The image shows a math puzzle game involving additions and subtractions. The goal is to fill in the missing numbers in the grid so that all the equations are correct. Let's solve it step by step.
Step 1: Understand the Puzzle Structure
The puzzle consists of a grid with various addition and subtraction operations. Each operation involves two numbers (one on each side of the operator) and a result. We need to determine the missing numbers to satisfy all the equations.
Step 2: Analyze the Equations
We will start from the top-left corner and work our way through the grid, solving each equation systematically.
#### Top Row:
1.
Top-left section:
- Equation: \( ? + 3 = 8 \)
- Solution: \( ? = 8 - 3 = 5 \)
2.
Top-middle section:
- Equation: \( 5 + ? = 12 \)
- Solution: \( ? = 12 - 5 = 7 \)
3.
Top-right section:
- Equation: \( ? + 1 = 5 \)
- Solution: \( ? = 5 - 1 = 4 \)
#### Middle Row:
1.
Middle-left section:
- Equation: \( 7 - ? = 2 \)
- Solution: \( ? = 7 - 2 = 5 \)
2.
Middle-middle section:
- Equation: \( ? + 3 = 10 \)
- Solution: \( ? = 10 - 3 = 7 \)
3.
Middle-right section:
- Equation: \( 4 - ? = 5 \)
- Solution: \( ? = 4 - 5 = -1 \)
#### Bottom Row:
1.
Bottom-left section:
- Equation: \( 5 + ? = 8 \)
- Solution: \( ? = 8 - 5 = 3 \)
2.
Bottom-middle section:
- Equation: \( 3 - ? = 2 \)
- Solution: \( ? = 3 - 2 = 1 \)
3.
Bottom-right section:
- Equation: \( ? + 4 = 7 \)
- Solution: \( ? = 7 - 4 = 3 \)
Step 3: Verify All Equations
Let's verify each equation with the solved values:
-
Top-left: \( 5 + 3 = 8 \) (Correct)
-
Top-middle: \( 5 + 7 = 12 \) (Correct)
-
Top-right: \( 4 + 1 = 5 \) (Correct)
-
Middle-left: \( 7 - 5 = 2 \) (Correct)
-
Middle-middle: \( 7 + 3 = 10 \) (Correct)
-
Middle-right: \( 4 - (-1) = 5 \) (Correct)
-
Bottom-left: \( 5 + 3 = 8 \) (Correct)
-
Bottom-middle: \( 3 - 1 = 2 \) (Correct)
-
Bottom-right: \( 3 + 4 = 7 \) (Correct)
All equations are satisfied.
Final Answer:
The completed grid with the missing numbers filled in is:
\[
\begin{array}{ccc}
5 & 7 & 4 \\
7 & 7 & -1 \\
5 & 3 & 3 \\
\end{array}
\]
Thus, the solution is:
\[
\boxed{5, 7, 4, 7, 7, -1, 5, 3, 3}
\]
Parent Tip: Review the logic above to help your child master the concept of puzzle math worksheet.