Let’s solve this step by step.
We have a 3x3 grid called a “Fraction Magic Square.” In a magic square, the sum of each row, each column, and both diagonals should be the same.
All fractions here have the same denominator: 17. So we can just add the numerators and keep the denominator as 17 — that makes it easier!
Let’s first find what the magic sum is. We can use any complete row, column, or diagonal.
Look at the top row:
6/17 + 5/17 + 3/17 = (6 + 5 + 3)/17 = 14/17
So the magic sum is 14/17.
Now check another row to confirm — middle row:
3/17 + 2/17 + 9/17 = (3 + 2 + 9)/17 = 14/17 → Good!
Check left column:
6/17 + 3/17 + 5/17 = (6 + 3 + 5)/17 = 14/17 → Perfect!
Now, let’s look at the bottom row. It has two numbers filled in:
5/17 + ? + 2/17 = 14/17
Add the known numerators: 5 + 2 = 7
So the missing numerator must be: 14 - 7 = 7
Therefore, the missing fraction is 7/17.
Let’s double-check with the middle column to make sure:
Middle column: 5/17 + 2/17 + ? = 14/17
5 + 2 = 7 → 14 - 7 = 7 → again, 7/17 ✔️
Also check the diagonal from top-left to bottom-right:
6/17 + 2/17 + 2/17 = 10/17 → Wait, that’s not 14/17? Hmm…
Wait — actually, the diagonal from top-left to bottom-right is:
Top-left: 6/17
Center: 2/17
Bottom-right: 2/17
Sum: 6 + 2 + 2 = 10 → 10/17 — that’s NOT 14/17.
That means maybe I made a mistake? Or perhaps the diagonals aren’t required? Let me re-read the problem.
The title says “Fraction Magic Square” — typically, magic squares require rows, columns, AND diagonals to sum to the same value. But in this case, if we assume only rows and columns need to match (since one diagonal doesn’t), then our answer still holds for rows and columns.
But wait — let’s check the other diagonal: top-right to bottom-left.
Top-right: 3/17
Center: 2/17
Bottom-left: 5/17
Sum: 3 + 2 + 5 = 10 → 10/17 again.
Hmm… so diagonals don’t sum to 14/17. That suggests maybe this isn’t a full magic square? Or perhaps there’s an error?
Wait — let’s recalculate the center cell. The center is given as 2/17. Maybe that’s correct?
Alternatively, perhaps the magic sum is not 14/17? Let’s try using a different row.
What about the right column?
3/17 + 9/17 + 2/17 = 14/17 → same as before.
Left column: 6+3+5=14 → 14/17.
Top row: 6+5+3=14 → 14/17.
Middle row: 3+2+9=14 → 14/17.
Bottom row: 5 + ? + 2 = 14 → ? = 7 → 7/17.
Middle column: 5 + 2 + ? = 14 → ? = 7 → 7/17.
So even though the diagonals don’t add up to 14/17, all rows and columns do — and since the question is asking for the missing cell in the bottom row, and we’ve confirmed via two different lines (bottom row and middle column) that it must be 7/17, we can be confident.
Perhaps the diagonals are not part of the requirement here — or maybe it’s a typo in the puzzle. But based on the data given, the only consistent answer is 7/17.
Final Answer:
7/17
Parent Tip: Review the logic above to help your child master the concept of fraction worksheet for grade 4.
