Math worksheet for practicing multiplication grids with missing numbers.

Let’s solve each multiplication grid step by step.

Each grid has:
- Two numbers on top (let’s call them A and B)
- Two numbers on the left side (let’s call them C and D)
- Four boxes inside:
→ Top-left = A × C
→ Top-right = B × C
→ Bottom-left = A × D
→ Bottom-right = B × D

We’ll use the given numbers to find the missing ones.

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Problem 1:

Given:
Top row: ? , ?
Left column: 4, ?
Inside:
→ 4 × ? = 12 → so top-left number is 12 ÷ 4 = 3
→ 4 × ? = 20 → so top-right number is 20 ÷ 4 = 5
Now we know top row is 3 and 5.

Bottom row:
→ ? × 3 = 18 → bottom-left multiplier is 18 ÷ 3 = 6
Check: 6 × 5 = 30 → matches! ✔

So for Problem 1:
Top: 3, 5
Left: 4, 6

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Problem 2:

Given:
Top: ?, ?
Left: 5, ?
Inside:
→ 5 × ? = 30 → top-left = 30 ÷ 5 = 6
→ 5 × ? = 40 → top-right = 40 ÷ 5 = 8
Top row: 6, 8

Bottom:
→ ? × 6 = 42 → bottom-left = 42 ÷ 6 = 7
Check: 7 × 8 = 56 → matches! ✔

So for Problem 2:
Top: 6, 8
Left: 5, 7

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Problem 3:

Given:
Top: ?, ?
Left: 3, ?
Inside:
→ 3 × ? = 15 → top-left = 15 ÷ 3 = 5
→ 3 × ? = 21 → top-right = 21 ÷ 3 = 7
Top: 5, 7

Bottom:
→ ? × 5 = 45 → bottom-left = 45 ÷ 5 = 9
Check: 9 × 7 = 63 → matches! ✔

So for Problem 3:
Top: 5, 7
Left: 3, 9

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Problem 4:

Given:
Top: ?, ?
Left: ?, 4
Inside:
→ ? × ? = 16
→ ? × ? = 24
→ 4 × ? = 28 → so top-left = 28 ÷ 4 = 7
→ 4 × ? = 42 → top-right = 42 ÷ 4 = 10.5? Wait — that can’t be right. Let me check again.

Wait — actually, look at the grid:

It says:

x [ ] [ ]
-------
[ ] | 16 24
[4] | 28 42

So bottom row is multiplied by 4.

So:

→ 4 × top-left = 28 → top-left = 28 ÷ 4 = 7
→ 4 × top-right = 42 → top-right = 42 ÷ 4 = 10.5? That’s not whole. Hmm.

Wait — maybe I misread. Let me re-express:

Actually, looking at the structure:

The left column multiplies the top row.

So if bottom-left is 28 and bottom multiplier is 4, then top-left = 28 ÷ 4 = 7.

Similarly, bottom-right = 42 = 4 × top-right → top-right = 42 ÷ 4 = 10.5? Not possible.

Wait — perhaps the 4 is NOT the bottom multiplier? Let me check the layout again.

Looking back at problem 4 in the original:

It shows:

x □ □
------
□ | 16 24
4 | 28 42

Ah! So the left column has two numbers: one unknown on top, and 4 on bottom.

So:

Let top row be A and B.

Then:

Unknown_left × A = 16
Unknown_left × B = 24
4 × A = 28 → so A = 28 ÷ 4 = 7
4 × B = 42 → B = 42 ÷ 4 = 10.5? Still not integer.

Wait — 42 ÷ 4 is 10.5? That can't be. Maybe it's a typo? Or did I misread?

Wait — let me double-check the image description from user.

User said: “4 x [ ] [ ]” with inside: 16, 24 on top row; 28, 42 on bottom row, and left side: blank, 4.

But 4 × ? = 42 → ? = 10.5 — not valid for this level.

Wait — perhaps the 4 is on TOP? No, the format is consistent: left column has two numbers, top row has two.

Alternative idea: Maybe the 4 is multiplying the columns? No.

Wait — let’s try this:

If 4 × A = 28 → A = 7
And 4 × B = 42 → B = 10.5 — invalid.

But 28 and 42 are both divisible by 14? 28=14×2, 42=14×3 — but 4 isn’t 14.

Wait — perhaps the bottom-left is not 4 × A, but something else?

No — standard multiplication grid: row multiplier × column multiplier = cell.

Another thought: Maybe the 4 is the TOP multiplier? But no, the "x" is above the top row, and left column is vertical.

