Final answer:
To complete the ratio table, maintain equivalent ratios by multiplying or dividing the numbers consistently. The completed pairs are 5 to 7, 10 to 14, 15 to 21, 20 to 28, and 25 to 35. The method used involves scaling the original pair up or down to maintain the ratio.
Step-by-step explanation:
To complete the ratio table so that each pair of numbers represents an equivalent rate, we need to ensure that all the ratios or rates in the table are equal. The initial pair given is 5 to 7, which we can express as the fraction 5/7. To find the missing numbers in the table, we will multiply or divide the numbers by the same amount to keep the ratios equivalent.
The next number in the table is 10, so we double the first number of the pair (5) to get the second pair, which should be 10 to 14 since doubling 7 also gives us 14 (10/14 is equivalent to 5/7). Following this pattern, the third pair is 20 to 28 since we multiply the original pair by 4 (20/28 = 5/7).
Now let's use this method to find the missing number that pairs with 21. To get from 7 to 21, we multiply by 3, so we should also multiply 5 by 3 to find the number that pairs with 21, resulting in 15. Therefore, 21 pairs with 15 to maintain the equivalent ratio (15/21 = 5/7). The number that pairs with 35 is found similarly by multiplying 5 by 7, resulting in 25. Therefore, the missing number for 35 is 25 (25/35 = 5/7).
The completed ratio table is: 5 to 7, 10 to 14, 15 to 21, 20 to 28, and 25 to 35.