Question

a grid (2x2 table) with numbers: top - left 63, top - right 35; bottom - left 27, bottom - right blank. task: find the missing number in the bottom - right cell.

Explanation:

Step1: Analyze the pattern in the first column

First, find the greatest common divisor (GCD) of 63 and 27. The factors of 63 are \(1, 3, 7, 9, 21, 63\) and the factors of 27 are \(1, 3, 9, 27\). The GCD of 63 and 27 is 9. So, \(63\div9 = 7\) and \(27\div9 = 3\).

Step2: Apply the pattern to the second column

Now, for the second column, we know one number is 35. Let the unknown number be \(x\). We assume the same GCD (9) is used for the ratio. From the first column, the ratio of the top number to the bottom number is \(7:3\). So, we can set up a proportion: \(\frac{35}{x}=\frac{7}{3}\). Cross - multiplying gives us \(7x = 35\times3\).

Step3: Solve for \(x\)

Calculate \(35\times3=105\). Then, \(x=\frac{105}{7}=15\). We can also check by finding the GCD of 35 and 15. The factors of 35 are \(1, 5, 7, 35\) and the factors of 15 are \(1, 3, 5, 15\). The GCD is 5. And \(35\div5 = 7\), \(15\div5 = 3\), which matches the ratio from the first column (\(7:3\)).

Answer:

15