What ratios form a proportion. Use equivalent ratios to test each pair
1. 4/9 , 2/3
2. 6/15 , 9/12
3. 12/16 , 15/20
4. 18/20 , 24/30
Thanks so much for helping me.
To determine if two ratios form a proportion, we need to check if they are equivalent ratios. Two ratios are equivalent if they have the same value.
To find out if ratios are equivalent, we can simplify them and check if the resulting fractions are equal. If they are equal, it means the ratios are equivalent and form a proportion.
Let's go through each pair of ratios and determine if they form a proportion:
1. The first pair is 4/9 and 2/3.
To see if they are equivalent, we can simplify them:
4/9 = (4 ÷ 1) / (9 ÷ 1) = 4/9
2/3 = (2 ÷ 1) / (3 ÷ 1) = 2/3
The simplified fractions are the same, so the ratios are equivalent. Therefore, 4/9 and 2/3 form a proportion.
2. The second pair is 6/15 and 9/12.
To simplify them:
6/15 = (6 ÷ 3) / (15 ÷ 3) = 2/5
9/12 = (9 ÷ 3) / (12 ÷ 3) = 3/4
The simplified fractions are not the same, so the ratios are not equivalent. Therefore, 6/15 and 9/12 do not form a proportion.
3. The third pair is 12/16 and 15/20.
To simplify them:
12/16 = (12 ÷ 4) / (16 ÷ 4) = 3/4
15/20 = (15 ÷ 5) / (20 ÷ 5) = 3/4
The simplified fractions are the same, so the ratios are equivalent. Therefore, 12/16 and 15/20 form a proportion.
4. The fourth pair is 18/20 and 24/30.
To simplify them:
18/20 = (18 ÷ 2) / (20 ÷ 2) = 9/10
24/30 = (24 ÷ 6) / (30 ÷ 6) = 4/5
The simplified fractions are not the same, so the ratios are not equivalent. Therefore, 18/20 and 24/30 do not form a proportion.
In summary:
1. 4/9 and 2/3 form a proportion.
2. 6/15 and 9/12 do not form a proportion.
3. 12/16 and 15/20 form a proportion.
4. 18/20 and 24/30 do not form a proportion.
well, to make a proportion, the two ratios must be equal
4/9 = 4/9
2/3 = 6/9
so, what do you think?
check the others.