Which pair of ratios does not form a true proportion?
a. 8:14 and 20:35
b. 6 to 10 and 15 to 25
c. 9/4 and 36/16
d. 12:15 and 30:40
a) 8/14 simplifies to 4/7, 20/35 simplifies to 4/7, so these form a true proportion
b) 6/10 simplifies to 3/5, 15/25 simplifies to 3/5, so these form a true proportion
c) 9/4 is already simplified, 36/16 simplifies to 9/4, so these form a true proportion
d) 12/15 simplifies to 4/5, 30/40 simplifies to 3/4, so these don't form a true proportion
Therefore, the correct option is D
To determine which pair of ratios does not form a true proportion, we need to check if the cross products of the ratios are equal.
Let's calculate the cross products for each pair of ratios:
a. 8 x 35 = 280 and 14 x 20 = 280
Since the cross products are equal, the ratio 8:14 and 20:35 forms a true proportion.
b. 6 x 25 = 150 and 10 x 15 = 150
Again, the cross products are equal, so the ratio 6 to 10 and 15 to 25 forms a true proportion.
c. 9 x 16 = 144 and 4 x 36 = 144
Once again, the cross products are equal, indicating that the ratio 9/4 and 36/16 forms a true proportion.
d. 12 x 40 = 480 and 15 x 30 = 450
The cross products are not equal. Therefore, the pair of ratios 12:15 and 30:40 does not form a true proportion.
So, the correct answer is d. 12:15 and 30:40.
To determine which pair of ratios does not form a true proportion, we need to check if the two ratios are equivalent.
To do this, we can simplify each ratio by dividing both numbers by their greatest common divisor.
Let's analyze each option:
a. 8:14 and 20:35
To simplify the first ratio 8:14, divide both numbers by their greatest common divisor, which is 2. This gives us 4:7.
To simplify the second ratio 20:35, divide both numbers by their greatest common divisor, which is 5. This gives us 4:7.
Since both ratios simplify to 4:7, this implies that the answer to option a is a true proportion.
b. 6 to 10 and 15 to 25
To simplify the first ratio 6 to 10, divide both numbers by their greatest common divisor, which is 2. This gives us 3 to 5.
To simplify the second ratio 15 to 25, divide both numbers by their greatest common divisor, which is 5. This gives us 3 to 5.
Since both ratios simplify to 3 to 5, this implies that the answer to option b is a true proportion.
c. 9/4 and 36/16
To simplify the first ratio 9/4, divide both numbers by their greatest common divisor, which is 1. This gives us 9/4.
To simplify the second ratio 36/16, divide both numbers by their greatest common divisor, which is 4. This gives us 9/4.
Since both ratios simplify to 9/4, this implies that the answer to option c is a true proportion.
d. 12:15 and 30:40
To simplify the first ratio 12:15, divide both numbers by their greatest common divisor, which is 3. This gives us 4:5.
To simplify the second ratio 30:40, divide both numbers by their greatest common divisor, which is 10. This gives us 3:4.
Since the simplified version of the first ratio is not equal to the simplified version of the second ratio, this means that the answer to option d is not a true proportion.
Therefore, the pair of ratios that does not form a true proportion is d. 12:15 and 30:40.