Select the Pairs of ratios that form a true proportion .
A) 3:6 and 5:10
B) 4/12 and 6/18
C) 20:5 and 10:3
D) 24/36 and 8/9
A) 3:6 and 5:10
To determine which pairs of ratios form a true proportion, we need to check if the cross products are equal.
A) 3:6 and 5:10.
To find the cross products, we multiply 3 x 10 and 6 x 5. The cross products are 30 and 30, which are equal. So, A) 3:6 and 5:10 form a true proportion.
B) 4/12 and 6/18.
To find the cross products, we multiply 4 x 18 and 12 x 6. The cross products are 72 and 72, which are equal. So, B) 4/12 and 6/18 form a true proportion.
C) 20:5 and 10:3.
To find the cross products, we multiply 20 x 3 and 5 x 10. The cross products are 60 and 50, which are not equal. So, C) 20:5 and 10:3 do not form a true proportion.
D) 24/36 and 8/9.
To find the cross products, we multiply 24 x 9 and 36 x 8. The cross products are 216 and 288, which are not equal. So, D) 24/36 and 8/9 do not form a true proportion.
The pairs of ratios that form a true proportion are A) 3:6 and 5:10 and B) 4/12 and 6/18.
To determine whether pairs of ratios form a true proportion, we need to simplify each ratio and check if they are equal.
Let's go through each option:
A) The first ratio 3:6 can be simplified by dividing both numbers by 3, resulting in 1:2. The second ratio 5:10 can also be divided by 5, resulting in 1:2. Since both simplified ratios are equal (1:2), option A forms a true proportion.
B) The first ratio 4/12 can be simplified by dividing both numbers by 4, resulting in 1/3. The second ratio 6/18 can be simplified by dividing both numbers by 6, resulting in 1/3. Since both simplified ratios are equal (1/3), option B forms a true proportion.
C) The first ratio 20:5 can be simplified by dividing both numbers by 5, resulting in 4:1. The second ratio 10:3 cannot be simplified further. Since the simplified ratios are not equal (4:1 ≠ 10:3), option C does not form a true proportion.
D) The first ratio 24/36 can be simplified by dividing both numbers by their greatest common divisor (GCD), which is 12. Dividing 24 and 36 by 12 gives us 2/3. The second ratio 8/9 cannot be simplified further. Since the simplified ratios are not equal (2/3 ≠ 8/9), option D does not form a true proportion.
In conclusion, options A) and B) form true proportions.