which pair of ratios form a true proportion?
4:7 and 8:21
20:5 and 10:3
24:36 and 8:9
36:12 and 3:1
The pair of ratios that form a true proportion is 20:5 and 10:3.
To check if two ratios form a proportion, you can cross-multiply and see if the products are equal.
For the first pair, 4 * 21 = 84 and 7 * 8 = 56. Since 84 is not equal to 56, this pair does not form a true proportion.
For the second pair, 20 * 3 = 60 and 5 * 10 = 50. Since 60 is equal to 60, this pair forms a true proportion.
For the third pair, 24 * 9 = 216 and 36 * 8 = 288. Since 216 is not equal to 288, this pair does not form a true proportion.
For the fourth pair, 36 * 1 = 36 and 12 * 3 = 36. Since 36 is equal to 36, this pair forms a true proportion.
To determine which pair of ratios forms a true proportion, we can cross-multiply and check if the products are equal. Let's go through each pair of ratios:
1. For the pair 4:7 and 8:21, we cross-multiply:
4 * 21 = 7 * 8
84 = 56
The cross-products are not equal, so this pair does not form a proportion.
2. For the pair 20:5 and 10:3, we cross-multiply:
20 * 3 = 5 * 10
60 = 50
The cross-products are not equal, so this pair does not form a proportion.
3. For the pair 24:36 and 8:9, we cross-multiply:
24 * 9 = 36 * 8
216 = 288
The cross-products are not equal, so this pair does not form a proportion.
4. For the pair 36:12 and 3:1, we cross-multiply:
36 * 1 = 12 * 3
36 = 36
The cross-products are equal, so this pair forms a proportion.
Therefore, the only pair of ratios that form a true proportion is 36:12 and 3:1.
To determine which pair of ratios form a true proportion, we need to check if the ratios are equivalent. A proportion is true if the two ratios are equal.
1. 4:7 and 8:21
To check if these ratios form a true proportion, we compare the cross products. The cross product is found by multiplying the numerator of one ratio with the denominator of the other ratio.
4 × 21 = 84
7 × 8 = 56
Since the cross products (84 and 56) are not equal, the pair of ratios 4:7 and 8:21 do not form a true proportion.
2. 20:5 and 10:3
We compare the cross products:
20 × 3 = 60
5 × 10 = 50
Since the cross products (60 and 50) are not equal, the pair of ratios 20:5 and 10:3 do not form a true proportion.
3. 24:36 and 8:9
We compare the cross products:
24 × 9 = 216
36 × 8 = 288
Again, the cross products (216 and 288) are not equal, so the pair of ratios 24:36 and 8:9 do not form a true proportion.
4. 36:12 and 3:1
Lastly, we compare the cross products:
36 × 1 = 36
12 × 3 = 36
The cross products (36 and 36) are equal. Therefore, the pair of ratios 36:12 and 3:1 form a true proportion.
Based on our analysis, the pair of ratios that form a true proportion is 36:12 and 3:1.