Equivalent Ratios in Tables Quick Check
1 of 51 of 5 Items
Question
Use the table to answer the question.
7 10
70 100
Display the missing equivalent part-to-part ratios in this two-column table.
(1 point)
Responses
13:10 and 45:42
ratio of 13 to 10 and ratio of 45 to 42
14:20 and 56:80
ratio of 14 to 20 and ratio of 56 to 80
20:14 and 80:56
ratio of 20 to 14 and ratio of 80 to 56
10:13 and 42:45
ratio of 10 to 13 and ratio of 42 to 45
ratio of 10 to 13 and ratio of 42 to 45
To find the missing equivalent part-to-part ratios in the table, we can use the given ratios as a guide.
Looking at the first row of the table, we see that the ratio is 7:10. To find an equivalent ratio, we can multiply both the numerator and the denominator of the ratio by the same number.
For example, if we multiply both 7 and 10 by 2, we get 14:20. But is this an equivalent ratio to 7:10? To answer that, we can simplify both ratios.
To simplify a ratio, we divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 14 and 20 is 2. So when we divide both 14 and 20 by 2, we get 7:10, which is the same as the original ratio. Therefore, 14:20 is not an equivalent ratio.
Let's try another multiplication. If we multiply both 7 and 10 by 10, we get 70:100. We can simplify this ratio by dividing both numbers by their GCD, which is 10. So when we divide both 70 and 100 by 10, we get 7:10. This is the same as the original ratio, so 70:100 is an equivalent ratio to 7:10.
Now let's move on to the second row of the table. The given ratio is 70:100. By following the same process, we can find an equivalent ratio. If we multiply both 70 and 100 by 3, we get 210:300. By dividing both numbers by their GCD of 30, we can simplify the ratio to 7:10, which is the same as the original ratio.
So the missing equivalent part-to-part ratios in the two-column table are:
- 14:20 and 210:300 (which simplify to 7:10 in both cases).
Therefore, the correct response is:
ratio of 14 to 20 and ratio of 210 to 300 (which simplify to ratio of 7 to 10 in both cases).