Question

complete the ratio table.
14 5
42 15
56
70 25
98

Explanation:

Step1: Find the ratio multiplier

First, check the ratio between the first two rows. For the first row, 14 and 5; second row, 42 and 15. Let's see the multiplier for the first column: \( \frac{42}{14} = 3 \), and for the second column: \( \frac{15}{5} = 3 \). So the ratio is consistent with a multiplier of 3? Wait, no, wait. Wait, let's check another row. Fourth row: 70 and 25. \( \frac{70}{14} = 5 \), \( \frac{25}{5} = 5 \). Oh, right! So the ratio between the first column and the second column is that the first column number divided by 14, multiplied by 5? Wait, no, let's see the pattern. Let's take the first column numbers: 14, 42, 56, 70, 98. Let's see the relationship with the second column: 5, 15,?, 25,?.

Wait, 14 corresponds to 5. 42 is 14 3, so 5 3 = 15. 70 is 14 5, so 5 5 = 25. Ah, so the multiplier for the second column is the same as the multiplier for the first column when divided by 14. So let's find the multiplier for each first column number:

• 14: 14 / 14 = 1, so 5 * 1 = 5
• 42: 42 / 14 = 3, so 5 * 3 = 15
• 56: 56 / 14 = 4, so 5 * 4 = 20
• 70: 70 / 14 = 5, so 5 * 5 = 25
• 98: 98 / 14 = 7, so 5 * 7 = 35

Let's verify: 14/5 = 2.8, 42/15 = 2.8, 56/20 = 2.8, 70/25 = 2.8, 98/35 = 2.8. Yes, that's consistent. So the ratio of first column to second column is 14:5, which simplifies to 2.8, or 14/5. So to find the second column number, we can take the first column number and divide by (14/5) = multiply by 5/14.

So for 56: 56 (5/14) = (56/14)5 = 4*5 = 20.

For 98: 98 (5/14) = (98/14)5 = 7*5 = 35.

Step2: Calculate the missing values

First missing value (for 56): 56 * (5/14) = 20.

Second missing value (for 98): 98 * (5/14) = 35.

Answer:

For the row with 56, the missing number is 20. For the row with 98, the missing number is 35. So the completed table has 20 in the third row (under 56) and 35 in the fifth row (under 98).