Which ratios form a proportion? Use equivalent ratios to test each pair.
A.) 4/9 , 2/3
B.) 6/15 , 9/12
C.) 12/16 , 15/20
D.) 18/20 , 24/30
To check if two ratios form a proportion, we need to compare them and see if they are equivalent or equal. We can do this by simplifying each ratio and then comparing them.
Let's test each pair:
A.) 4/9, 2/3
To simplify 4/9, we can divide both the numerator and the denominator by their greatest common divisor (GCD), which is 1:
4 ÷ 1 / 9 ÷ 1 = 4/9
To simplify 2/3, we can also divide both the numerator and the denominator by their GCD, which is 1:
2 ÷ 1 / 3 ÷ 1 = 2/3
Since both simplified ratios are equal to each other (4/9 = 2/3), this means that A.) 4/9 and 2/3 form a proportion.
B.) 6/15, 9/12
To simplify 6/15, we can divide both the numerator and the denominator by their GCD, which is 3:
6 ÷ 3 / 15 ÷ 3 = 2/5
To simplify 9/12, we can divide both the numerator and the denominator by their GCD, which is 3:
9 ÷ 3 / 12 ÷ 3 = 3/4
Since the simplified ratios are not equal to each other (2/5 ≠ 3/4), this means that B.) 6/15 and 9/12 do not form a proportion.
C.) 12/16, 15/20
To simplify 12/16, we can divide both the numerator and the denominator by their GCD, which is 4:
12 ÷ 4 / 16 ÷ 4 = 3/4
To simplify 15/20, we can divide both the numerator and the denominator by their GCD, which is 5:
15 ÷ 5 / 20 ÷ 5 = 3/4
Since both simplified ratios are equal to each other (12/16 = 15/20 = 3/4), this means that C.) 12/16 and 15/20 form a proportion.
D.) 18/20, 24/30
To simplify 18/20, we can divide both the numerator and the denominator by their GCD, which is 2:
18 ÷ 2 / 20 ÷ 2 = 9/10
To simplify 24/30, we can divide both the numerator and the denominator by their GCD, which is 6:
24 ÷ 6 / 30 ÷ 6 = 4/5
Since the simplified ratios are not equal to each other (9/10 ≠ 4/5), this means that D.) 18/20 and 24/30 do not form a proportion.
In summary,
The ratios that form a proportion are:
A.) 4/9, 2/3
C.) 12/16, 15/20
To determine which ratios form a proportion, we can use equivalent ratios. Two ratios are said to form a proportion if they are equal when simplified.
To test each pair of ratios:
A.) 4/9 , 2/3
We can simplify both ratios:
4/9 cannot be simplified any further.
2/3 is already in simplest form.
Since the simplified ratios are not equal, this pair of ratios does not form a proportion.
B.) 6/15 , 9/12
We can simplify both ratios:
6/15 simplifies to 2/5 by dividing both the numerator and denominator by their greatest common divisor, which is 3.
9/12 simplifies to 3/4 by dividing both the numerator and denominator by their greatest common divisor, which is 3.
Since the simplified ratios are not equal, this pair of ratios does not form a proportion.
C.) 12/16 , 15/20
We can simplify both ratios:
12/16 simplifies to 3/4 by dividing both the numerator and denominator by their greatest common divisor, which is 4.
15/20 simplifies to 3/4 by dividing both the numerator and denominator by their greatest common divisor, which is 5.
Since the simplified ratios are equal, this pair of ratios forms a proportion.
D.) 18/20 , 24/30
We can simplify both ratios:
18/20 simplifies to 9/10 by dividing both the numerator and denominator by their greatest common divisor, which is 2.
24/30 simplifies to 4/5 by dividing both the numerator and denominator by their greatest common divisor, which is 6.
Since the simplified ratios are not equal, this pair of ratios does not form a proportion.
Therefore, the answer is C.) 12/16 , 15/20, as this pair of ratios forms a proportion.