Use the table to answer the question.
bottle 2
6
10 12
case 10 30 50 60
Simplify each ratio in the table to prove that all the ratios are equivalent.
(2 points)
210=
, 630=
, 1050=
, 1260=
thats wrong
To prove that all the ratios in the table are equivalent, we need to simplify each ratio.
First, let's simplify the ratio 2:10.
We can divide both numbers by their greatest common divisor (GCD) which is 2.
So, 2 ÷ 2 = 1 and 10 ÷ 2 = 5.
Therefore, the simplified ratio of 2:10 is 1:5.
Next, let's simplify the ratio 6:30.
Again, the GCD between 6 and 30 is 6.
So, 6 ÷ 6 = 1 and 30 ÷ 6 = 5.
The simplified ratio of 6:30 is 1:5.
Now, let's simplify the ratio 10:50.
The GCD between 10 and 50 is 10.
Hence, 10 ÷ 10 = 1 and 50 ÷ 10 = 5.
The simplified ratio of 10:50 is 1:5.
Lastly, let's simplify the ratio 12:60.
The GCD between 12 and 60 is 12.
So, 12 ÷ 12 = 1 and 60 ÷ 12 = 5.
The simplified ratio of 12:60 is 1:5.
Therefore, the simplified ratios for each ratio in the table are:
2:10 simplifies to 1:5
6:30 simplifies to 1:5
10:50 simplifies to 1:5
12:60 simplifies to 1:5.
This shows that all the ratios in the table are equivalent.
To prove that all the ratios are equivalent, we need to simplify each ratio in the table and show that they have the same result.
Let's start with the first ratio: 2:6.
To simplify this ratio, we divide both numbers by their greatest common factor, which in this case is 2.
2 ÷ 2 = 1
6 ÷ 2 = 3
So the simplified ratio is 1:3.
Next, let's look at the second ratio: 10:12.
Again, we divide both numbers by their greatest common factor, which is 2.
10 ÷ 2 = 5
12 ÷ 2 = 6
Therefore, the simplified ratio is 5:6.
Now, let's move on to the third ratio: 10:30.
Dividing both numbers by their greatest common factor of 10:
10 ÷ 10 = 1
30 ÷ 10 = 3
Hence, the simplified ratio is 1:3.
Lastly, the fourth ratio: 50:60.
We divide both numbers by their greatest common factor of 10:
50 ÷ 10 = 5
60 ÷ 10 = 6
So, the simplified ratio is 5:6.
To summarize, after simplifying each ratio in the table, we find the following equivalences:
1:3 = 5:6 = 1:3 = 5:6
This demonstrates that all the ratios in the table are equivalent.
To simplify each ratio in the table, we divide both numbers in the ratio by their greatest common factor.
For the ratio "bottle:case", the greatest common factor of 2 and 10 is 2:
2/2 = 1
10/2 = 5
Therefore, the simplified ratio is 1:5.
For the ratio "6:10", the greatest common factor of 6 and 10 is 2:
6/2 = 3
10/2 = 5
Therefore, the simplified ratio is 3:5.
For the ratio "10:30", the greatest common factor of 10 and 30 is 10:
10/10 = 1
30/10 = 3
Therefore, the simplified ratio is 1:3.
For the ratio "12:50", the greatest common factor of 12 and 50 is 2:
12/2 = 6
50/2 = 25
Therefore, the simplified ratio is 6:25.
The simplified ratios are:
1:5
3:5
1:3
6:25