Wait — let’s look at problem 5 or others to confirm pattern.

In problem 1: left column 4 and ?, top row ? and ?, cells: 12,20 / 18,30

We found: 4×3=12, 4×5=20, 6×3=18, 6×5=30 — works.

Same for others.

Back to problem 4:

Cells:
Row1: 16, 24
Row2: 28, 42
Left col: ?, 4
Top row: ?, ?

So:

Let left-top = L, left-bottom = 4
Top-left = T1, top-right = T2

Then:

L × T1 = 16
L × T2 = 24
4 × T1 = 28 → T1 = 7
4 × T2 = 42 → T2 = 10.5 — still bad.

Unless... wait, 42 ÷ 4 is 10.5, but maybe it's 42 ÷ 6 = 7? No.

Perhaps the 4 is not the bottom multiplier? But in all other problems, the left column has two numbers, and they multiply the top row.

Wait — let’s calculate GCD of 28 and 42: gcd(28,42)=14. 28=14×2, 42=14×3. So if bottom multiplier was 14, then top would be 2 and 3. But it's written as 4.

This suggests a possible error — but since this is a worksheet, likely I’m misreading.

Wait — another idea: perhaps the "4" is in the top row? Let me re-read the user's text.

User wrote for problem 4:

"4. x □ □
□ | 16 24
4 | 28 42"

Yes, so left column: first blank, second is 4.

But 4 × T1 = 28 → T1=7
4 × T2 = 42 → T2=10.5 — impossible.

Unless... 42 is a typo? Should be 40? Then T2=10, and L×7=16? 16÷7 not integer.

Or should be 35? 35÷4=8.75 — no.

Wait — what if the bottom-left is not 4 × T1, but T1 × 4? Same thing.

Perhaps the grid is transposed? Unlikely.

Let’s try assuming the top row is known from the first row.

From first row: L × T1 = 16, L × T2 = 24 → so T2/T1 = 24/16 = 3/2 → T2 = (3/2)T1

From second row: 4 × T1 = 28 → T1=7, T2=10.5 — same issue.

But 7 and 10.5 — 10.5 is 21/2, not nice.

Wait — perhaps the 4 is not the multiplier, but part of the product? No.

Another thought: in some grids, the left column might be the result, but no, the "x" indicates multiplication between row and column headers.

Let’s skip and come back.

Look at problem 6:

"6. x □ □
5 | 20 40
5 | 32 64"

Wait, left column both 5? That can’t be — probably a typo in my reading.

User wrote: "6. x □ □
5 | 20 40
5 | 32 64" — but that would mean same multiplier gives different products — impossible unless top row changes, but it doesn't.

Probably it's:

Left column: 5 and ?
Top row: ? and ?
Cells: 20,40 / 32,64

So:

5 × T1 = 20 → T1=4
5 × T2 = 40 → T2=8
Then bottom: ? × 4 = 32 → ? = 8
? × 8 = 64 → 8×8=64 — yes! So left-bottom is 8.

So for problem 6: top: 4,8; left: 5,8

Back to problem 4.

Perhaps the "4" is a mistake, and it's supposed to be 7? Let's test.

If bottom multiplier is 7, then:

7 × T1 = 28 → T1=4
7 × T2 = 42 → T2=6
Then top row: 4,6
Then L × 4 = 16 → L=4
L × 6 = 24 → 4×6=24 — perfect!

So likely, the "4" in the left column for problem 4 is a typo, and it should be 7? But the user's image says 4.

Wait — in the user's text, for problem 4, it's written as:

"4. x □ □
□ | 16 24
4 | 28 42"

But mathematically, it only works if the bottom-left multiplier is 7, not 4.

Perhaps I have the rows switched? What if the "4" is the top multiplier?

Let's try that.

Suppose the left column is for the rows, but perhaps the "4" is in the top row? No, the format is consistent.

Another idea: perhaps the grid is:

x A B
------
C | CA CB
D | DA DB

For problem 4:

CA=16, CB=24, DA=28, DB=42, D=4

So D*A=28, D*B=42, so A=7, B=10.5 — still bad.

Unless B is 10.5, but that's not typical for this level.

Perhaps the 42 is 48? 48÷4=12, then A=7, B=12, then L*7=16? 16/7 not integer.

Or 42 is 35? 35÷4=8.75 — no.

Wait — let's calculate the ratio.

From first row: CB/CA = 24/16 = 3/2

From second row: DB/DA = 42/28 = 3/2 — same ratio, good.

So the top row numbers are in ratio 2:3.

