Select all the pairs of ratios that form a proportion.
A. one sixth and four over twenty
B. seven ninths and twenty eight over thirty six
C. fourteen over eighteen and twenty one over twenty seven
D. thirty over eighty and six over eighteen
pls say answers
To determine if two ratios form a proportion, we need to check if their cross products are equal. So, let's calculate the cross products for each pair of ratios:
A. one sixth and four over twenty: Cross products = (1)(20) = 20 and (4)(6) = 24. Not equal.
B. seven ninths and twenty eight over thirty six: Cross products = (7)(36) = 252 and (9)(28) = 252. Equal.
C. fourteen over eighteen and twenty one over twenty seven: Cross products = (14)(27) = 378 and (18)(21) = 378. Equal.
D. thirty over eighty and six over eighteen: Cross products = (30)(18) = 540 and (80)(6) = 480. Not equal.
From the calculations above, we can see that only option B (seven ninths and twenty eight over thirty six) and option C (fourteen over eighteen and twenty one over twenty seven) form proportions.
To determine if a pair of ratios forms a proportion, we need to check if they are equivalent. Two ratios are equivalent if their cross products are equal.
The cross product of a pair of ratios is obtained by multiplying the numerator of the first ratio with the denominator of the second ratio, and multiplying the denominator of the first ratio with the numerator of the second ratio.
Let's go through each pair of ratios:
A. one sixth and four over twenty
Cross product: (1 * 20) = (4 * 6) = 20 ≠ 24
The cross products are not equal, so this pair of ratios does not form a proportion.
B. seven ninths and twenty eight over thirty six
Cross product: (7 * 36) = (9 * 28) = 252 = 252
The cross products are equal, so this pair of ratios forms a proportion.
C. fourteen over eighteen and twenty one over twenty seven
Cross product: (14 * 27) = (18 * 21) = 378 ≠ 378
The cross products are not equal, so this pair of ratios does not form a proportion.
D. thirty over eighty and six over eighteen
Cross product: (30 * 18) = (80 * 6) = 540 = 480
The cross products are not equal, so this pair of ratios does not form a proportion.
The pair of ratios that forms a proportion is B. seven ninths and twenty eight over thirty six.
1/6 = 4/24, not 4/20
now try the others