100+ Free Math Games for Grade 4 ONLINE Practice - Free Printable

To solve this puzzle, we need to find the numbers that go in the empty gray boxes. We can do this by looking at the rows (horizontal) and columns (vertical) one by one.

Let's label the empty boxes with letters to keep track of them:
* Row 1: A + 9 = B; B - 3 = C
* Row 2: D + 8 = 17; 17 - E = 15
* Row 3: 19 - F = G; G - 1 = H
* Row 4: 9 + I = 17; 17 - J = 10
* Row 5: K + 9 = L; L - M = N

Now let's look at the columns (vertical):
* Col 1: A + D = 19; 19 - 9 = K
* Col 2: 9 + 8 = F; F - I = 9
* Col 3: B - E = G; G + 17 = L
* Col 4: 3 + 15 = H; H - 10 = M
* Col 5: C - 15 = H; H + 10 = N

Step 1: Solve Row 2
* $D + 8 = 17$. To find D, subtract 8 from 17. $17 - 8 = 9$. So, D = 9.
* $17 - E = 15$. To find E, subtract 15 from 17. $17 - 15 = 2$. So, E = 2.

Step 2: Solve Column 1
* We know D is 9. The equation is $A + D = 19$, which means $A + 9 = 19$.
* Subtract 9 from 19. $19 - 9 = 10$. So, A = 10.
* The next part is $19 - 9 = K$. $19 - 9 = 10$. So, K = 10.

Step 3: Solve Row 1
* We know A is 10. The equation is $A + 9 = B$, which means $10 + 9 = B$.
* $10 + 9 = 19$. So, B = 19.
* The next part is $B - 3 = C$, which means $19 - 3 = C$.
* $19 - 3 = 16$. So, C = 16.

Step 4: Solve Column 2
* The top part is $9 + 8 = F$.
* $9 + 8 = 17$. So, F = 17.
* The bottom part is $F - I = 9$. Since F is 17, it is $17 - I = 9$.
* $17 - 9 = 8$. So, I = 8.

Step 5: Solve Row 4
* Check: $9 + I = 17$. Since I is 8, $9 + 8 = 17$. This matches!
* The next part is $17 - J = 10$.
* $17 - 10 = 7$. So, J = 7.

Step 6: Solve Column 3
* The middle part is $B - E = G$. We know B is 19 and E is 2.
* $19 - 2 = 17$. So, G = 17.
* Check with Row 3 start: $19 - F = G$. We found F is 17. $19 - 17 = 2$? Wait. Let's re-read the grid carefully.
* Row 3 starts with "19 - [Box] = [Box]". The box under the minus sign is F. The result box is G.
* Col 2 says $9+8=F$. So $F=17$.
* Row 3 says $19 - 17 = G$. So $G=2$.
* Let's re-check Col 3 logic. Col 3 is: Box B, minus Box E, equals Box G.
* $B=19$, $E=2$. $19-2=17$. So Col 3 implies $G=17$.
* Row 3 implies $G=2$. There is a contradiction. Let me re-read the image structure.

Let's look at the connections again.
Row 1: `[A] + 9 = [B]` then `[B] - 3 = [C]`
Row 2: `[D] + 8 = 17` then `17 - [E] = 15`
Row 3: `19 - [F] = [G]` then `[G] - 1 = [H]`
Row 4: `9 + [I] = 17` then `17 - [J] = 10`
Row 5: `[K] + 9 = [L]` then `[L] - [M] = [N]`

Col 1: `[A] + [D] = 19` then `19 - 9 = [K]`
Col 2: `9 + 8 = [F]` then `[F] - [I] = 9`
Col 3: `[B] - [E] = [G]` then `[G] + 17 = [L]` ... Wait, looking at the image, Row 4 Col 3 is `17`. The operator below it is `+`. So it is `[G] + 17 = [L]`.
Col 4: `3 + 15 = [H]` then `[H] - 10 = [M]`
Col 5: `[C] - 15 = [H]` ... Wait. Row 2 ends with 15. Row 3 ends with H. The operator between them is `-`. So `[C] - 15 = [H]`? No, usually these grids flow down.
Let's trace Column 5 carefully.
Top box is C. Below it is `-`. Below that is 15 (from Row 2 end). Below that is `=`. Below that is H (from Row 3 end).
So, $C - 15 = H$.
Below H is `+`. Below that is 10 (from Row 4 end). Below that is `=`. Below that is N.
So, $H + 10 = N$.

