Question

complete the ratio table.
6\t7
□\t42
66\t77
□\t84
□\t98

Explanation:

Step1: Find the ratio of the first two numbers.

The ratio of the first column to the second column is $\frac{6}{7}$. So we can find the missing numbers by using this ratio. For a given number \( y \) in the second column, the number \( x \) in the first column is \( x = y\times\frac{6}{7} \).

Step2: Find the first missing number (when second column is 42).

Substitute \( y = 42 \) into the formula \( x = y\times\frac{6}{7} \).
\( x = 42\times\frac{6}{7}= 6\times6 = 36 \)

Step3: Find the second missing number (when second column is 84).

Substitute \( y = 84 \) into the formula \( x = y\times\frac{6}{7} \).
\( x = 84\times\frac{6}{7}= 12\times6 = 72 \)

Step4: Find the third missing number (when second column is 98).

Substitute \( y = 98 \) into the formula \( x = y\times\frac{6}{7} \).
\( x = 98\times\frac{6}{7}= 14\times6 = 84 \)

Answer:

The completed ratio table (from top to bottom for the first column missing values) is 36, 72, 84.