Select the Pairs of ratios that form a true proportion . Choose all that apply.
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
B) 4/12 and 6/18
C) 20:5 and 10:3
D) 24/36 and 8/9
The pairs of ratios that form a true proportion are A) 3:6 and 5:10.
To determine which pairs of ratios form a true proportion, we need to check if the ratios are equal.
Let's go through each option:
A) 3:6 and 5:10
To determine if these ratios form a proportion, we need to simplify them:
3/6 = 1/2
5/10 = 1/2
Since the simplified ratios are equal (both are 1/2), this pair forms a true proportion.
B) 4/12 and 6/18
Again, we simplify the ratios:
4/12 = 1/3
6/18 = 1/3
The simplified ratios are the same (both are 1/3), so this pair is also a true proportion.
C) 20:5 and 10:3
Simplifying the ratios:
20/5 = 4/1
10/3 = 10/3
These ratios are not equal, so this pair does not form a true proportion.
D) 24/36 and 8/9
Simplifying the ratios:
24/36 = 2/3
8/9 = 8/9
These ratios are not equal, so this pair does not form a true proportion.
Therefore, the pairs of ratios that form true proportions are A) (3:6 and 5:10) and B) (4/12 and 6/18).
To determine if the pairs of ratios form a true proportion, we need to check if the cross-products are equal. Let's evaluate each option:
A) 3:6 is equivalent to 1:2, and 5:10 simplifies to 1:2. The cross-products are 1 x 2 = 2 and 2 x 1 = 2, which are equal. Therefore, option A forms a true proportion.
B) 4/12 is equivalent to 1/3, and 6/18 simplifies to 1/3. The cross-products are 1 x 3 = 3 and 1 x 3 = 3, which are equal. Therefore, option B forms a true proportion.
C) 20:5 simplifies to 4:1, and 10:3 cannot be simplified. The cross-products are 4 x 3 = 12 and 1 x 10 = 10, which are not equal. Therefore, option C does not form a true proportion.
D) 24/36 is equivalent to 2/3, and 8/9 also simplifies to 8/9. The cross-products are 2 x 9 = 18 and 3 x 8 = 24, which are not equal. Therefore, option D does not form a true proportion.
Based on the evaluation, the pairs of ratios that form a true proportion are:
A) 3:6 and 5:10
B) 4/12 and 6/18