Let's re-evaluate based on this strict column reading.

Recalculating Step-by-Step:

1. Row 2:
* $D + 8 = 17 \rightarrow D = 9$.
* $17 - E = 15 \rightarrow E = 2$.

2. Column 1:
* $A + D = 19$. Since $D=9$, $A + 9 = 19 \rightarrow A = 10$.
* $19 - 9 = K \rightarrow K = 10$.

3. Row 1:
* $A + 9 = B$. Since $A=10$, $10 + 9 = 19 \rightarrow B = 19$.
* $B - 3 = C$. Since $B=19$, $19 - 3 = 16 \rightarrow C = 16$.

4. Column 2:
* $9 + 8 = F \rightarrow F = 17$.
* $F - I = 9$. Since $F=17$, $17 - I = 9 \rightarrow I = 8$.

5. Row 4:
* $9 + I = 17$. Since $I=8$, $9+8=17$. (Consistent).
* $17 - J = 10 \rightarrow J = 7$.

6. Column 4:
* Top part: $3 + 15 = H$. (From Row 1 '3', Row 2 '15').
* $3 + 15 = 18 \rightarrow H = 18$.
* Bottom part: $H - 10 = M$. Since $H=18$, $18 - 10 = 8 \rightarrow M = 8$.

7. Check Consistency for H using Column 5:
* Column 5 equation: $C - 15 = H$.
* We found $C = 16$.
* $16 - 15 = 1$.
* But Column 4 gave us $H = 18$.
* Contradiction! $1 \neq 18$.

Let me look at the image operators again very closely.

Column 4:
Row 1 has `3`.
Operator below is `-`.
Row 2 has `15`? No, Row 2 ends with `15`. The box to the left of 15 is empty (E). The box above E is 3.
Let's trace Column 4 vertically:
Box (empty, let's call it X, which is actually the result of B-3=C? No, C is Col 5).

Let's map coordinates (Row, Col):
R1: [A] + 9 = [B] | [B] - 3 = [C] --> Wait, the grid is 5x5 boxes for numbers?
Let's count boxes.
Row 1: Box, Plus, 9, Equals, Box, Minus, 3, Equals, Box.
This implies the "Box" after Equals is the same as the "Box" before Minus.
So, $A+9=B$. Then $B-3=C$.

Row 2: Box, Plus, 8, Equals, 17, Minus, Box, Equals, 15.
So, $D+8=17$. Then $17-E=15$.

Vertical Connections:
Col 1: A, Plus, D, Equals, 19, Minus, 9, Equals, K.
So, $A+D=19$. Then $19-9=K$.

Col 2: 9, Plus, 8, Equals, F, Minus, I, Equals, 9.
So, $9+8=F$. Then $F-I=9$.

Col 3: B, Minus, E, Equals, G, Plus, 17, Equals, L.
Wait, look at Row 3 and 4 in Col 3.
Row 3: 19 - F = G. (Here F is the result of Col 2 top).
Row 4: 9 + I = 17. (Here 17 is a fixed number).
The vertical connection in Col 3 goes:
Box B (from R1).
Minus sign.
Box E (from R2).
Equals sign.
Box G (from R3).
Plus sign.
Box/Number 17 (from R4).
Equals sign.
Box L (from R5).
So, $B - E = G$. And $G + 17 = L$.

