5:11 and 6:12
7:13 and 21:39
8:14 and 24:30
10:20 and 20:30 which pair of ratios form a proportion?
To determine whether two ratios form a proportion, we need to check if they are equal to each other. Let's examine each pair of ratios:
1) 5:11 and 6:12
To compare the ratios, we need to ensure that the corresponding terms are in the same order. Let's write them as fractions:
5/11 and 6/12
Now, let's simplify both fractions to their simplest form:
5/11 = (5 ÷ 1) / (11 ÷ 1) = 5/11
6/12 = (6 ÷ 6) / (12 ÷ 6) = 1/2
Since the simplified fractions 5/11 and 1/2 are not equal, this pair of ratios does not form a proportion.
2) 7:13 and 21:39
Writing these ratios as fractions:
7/13 and 21/39
Simplifying both fractions:
7/13 = (7 ÷ 1) / (13 ÷ 1) = 7/13
21/39 = (21 ÷ 3) / (39 ÷ 3) = 7/13
Both fractions simplify to the same value, which means this pair of ratios forms a proportion.
3) 8:14 and 24:30
Writing these ratios as fractions:
8/14 and 24/30
Simplifying both fractions:
8/14 = (8 ÷ 2) / (14 ÷ 2) = 4/7
24/30 = (24 ÷ 6) / (30 ÷ 6) = 4/5
Since the simplified fractions 4/7 and 4/5 are not equal, this pair of ratios does not form a proportion.
4) 10:20 and 20:30
Writing these ratios as fractions:
10/20 and 20/30
Simplifying both fractions:
10/20 = (10 ÷ 10) / (20 ÷ 10) = 1/2
20/30 = (20 ÷ 10) / (30 ÷ 10) = 2/3
Since the simplified fractions 1/2 and 2/3 are not equal, this pair of ratios does not form a proportion.
Therefore, the only pair of ratios that form a proportion is 7:13 and 21:39.