Question

Which ratios form a proportion? Use equivalent ratios to test each pair.

4/9,2/3
6/15,9/12
12/16,15/20
18/20,24/30

Answer 1

well, 2/3 = 6/9, so not this one
find the common denominator, and if the numerators are the same, you have a proportion

Answer 2

4 / 9 , 2 / 3 is not a proportion.

4 / 9 = ( 2 / 3 )²

This is not a proportion.

6 / 15 , 9 / 12 is not a proportion.

6 / 15 = 3 • 2 / 3 • 5 = 2 / 5

9 / 12 = 3 • 3 / 3 • 4 = 3 / 4

12 / 16 , 15 / 20 is a proportion.

12 / 16 = 4 • 3 / 4 • 4 = 3 / 4

15 / 20 = 5 • 3 / 5 • 4 = 3 / 4

12 / 16 = 15 / 12 = 3 / 4

18 / 20 , 24 / 30 is not a proportion.

18 / 20 = 2 • 9 / 2 • 10 = 9 / 10

24 / 30 = 6 • 4 / 6 • 5 = 4 / 5

Answer 3

OR

Find Least common multiple ( LCM ) of deniminators.

4 / 9 , 2 / 3

LCM of 3 and 9 is 9.

2 / 3 = 3 • 2 / 3 • 3 = 6 / 9

4 / 9 , 2 / 3 is not a proportion because 4 / 9 is not equal 2 / 3.

4 / 9 is not equal 6 / 9.

6 / 15 , 9 / 12

LCM of 12 and 15 is 60.

6 / 15 = 4 • 6 / 4 • 15 = 24 / 60

9 / 12 = 5 • 9 / 5 • 12 = 45 / 60

6 / 15 , 9 / 12 is not a proportion because 6 / 15 is not equal 9 / 12

24 / 60 not equal 45 / 60

12 / 16 , 15 / 20

LCM of 16 and 20 is 80.

12 / 16 = 5 • 12 / 5 • 16 = 60 / 80

15 / 20 = 4 • 15 / 4 • 20 = 60 / 80

12 / 16, 15 / 20 is a proportion because 12 / 16 is equal 15 / 20

60 / 80 is equal 60 / 80

18 / 20 , 24 / 30

LCM of 20 and 30 is 60

18 / 20 = 3 • 18 / 3 • 20 = 54 / 60

24 / 30 = 2 • 24 / 2 • 30 = 48 / 60

18 / 20 , 24 / 30 is not a proportion
because 18 / 20 is not equal 24 / 30

54 / 60 not equal 48 / 60