Col 4:
Box/Number 3 (from R1).
Minus sign.
Box/Number 15 (from R2).
Equals sign.
Box H (from R3).
Minus sign.
Box/Number 10 (from R4).
Equals sign.
Box M (from R5).
So, $3 - 15 = H$? That would be negative. Unlikely for this level.
Let's re-read the operator between 3 and 15. It looks like a minus `-`.
Is it possible the order is Top - Bottom? Or Bottom - Top?
Usually, it reads downwards. $3 - 15$ is problematic.
Could the operator be a plus? It looks like a single horizontal dash.
Could the number in R2 be something else? It says `15`.
Could the number in R1 be something else? It says `3`.

Let's look at Col 5.
Box C (from R1).
Minus sign.
Box/Number 15 (from R2).
Equals sign.
Box H (from R3).
Plus sign.
Box/Number 10 (from R4).
Equals sign.
Box N (from R5).
So, $C - 15 = H$. And $H + 10 = N$.

Let's re-evaluate Col 4.
Maybe the operator is not minus?
In R1, it is `B - 3 = C`.
In R2, it is `17 - E = 15`.
The vertical strip corresponding to the "3" and "15" is Col 4.
The operator between them is `-`.
If it is $3 - 15$, H = -12.
If it is $15 - 3$, H = 12.
Let's test if H=12 works elsewhere.

From Col 5: $C - 15 = H$.
We calculated $C = 16$.
$16 - 15 = 1$. So $H = 1$.

Now we have a conflict for H.
Col 4 suggests H is related to 3 and 15.
Col 5 suggests H is related to C and 15.

Let's look at the grid alignment again.
Row 3 is: `19 - F = G` then `G - 1 = H`.
Ah! I missed the `- 1` in Row 3!
Let's re-read Row 3 carefully from the image.
Image: `[Gray] + 8 = 17 - [Gray] = 15` (Row 2)
Image: `19 - [Gray] = [Gray] - 1 = [Gray]` (Row 3)
Yes! Row 3 is: $19 - F = G$ AND $G - 1 = H$.

My previous Col 4 analysis assumed the vertical flow was just numbers. But Row 3 generates H internally too.

Let's restart the calculation with the correct Row 3 equation: $G - 1 = H$.

Restarting Calculations:

1. Row 2:
$D + 8 = 17 \Rightarrow D = 9$.
$17 - E = 15 \Rightarrow E = 2$.

2. Column 1:
$A + D = 19 \Rightarrow A + 9 = 19 \Rightarrow A = 10$.
$19 - 9 = K \Rightarrow K = 10$.

3. Row 1:
$A + 9 = B \Rightarrow 10 + 9 = 19 \Rightarrow B = 19$.
$B - 3 = C \Rightarrow 19 - 3 = 16 \Rightarrow C = 16$.

4. Column 2:
$9 + 8 = F \Rightarrow F = 17$.
$F - I = 9 \Rightarrow 17 - I = 9 \Rightarrow I = 8$.

5. Row 4:
$9 + I = 17 \Rightarrow 9 + 8 = 17$ (Checks out).
$17 - J = 10 \Rightarrow J = 7$.

6. Column 3:
$B - E = G \Rightarrow 19 - 2 = 17 \Rightarrow G = 17$.
Check with Row 3 start: $19 - F = G$. We found $F=17$. $19 - 17 = 2$.
Conflict: Column 3 says $G=17$. Row 3 says $G=2$.

Why is there a conflict?
Let's re-read Col 3 vertical operation.
Top: B (19).
Operator: `-`.
Middle: E (2).
Operator: `=`.
Result: G.
So $19 - 2 = 17$.

Let's re-read Row 3 horizontal operation.
Left: 19.
Operator: `-`.
Middle: F.
Operator: `=`.
Result: G.
We found F from Col 2: $9+8=F \Rightarrow F=17$.
So $19 - 17 = 2$.

So $G$ cannot be both 17 and 2.
Did I identify the boxes correctly?

