Question

1 complete each factor puzzle.

Explanation:

Step1: Analyze factor - product relationships

Let the missing numbers be \(a\), \(b\), \(c\) (from left - to - right and top - to - bottom). Assume that the numbers in the grid follow the rule that the product of the numbers in each row and each column is consistent. First, consider the top - right number \(12\) and bottom - right number \(8\). Let the common product of each row and column be \(P\).

Step2: Find the common product

Since the product of the numbers in the right - hand column is \(P = 12\times8=96\).

Step3: Calculate the missing numbers

For the top - left number \(15\), in the top row, if the product of the top row is \(96\), then the number in the top - left cell \(a\) and \(15\) and the number in the middle of the top row (which we don't need to name separately for this calculation) satisfy \(15\times a\times12 = 96\). But a more straightforward way is to consider the left - hand column. Since the product of the right - hand column is \(96\), for the left - hand column, if the product of the left - hand column is also \(96\), and one number is \(15\), then the number below \(15\) (let's call it \(b\)) satisfies \(15\times b=96\div8 = 12\), so \(b=\frac{12}{15}=\frac{4}{5}\). And for the bottom - left number \(c\), since the product of the bottom row is \(96\) and one number is \(8\), and the number above it is \(\frac{4}{5}\), then \(c=\frac{96}{8\times\frac{4}{5}}=\frac{96}{\frac{32}{5}} = 15\).

Answer:

The missing number in the bottom - left cell is \(15\), and the missing number in the middle of the bottom row is \(\frac{4}{5}\)