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
well, 2/3 = 6/9, so not this one
find the common denominator, and if the numerators are the same, you have a proportion
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
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
To determine if two ratios form a proportion, we need to check if they are equivalent. Equivalent ratios have the same value.
Let's test each pair of ratios using equivalent ratios:
1. Pair: 4/9 and 2/3
To check if they are equivalent, we need to find a common multiplier that we can apply to both ratios. We can multiply the numerator and denominator of the first ratio by 3 to get 12/27. The second ratio can be multiplied by 9 to get 18/27. These new ratios have the same value, so the pair forms a proportion.
2. Pair: 6/15 and 9/12
We can simplify the first ratio by dividing both the numerator and denominator by 3 to get 2/5. The second ratio can be simplified by dividing both the numerator and denominator by 3 to get 3/4. Since these simplified ratios are not equivalent, the pair does not form a proportion.
3. Pair: 12/16 and 15/20
Both ratios can be simplified by dividing the numerator and denominator by 4. The first ratio simplifies to 3/4, and the second ratio simplifies to 3/4. These simplified ratios have the same value, so the pair forms a proportion.
4. Pair: 18/20 and 24/30
We can simplify the first ratio by dividing both the numerator and denominator by 2 to get 9/10. The second ratio can be simplified by dividing both the numerator and denominator by 6 to get 4/5. Since these simplified ratios are not equivalent, the pair does not form a proportion.
In summary, the pairs that form proportions are 4/9 and 2/3, as well as 12/16 and 15/20.