Let's look at the image again.
Row 1: Box, +, 9, =, Box, -, 3, =, Box
Row 2: Box, +, 8, =, 17, -, Box, =, 15
Row 3: 19, -, Box, =, Box, -, 1, =, Box
Row 4: 9, +, Box, =, 17, -, Box, =, 10
Row 5: Box, +, 9, =, Box, -, Box, =, Box

Verticals:
Col 1: Box, +, Box, =, 19, -, 9, =, Box
Col 2: 9, +, 8, =, Box, -, Box, =, 9 <-- Wait.
Let's look at Col 2 bottom.
Row 4 has `9 + [Box] = 17`. The box is I.
Below I is `=`.
Below that is `9`.
Above I is `Box` (F).
Above F is `8`.
Above 8 is `+`.
Above + is `9`.
So Col 2 is: $9 + 8 = F$. Then $F - I = 9$?
Let's check the operator between F and I.
Row 3 is `19 - F = G`. The operator under F is `-`?
Looking at the grid lines:
Row 3 Col 2 contains F.
Row 4 Col 2 contains I.
Between Row 3 and Row 4, there is an orange bar with operators.
Under Col 2, the operator is `-`.
So yes, $F - I = 9$ (where 9 is the number in Row 5 Col 1? No, Row 5 Col 2 is 9).
Wait, Row 5 is `[K] + 9 = [L] ...`
So Row 5 Col 2 is `9`.
So Col 2 ends with `... = 9`.
So $F - I = 9$ is correct.

So where is the error?
$B - E = G$ vs $19 - F = G$.
$B=19, E=2 \Rightarrow G=17$.
$F=17 \Rightarrow 19-17=2 \Rightarrow G=2$.

Is it possible that Col 3 operator is NOT minus?
Image: Row 1 Col 4 is `-`. Row 2 Col 4 is `-`.
Col 3 corresponds to the results of the first half of the rows.
Row 1: `... = [B]`. Below B is `-`.
Row 2: `... = 17`. Below 17 is `-`.
Row 3: `... = [G]`. Below G is `+`.

So Col 3 is:
$B$
$-$
$E$ (Wait, E is in Col 4? No.)

Let's map indices strictly.
Indices 1 to 9 for number slots?
Let's use (Row, Position).
Pos 1: Num. Pos 2: Op. Pos 3: Num. Pos 4: Op. Pos 5: Num. Pos 6: Op. Pos 7: Num. Pos 8: Op. Pos 9: Num.

Row 1: A, +, 9, =, B, -, 3, =, C
Row 2: D, +, 8, =, 17, -, E, =, 15
Row 3: 19, -, F, =, G, -, 1, =, H
Row 4: 9, +, I, =, 17, -, J, =, 10
Row 5: K, +, 9, =, L, -, M, =, N

Now Verticals align with Positions 1, 3, 5, 7, 9.

Position 1 (Col 1):
A
+
D
=
19
-
9
=
K
Eq: $A+D=19$, $19-9=K$.

Position 3 (Col 2):
9
+
8
=
F
-
I
=
9
Eq: $9+8=F$, $F-I=9$.

Position 5 (Col 3):
B
-
17 <-- Wait. Row 2 Pos 5 is 17.
=
G
+
17 <-- Row 4 Pos 5 is 17.
=
L
Eq: $B - 17 = G$? NO. The operator is between Row 1 and Row 2.
The operator in the orange bar between R1 and R2 at Pos 5 is `-`.
So $B - 17 = G$?
Let's check the image.
Row 1 Pos 5 is B.
Row 2 Pos 5 is 17.
Between them is `-`.
So $B - 17 = G$?
But earlier I thought it was $B - E = G$. E is at Pos 7.
This changes everything.

Let's re-verify the columns based on Positions 1, 3, 5, 7, 9.

Col 1 (Pos 1): $A, D, 19, 9, K$. Ops: $+, =, -, =$.
$A+D=19$. $19-9=K$.

Col 2 (Pos 3): $9, 8, F, I, 9$. Ops: $+, =, -, =$.
$9+8=F$. $F-I=9$.

Col 3 (Pos 5): $B, 17, G, 17, L$. Ops: $-, =, +, =$.
$B - 17 = G$.
$G + 17 = L$.