Let T1 = 2k, T2 = 3k

Then D * 2k = 28, D * 3k = 42

Divide: (D*3k)/(D*2k) = 42/28 => 3/2 = 3/2 — always true.

From D*2k = 28, and D*3k = 42, we can solve.

From first: D*k = 14

From second: D*k = 14 — same.

So D*k = 14

Also, L * 2k = 16, L * 3k = 24

L*2k=16, L*3k=24 — divide: 3/2 = 24/16 = 3/2 — good.

L*2k=16, and D*k=14

We need integers.

Possible k such that 2k divides 16, and k divides 14.

Factors of 14: 1,2,7,14

Try k=2: then D*2=14 → D=7

L*4=16 → L=4

Then T1=4, T2=6

Check: L*T1=4*4=16, L*T2=4*6=24, D*T1=7*4=28, D*T2=7*6=42 — perfect!

So the bottom-left multiplier is 7, not 4. But in the problem, it's written as 4. This must be a typo in the worksheet or in the user's transcription.

Since the math only works with 7, and 4 is likely a mistake, I'll assume it's 7 for the sake of solving.

Perhaps the "4" is for a different position.

Another possibility: in the grid, the "4" is the value for the bottom-left cell, but no, the cells are 16,24,28,42, and 4 is on the left.

I think there's a typo, and it should be 7.

For now, I'll proceed with the calculation that makes sense: bottom-left multiplier is 7.

So for problem 4:

Top row: 4, 6
Left column: 4, 7

Because:
4×4=16, 4×6=24, 7×4=28, 7×6=42

Yes.

So despite the "4" written, it must be 7. Perhaps it's a handwriting issue.

I'll go with that.

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Problem 5:

Given:
Top: ?, ?
Left: 7, ?
Inside:
→ 7 × ? = 21 → top-left = 21 ÷ 7 = 3
→ 7 × ? = 42 → top-right = 42 ÷ 7 = 6
Top: 3, 6

Bottom:
→ ? × 3 = 27 → bottom-left = 27 ÷ 3 = 9
Check: 9 × 6 = 54 → matches! ✔

So for Problem 5:
Top: 3, 6
Left: 7, 9

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Problem 6:

As earlier:

Left: 5, ?
Top: ?, ?
Cells: 20,40 / 32,64

5 × T1 = 20 → T1=4
5 × T2 = 40 → T2=8
? × 4 = 32 → ? = 8
8 × 8 = 64 — yes.

So top: 4,8; left: 5,8

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Problem 7:

Given:
Top: ?, ?
Left: 6, ?
Inside:
→ 6 × ? = 24 → top-left = 24 ÷ 6 = 4
→ 6 × ? = 54 → top-right = 54 ÷ 6 = 9
Top: 4, 9

Bottom:
→ ? × 4 = 32 → bottom-left = 32 ÷ 4 = 8
Check: 8 × 9 = 72 → matches! ✔

So for Problem 7:
Top: 4, 9
Left: 6, 8

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Problem 8:

Given:
Top: ?, ?
Left: 3, ?
Inside:
→ 3 × ? = 18 → top-left = 18 ÷ 3 = 6
→ 3 × ? = 30 → top-right = 30 ÷ 3 = 10
Top: 6, 10

Bottom:
→ ? × 6 = 42 → bottom-left = 42 ÷ 6 = 7
Check: 7 × 10 = 70 → matches! ✔

So for Problem 8:
Top: 6, 10
Left: 3, 7

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Now, summarizing all answers:

Problem 1: Top: 3,5; Left: 4,6
Problem 2: Top: 6,8; Left: 5,7
Problem 3: Top: 5,7; Left: 3,9
Problem 4: Top: 4,6; Left: 4,7 *(assuming the "4" was meant to be 7)*
Problem 5: Top: 3,6; Left: 7,9
Problem 6: Top: 4,8; Left: 5,8
Problem 7: Top: 4,9; Left: 6,8
Problem 8: Top: 6,10; Left: 3,7

For problem 4, since the worksheet likely has a typo, but based on math, it must be 7. If forced to use 4, it doesn't work, so I'll go with the mathematical solution.

Final Answer:

1. Top: 3, 5; Left: 4, 6
2. Top: 6, 8; Left: 5, 7
3. Top: 5, 7; Left: 3, 9
4. Top: 4, 6; Left: 4, 7
5. Top: 3, 6; Left: 7, 9
6. Top: 4, 8; Left: 5, 8
7. Top: 4, 9; Left: 6, 8
8. Top: 6, 10; Left: 3, 7