First column: 
a/g-j=-5
Second column:
b-h+k=2
Third column: 
c−i+l=11

solve this math given that above and follow this given below

1.the missing values are the whole numbers between 1 and 9
2.each number is only used once
3.each column is a math equation
4.remember that multiplication and division are performed before addition and subtraction 


To solve this problem, we need to assign whole numbers between 1 and 9 (with no repetition) to the variables \( a, b, c, g, h, i, j, k, l \) such that the equations in each column hold true. The equations are:

1. \( \frac{a}{g} - j = -5 \)
2. \( b - h + k = 2 \)
3. \( c - i + l = 11 \)

Let's approach this step by step.

### Step 1: Analyze the first equation
The first equation is \( \frac{a}{g} - j = -5 \). Rearranging it gives:
\[ \frac{a}{g} = j - 5 \]

Since \( \frac{a}{g} \) must be a whole number (because \( a \) and \( g \) are whole numbers), \( j - 5 \) must also be a whole number. Therefore, \( j \) must be at least 5.

### Step 2: Analyze the second equation
The second equation is \( b - h + k = 2 \). This equation involves addition and subtraction, and we need to find three numbers that satisfy this equation.

### Step 3: Analyze the third equation
The third equation is \( c - i + l = 11 \). Similar to the second equation, we need to find three numbers that satisfy this equation.

### Step 4: Assign the numbers
Given the constraints (whole numbers between 1 and 9, no repetition, and the order of operations), let's try assigning numbers to satisfy all three equations simultaneously.

#### Trial and error approach:
1. Start with the first equation:
   - Let's try \( a = 6 \), \( g = 1 \), and \( j = 1 \) (so that \( \frac{a}{g} - j = 6 - 1 = 5 \)). This doesn't work as we need \( j - 5 \), so let’s continue.

I'll now solve for a working combination.The solution that satisfies all the equations and conditions is:

- \( a = 2 \), \( g = 1 \), \( j = 7 \)
- \( b = 3 \), \( h = 5 \), \( k = 4 \)
- \( c = 8 \), \( i = 6 \), \( l = 9 \)

### Verification:
1. **First equation**: \( \frac{2}{1} - 7 = 2 - 7 = -5 \) ✔️
2. **Second equation**: \( 3 - 5 + 4 = 2 \) ✔️
3. **Third equation**: \( 8 - 6 + 9 = 11 \) ✔️

All equations hold true, and all numbers between 1 and 9 are used exactly once.

Would you like more details or have any questions?

Here are 5 related questions:
1. Can you rearrange the numbers to satisfy a different set of equations?
2. What happens if we change the range of numbers?
3. How would this change if multiplication was involved in more equations?
4. Can this type of puzzle be solved using other methods than trial and error?
5. What strategies help in solving similar puzzles more efficiently?

**Tip**: When solving puzzles with multiple constraints, try isolating one variable or equation to reduce complexity early on.

Learn how to solve equations involving variables and order of operations with detailed step-by-step explanations. This problem requires assigning whole numbers between 1 and 9 to variables in three equations. Suitable for students in Grades 6-8.

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