Col 4 (Pos 7): $3, E, 1, J, M$. Ops: $-, =, -, =$.
Wait, look at Row 3 Pos 7. It is `1`.
Look at Row 4 Pos 7. It is `J`.
Look at Row 2 Pos 7. It is `E`.
Look at Row 1 Pos 7. It is `3`.
Operators between them:
R1-R2: `-`. So $3 - E = 1$? Or $3 - E = \text{something}$?
The `=` is between R2 and R3.
So: $3 - E = 1$?
Let's check the operator signs in the vertical strip for Pos 7.
Between R1(3) and R2(E): `-`.
Between R2(E) and R3(1): `=`.
So $3 - E = 1$.
Between R3(1) and R4(J): `-`.
Between R4(J) and R5(M): `=`.
So $1 - J = M$.

Col 5 (Pos 9): $C, 15, H, 10, N$. Ops: $-, =, +, =$.
Between R1(C) and R2(15): `-`.
Between R2(15) and R3(H): `=`.
So $C - 15 = H$.
Between R3(H) and R4(10): `+`.
Between R4(10) and R5(N): `=`.
So $H + 10 = N$.

Okay, this structure seems consistent. Let's solve again.

Step 1: Solve Col 2 (Pos 3)
$9 + 8 = F \Rightarrow F = 17$.
$F - I = 9 \Rightarrow 17 - I = 9 \Rightarrow I = 8$.

Step 2: Solve Row 4
$9 + I = 17 \Rightarrow 9 + 8 = 17$. (Consistent).
$17 - J = 10 \Rightarrow J = 7$.

Step 3: Solve Col 4 (Pos 7)
$3 - E = 1 \Rightarrow E = 2$.
$1 - J = M$. We know $J=7$.
$1 - 7 = -6$.
Negative numbers? In a primary school puzzle?
Let's re-read the operator between R3(1) and R4(J).
Image: Row 3 is `... - 1 = ...`. Row 4 is `... - J = ...`.
Vertical strip at Pos 7.
R3 value is 1.
R4 value is J.
Operator between them is `+`?
Let's look at the orange block between Row 3 and Row 4.
Pos 1: `-`. Pos 3: `-`. Pos 5: `+`. Pos 7: `+`. Pos 9: `+`.
Ah! The operator between R3 and R4 at Pos 7 is `+`.
So, $1 + J = M$.

Let's re-read the operator between R1 and R2 at Pos 7.
R1 value 3. R2 value E.
Operator is `-`.
Equation: $3 - E = 1$?
If $E=2$, $3-2=1$. This works perfectly.

So, $E = 2$.
And $M = 1 + J$. Since $J=7$, $M = 1 + 7 = 8$.

Step 4: Solve Row 2
$D + 8 = 17 \Rightarrow D = 9$.
$17 - E = 15$. Check: $17 - 2 = 15$. (Consistent).

Step 5: Solve Col 1 (Pos 1)
$A + D = 19 \Rightarrow A + 9 = 19 \Rightarrow A = 10$.
$19 - 9 = K \Rightarrow K = 10$.

Step 6: Solve Row 1
$A + 9 = B \Rightarrow 10 + 9 = 19 \Rightarrow B = 19$.
$B - 3 = C \Rightarrow 19 - 3 = 16 \Rightarrow C = 16$.

Step 7: Solve Col 5 (Pos 9)
$C - 15 = H \Rightarrow 16 - 15 = 1 \Rightarrow H = 1$.
$H + 10 = N \Rightarrow 1 + 10 = 11 \Rightarrow N = 11$.

Step 8: Solve Row 3
$19 - F = G$. We know $F=17$.
$19 - 17 = 2 \Rightarrow G = 2$.
$G - 1 = H$. Check: $2 - 1 = 1$. We found $H=1$. (Consistent).

Step 9: Solve Col 3 (Pos 5)
$B - 17 = G$. We know $B=19, G=2$.
$19 - 17 = 2$. (Consistent).
$G + 17 = L$. We know $G=2$.
$2 + 17 = 19 \Rightarrow L = 19$.

Step 10: Solve Row 5
$K + 9 = L$. We know $K=10, L=19$.
$10 + 9 = 19$. (Consistent).
$