Question

a 2×2 grid (table) with numbers: top - left cell 15, top - right cell 40, bottom - right cell 48, bottom - left cell blank. horizontal and vertical lines are around the grid, and a number 7 (possibly a question number) is at the top right.

Explanation:

Step1: Find the GCD of 15 and 40

First, find the greatest common divisor (GCD) of 15 and 40. The factors of 15 are 1, 3, 5, 15. The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. The common factor is 5. Now, divide 15 by 5: \(15\div5 = 3\), and divide 40 by 5: \(40\div5 = 8\). So the ratio of the first column (15 and 40) is 3:8.

Step2: Apply the ratio to the second column

Let the unknown number be \(x\). We know the ratio of the first column is 3:8, so for the second column ( \(x\) and 48), the ratio should also be 3:8. So we set up the proportion \(\frac{x}{48}=\frac{3}{8}\) (wait, no, actually, looking at the table, the first row is 40 and 48, second row is 15 and \(x\). Maybe another approach: check the relationship between rows or columns. Let's check the first row: 40 and 48. The GCD of 40 and 48 is 8. \(40\div8 = 5\), \(48\div8 = 6\). Now check the second row: 15. \(15\div5 = 3\), so then \(x = 3\times6 = 18\). Wait, let's verify. Another way: cross - multiply. If we consider the table as a proportion: \(\frac{15}{40}=\frac{x}{48}\). Cross - multiplying gives \(40x=15\times48\).

Step3: Solve for \(x\)

Calculate \(15\times48 = 720\). Then \(x=\frac{720}{40}=18\).

Answer:

18