: 1 * 9 = 3 * 3 -> 9 = 9
This one checks out! They form a proportion.
B. 2/3 * 4/9
Cross products: 2 * 9 = 3 * 4 -> 18 ≠ 12
Well, it seems like this pair didn't quite measure up. The cross products are not equal, so they do not form a proportion. Good observation!
C. 2/3 * 4/6
Cross products: 2 * 6 = 3 * 4 -> 12 = 12
This one passes the proportion test. They form a proportion.
D. 1/3 * 2/6
Cross products: 1 * 6 = 3 * 2 -> 6 = 6
Oh ho! Looks like these ratios are definitely proportional.
So, Partner, it seems like Option B, 2/3 * 4/9, is the odd one out. It does not form a proportion. Great job spotting that!
To determine which pairs of ratios cannot form a proportion, we can use the cross product property. The cross product property states that if we have two proportions, where the product of the means equals the product of the extremes, then they are proportionate.
Let's evaluate each pair of ratios using the cross product property:
A. 1/3 * 3/9 = 1/9 vs. 3/3 = 1
Cross products: 1 × 9 = 3 × 1
Since the cross products are equal, the ratios can form a proportion.
B. 2/3 * 4/9 = 8/27 vs. 3/2 = 1.5
Cross products: 8 × 2 = 27 × 1.5 = 40 ≠ 40.5
Since the cross products are not equal, the ratios cannot form a proportion.
C. 2/3 * 4/6 = 8/18 = 4/9 vs. 3/2 = 1.5
Cross products: 4 × 2 = 9 × 1.5 = 8 ≠ 13.5
Since the cross products are not equal, the ratios cannot form a proportion.
D. 1/3 * 2/6 = 2/18 = 1/9 vs. 3/1 = 3
Cross products: 1 × 1 = 9 × 3
Since the cross products are equal, the ratios can form a proportion.
Based on this evaluation, the pair of ratios that cannot form a proportion is B, 2/3 * 4/9. The cross products do not equal each other.