Which pair of ratios form a true proportion? (1 point)
Responses
4:7 and 8:21
4:7 and 8:21
20:5 and 10:3
20:5 and 10:3
24:36 and 8:9
24:36 and 8:9
36:12 and 3:1
The pair of ratios that form a true proportion is 24:36 and 8:9.
To determine which pair of ratios form a true proportion, we need to check if their cross products are equal.
Let's check each pair of ratios:
1) 4:7 and 8:21
Cross products: 4 * 21 = 84 and 7 * 8 = 56
Since the cross products are not equal (84 ≠ 56), this pair does not form a true proportion.
2) 20:5 and 10:3
Cross products: 20 * 3 = 60 and 5 * 10 = 50
Since the cross products are not equal (60 ≠ 50), this pair does not form a true proportion.
3) 24:36 and 8:9
Cross products: 24 * 9 = 216 and 36 * 8 = 288
Since the cross products are not equal (216 ≠ 288), this pair does not form a true proportion.
4) 36:12 and 3:1
Cross products: 36 * 1 = 36 and 12 * 3 = 36
Since the cross products are equal (36 = 36), this pair forms a true proportion.
Therefore, the pair of ratios that form a true proportion is 36:12 and 3:1.
To determine which pair of ratios forms a true proportion, we need to compare the ratios by simplifying them. A proportion is true if the simplified ratios are equal to each other.
Let's simplify each pair of ratios:
1) 4:7 and 8:21
To simplify 4:7, we divide both numbers by their greatest common divisor, which is 1. Therefore, the simplified ratio is 4:7.
To simplify 8:21, we divide both numbers by their greatest common divisor, which is also 1. Therefore, the simplified ratio is 8:21.
The simplified ratios, 4:7 and 8:21, are not equal, so this pair of ratios does not form a true proportion.
2) 20:5 and 10:3
To simplify 20:5, we divide both numbers by their greatest common divisor, which is 5. Therefore, the simplified ratio is 4:1.
To simplify 10:3, we divide both numbers by their greatest common divisor, which is 1. Therefore, the simplified ratio is 10:3.
The simplified ratios, 4:1 and 10:3, are not equal, so this pair of ratios does not form a true proportion.
3) 24:36 and 8:9
To simplify 24:36, we divide both numbers by their greatest common divisor, which is 12. Therefore, the simplified ratio is 2:3.
To simplify 8:9, we divide both numbers by their greatest common divisor, which is 1. Therefore, the simplified ratio is 8:9.
The simplified ratios, 2:3 and 8:9, are not equal, so this pair of ratios does not form a true proportion.
4) 36:12 and 3:1
To simplify 36:12, we divide both numbers by their greatest common divisor, which is 12. Therefore, the simplified ratio is 3:1.
To simplify 3:1, we divide both numbers by their greatest common divisor, which is 1. Therefore, the simplified ratio is 3:1.
The simplified ratios, 3:1 and 3:1, are equal, so this pair of ratios forms a true proportion.
Therefore, the pair of ratios that form a true proportion is 36:12 and 3:1.