Complete the table by filling in the missing values, assuming the relationship a * b = a.b is applied.

Solution:

The problem presents a table with columns labeled 'a', 'b', and 'a ⋅ b'. The relationship between these columns is that the value in the 'a ⋅ b' column is the product of the values in the 'a' and 'b' columns.

We need to fill in the missing values based on this relationship.

Calculations:

• Row 1: a = 70, b = 14. a ⋅ b = 70 * 14 = 980.
• Row 2: a ⋅ b = 88, b = 8. a = 88 / 8 = 11.
• Row 3: a = 12. This row needs more context to determine the missing values. Assuming this is part of a larger problem or grid where 'a' values are listed.
• Row 4: b = 4. This row also needs more context.
• Row 5: a ⋅ b = 160, b = 19. a = 160 / 19 (not a whole number, suggesting a potential error in the image or context, or it's a decimal multiplication). If we assume 160 is a * b and b is 19, then a = 160/19. However, if we look at other rows, it's more likely a = 160 and b = 19 for a * b. Let's re-evaluate the structure based on the crops.

Let's interpret the table based on the visible grid and numbers, assuming the columns are ordered as 'a·b', 'b', 'a' from left to right, and the values are listed row by row.

Let's re-interpret the table structure based on the OCR and the visual layout, assuming the columns are 'a·b', 'b', and 'a'. It seems the provided OCR might have interpreted rows as columns and vice versa, or the table is structured in an unconventional way.

Based on the image and crops, the columns are likely 'a·b', 'b', and 'a'. The rows contain values that fill in this structure.

Corrected interpretation of the table layout:

Let's fill in the values row by row, calculating the missing parts.

Row 1: a = 70, b = 14. a ⋅ b = 70 * 14 = 980. (The cell for 'a ⋅ b' is empty in the image, but this is the calculation.)

Row 2: a ⋅ b = 88, b = 8. a = 88 / 8 = 11. (The cell for 'a' is empty in the image, calculated as 11.)

Row 3: a = 12. (The cells for 'b' and 'a ⋅ b' are empty. We cannot determine them without more information or context.)

Row 4: b = 4. (The cells for 'a' and 'a ⋅ b' are empty.)

Row 5: a ⋅ b = 100. (Cells for 'b' and 'a' are empty.)

Row 6: b = 19. (Cells for 'a ⋅ b' and 'a' are empty.)

Row 7: a ⋅ b = 160. (Cells for 'b' and 'a' are empty.)

Row 8: a = 40. (Cells for 'b' and 'a ⋅ b' are empty.)

Row 9: a = 7. (Cells for 'b' and 'a ⋅ b' are empty.)

Row 10: a ⋅ b = 130. (Cells for 'b' and 'a' are empty.)

It appears the table has incomplete data or the image is a partial view of a larger problem. However, based on the visible numbers and the explicit relationship 'a ⋅ b', we can fill some gaps:

Let's consider the most likely interpretation of the visible numbers in their respective columns, where the header dictates the column's meaning.

Row 1: 'b' = 14, 'a' = 70. Therefore, 'a ⋅ b' = 70 * 14 = 980. This value is not explicitly shown in the 'a ⋅ b' column for this row.

Row 2: 'a ⋅ b' = 88, 'b' = 8. Therefore, 'a' = 88 / 8 = 11. This value (11) would fill the empty 'a' cell in this row.

Row 3: 'a' = 12. The other values are unknown.

Row 4: 'b' = 4. The other values are unknown.

Row 5: 'a ⋅ b' = 100. The other values are unknown.

Row 6: 'b' = 19. The other values are unknown.

Row 7: 'a ⋅ b' = 160. The other values are unknown.

Row 8: 'a' = 40. The other values are unknown.

Row 9: 'a' = 7. The other values are unknown.

Row 10: 'a ⋅ b' = 130. The other values are unknown.

Given the structure and the incomplete nature of the provided image, it is impossible to fill the entire table. However, we can deduce one missing value for 'a' based on the values provided in row 2.

Revised table based on direct interpretation and calculation where possible:

The question asks to complete the table by filling in the missing values. From the OCR and the visual representation, we can deduce the following:

The relationship is given by a * b = a.b.

Row 1: 'b' = 14, 'a' = 70. 'a ⋅ b' = 70 * 14 = 980.

Row 2: 'a ⋅ b' = 88, 'b' = 8. 'a' = 88 / 8 = 11.

Other rows have insufficient information to calculate the missing values. For instance, if 'a' is 12 (row 3), we don't know 'b' to calculate 'a ⋅ b'. Similarly, for row 4, if 'b' is 4, we don't know 'a'.

The provided image shows calculations in a grid to the right, which appear to be separate multiplication problems and do not directly relate to filling the table, other than perhaps providing examples of multiplication.

The main task is to fill the table. Based on the visible data and the rule, the completed portions are:

Answer:

The table is filled as follows based on the available data and the rule a * b = a.b:

Row 1: a = 70, b = 14, a ⋅ b = 980

Row 2: a ⋅ b = 88, b = 8, a = 11

Other cells cannot be determined from the given information.