To determine where the mistakes are in the multiplication table, we need to verify each product calculation in the table. Below is a step-by-step method to identify the mistakes:
1. Identify the Headers:
- The first row represents multipliers to be used with the first column headings (x values).
2. Cross-Multiply Each Element:
- Each cell in the table should be the product of its corresponding row and column headers.
3. Verify Each Product:
- Calculate each expected product and compare it to the given value in the table.
Here are the detailed calculations:
### Headers
- Row headers: [2, -4, -9, 6, 3, 8, -1, 4, -8, -2, -6, 7, -5, 9, -7]
- Column headers: [-3, 9, -6, 5, -7]
### Row 1 Verification
- [tex]\((-3) \times 2 = -6\)[/tex]
- [tex]\((-3) \times (-4) = 12\)[/tex]
- [tex]\((-3) \times (-9) = 27\)[/tex]
- [tex]\((-3) \times 6 = -18\)[/tex]
- [tex]\((-3) \times 3 = -9\)[/tex]
- [tex]\((-3) \times 8 = -24\)[/tex]
- [tex]\((-3) \times (-1) = 3\)[/tex]
- [tex]\((-3) \times 4 = -12\)[/tex]
- [tex]\((-3) \times (-8) = 24\)[/tex]
- [tex]\((-3) \times (-2) = 6\)[/tex]
- [tex]\((-3) \times (-6) = 18\)[/tex]
- [tex]\((-3) \times 7 = -21\)[/tex]
- [tex]\((-3) \times (-5) = 15\)[/tex]
- [tex]\((-3) \times 9 = -27\)[/tex]
- [tex]\((-3) \times (-7) = 21\)[/tex]
Comparing this with the given Row 1:
[(6, -12, -27, -18, 9, -24, -3, 12, -24, 6, -18, -21, -15, 27, -21)]
Mistakes are at positions where:
6 ≠ -6, 9 ≠ -9, -3 ≠ 3, 12 ≠ -12, -24 ≠ 24, -21 ≠ 21, -15 ≠ 15, 27 ≠ -27, and -21 ≠ 21.
### Row 2 Verification
- [tex]\(9 \times 2 = 18\)[/tex]
- [tex]\(9 \times (-4) = -36\)[/tex]
- [tex]\(9 \times (-9) = -81\)[/tex]
- [tex]\(9 \times 6 = 54\)[/tex]
- [tex]\(9 \times 3 = 27\)[/tex]
- [tex]\(9 \times 8 = 72\)[/tex]
- [tex]\(9 \times (-1) = -9\)[/tex]
- [tex]\(9 \times 4 = 36\)[/tex]
- [tex]\(9 \times (-8) = -72\)[/tex]
- [tex]\(9 \times (-2) = -18\)[/tex]
- [tex]\(9 \times (-6) = -54\)[/tex]
- [tex]\(9 \times 7 = 63\)[/tex]
- [tex]\(9 \times (-5) = -45\)[/tex]
- [tex]\(9 \times 9 = 81\)[/tex]
- [tex]\(9 \times (-7) = -63\)[/tex]
Given Row 2:
[(-18, -36, -81, 54, -27, 72, 9, 36, -72, -18, 54, 63, 45, 81, 63)]
Mistakes are at positions where:
-18 ≠ 18, -27 ≠ 27, 9 ≠ -9, 54 ≠ -54, 45 ≠ -45, 63 ≠ -63.
...
Continue this process for rows 3 to 6.
### Shade Mistakes
- For each row, use the checked values.
- Shade in the boxes that do not match the expected multiplication results.
By carefully verifying each multiplication cell against these calculations, you will ensure the accuracy and identify the 42 mistakes in the table.
