Problem Description:
The task involves solving a series of multiplication equations and then shading the areas in the grid where the product (answer) is an
odd number. The grid contains various multiplication problems, and each problem corresponds to a specific region in the grid.
Step-by-Step Solution:
1.
Understand the Task:
- Solve each multiplication equation.
- Determine if the product is odd or even.
- Shade the regions corresponding to equations with odd products.
2.
Key Rule for Odd and Even Products:
- The product of two numbers is
odd only if both numbers are odd.
- If either (or both) of the numbers being multiplied is even, the product will be
even.
3.
Solve Each Equation and Identify Odd Products:
We will go through each equation systematically and determine whether the product is odd or even.
#### Top Row:
- \( 8 \times 2 = 16 \) (Even)
- \( 7 \times 4 = 28 \) (Even)
- \( 6 \times 5 = 30 \) (Even)
- \( 8 \times 12 = 96 \) (Even)
- \( 8 \times 8 = 64 \) (Even)
#### Second Row:
- \( 7 \times 6 = 42 \) (Even)
- \( 7 \times 7 = 49 \) (Odd)
- \( 7 \times 2 = 14 \) (Even)
- \( 8 \times 5 = 40 \) (Even)
#### Third Row:
- \( 6 \times 9 = 54 \) (Even)
- \( 7 \times 7 = 49 \) (Odd)
- \( 6 \times 6 = 36 \) (Even)
- \( 5 \times 5 = 25 \) (Odd)
- \( 8 \times 5 = 40 \) (Even)
#### Fourth Row:
- \( 6 \times 2 = 12 \) (Even)
- \( 8 \times 4 = 32 \) (Even)
- \( 6 \times 9 = 54 \) (Even)
- \( 8 \times 7 = 56 \) (Even)
- \( 7 \times 5 = 35 \) (Odd)
#### Fifth Row:
- \( 6 \times 3 = 18 \) (Even)
- \( 8 \times 9 = 72 \) (Even)
- \( 7 \times 3 = 21 \) (Odd)
- \( 6 \times 10 = 60 \) (Even)
- \( 7 \times 11 = 77 \) (Odd)
- \( 5 \times 11 = 55 \) (Odd)
#### Sixth Row:
- \( 6 \times 11 = 66 \) (Even)
- \( 6 \times 12 = 72 \) (Even)
- \( 7 \times 11 = 77 \) (Odd)
- \( 6 \times 8 = 48 \) (Even)
- \( 7 \times 6 = 42 \) (Even)
#### Seventh Row:
- \( 6 \times 9 = 54 \) (Even)
- \( 7 \times 8 = 56 \) (Even)
- \( 8 \times 10 = 80 \) (Even)
- \( 7 \times 10 = 70 \) (Even)
- \( 8 \times 6 = 48 \) (Even)
4.
Shade the Regions with Odd Products:
Based on the calculations above, the regions corresponding to odd products are:
- \( 7 \times 7 = 49 \)
- \( 7 \times 7 = 49 \)
- \( 5 \times 5 = 25 \)
- \( 7 \times 5 = 35 \)
- \( 7 \times 3 = 21 \)
- \( 7 \times 11 = 77 \)
- \( 5 \times 11 = 55 \)
- \( 7 \times 11 = 77 \)
5.
Final Answer:
The regions to be shaded are those corresponding to the equations that yield odd products. These are:
- \( 7 \times 7 \)
- \( 7 \times 7 \)
- \( 5 \times 5 \)
- \( 7 \times 5 \)
- \( 7 \times 3 \)
- \( 7 \times 11 \)
- \( 5 \times 11 \)
- \( 7 \times 11 \)
Boxed Answer:
\[
\boxed{7 \times 7, 7 \times 7, 5 \times 5, 7 \times 5, 7 \times 3, 7 \times 11, 5 \times 11, 7 \times 11}
\]
Parent Tip: Review the logic above to help your child master the concept of printable fun math worksheet.