Students practice arithmetic by filling in the missing number to complete each equation on this printable worksheet.

You’ve uploaded a worksheet titled “Missing Numbers” with 10 problems where you need to fill in the missing number (represented by a box □) to make each equation true.

Let’s solve each one step-by-step and explain the reasoning.

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Problem 1:

> 7 - 3 + □ = 38

Step 1: Simplify known part:
7 - 3 = 4

So:
4 + □ = 38

Step 2: Subtract 4 from both sides:
□ = 38 - 4 = 34

✔ Answer: 34

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Problem 2:

> 64 ÷ □ + 2 - 6 = 5

Step 1: Simplify constants:
2 - 6 = -4

So:
64 ÷ □ - 4 = 5

Step 2: Add 4 to both sides:
64 ÷ □ = 9

Step 3: Solve for □:
□ = 64 ÷ 9 ≈ 7.11...

Wait — that’s not a whole number. Let’s double-check.

Actually, let’s re-solve carefully:

64 ÷ □ + 2 - 6 = 5
→ 64 ÷ □ - 4 = 5
→ 64 ÷ □ = 9
→ □ = 64 / 9 → Not an integer.

But this is likely meant for elementary math — perhaps there’s a typo? Or maybe we misread the order?

Let’s assume standard left-to-right or PEMDAS.

PEMDAS: Division first, then addition/subtraction left to right.

So:
(64 ÷ □) + 2 - 6 = 5
→ (64 ÷ □) - 4 = 5
→ 64 ÷ □ = 9
→ □ = 64/9 — still not nice.

Alternatively, maybe it’s:
64 ÷ (□ + 2) - 6 = 5? But no parentheses are shown.

Given the context of the worksheet, it’s possible this problem has a typo, OR we’re expected to accept fractions.

But let’s check if maybe it’s 64 ÷ 8 + 2 - 6 = ?
→ 8 + 2 - 6 = 4 → too low.

Try □ = 8 → 64÷8=8 → 8+2-6=4 ≠5
□ = 16 → 64÷16=4 → 4+2-6=0
□ = 4 → 16+2-6=12
□ = 32 → 2+2-6=-2

None give 5.

Wait — what if the equation is:
64 ÷ □ + (2 - 6) = 5 → same as before.

Perhaps the intended answer is 8, but that gives 4.

Alternatively, maybe it’s 64 ÷ □ = 9, so □ = 64/9 — but that’s unusual.

Let’s skip and come back — maybe it’s a trick.

Actually, let me try solving again:

64 ÷ x + 2 - 6 = 5
→ 64/x - 4 = 5
→ 64/x = 9
→ x = 64/9 ≈ 7.11

Since other problems use integers, perhaps the problem is misprinted. But for now, we’ll go with 64/9 or 7 1/9.

But let’s hold off — maybe I made a mistake.

Wait — what if the equation is:
(64 ÷ □ + 2) - 6 = 5 → same thing.

No. Perhaps the original problem was meant to be:

> 64 ÷ □ + 2 = 11 → then □ = 8? But that’s not what’s written.

Given the constraints, I’ll note this may be an error, but proceed with exact math.

✔ Answer: 64/9 (or approximately 7.11)

But since this is likely for grade school, perhaps it's a typo and should be 64 ÷ 8 + 2 - 6 = 4, or maybe 64 ÷ 8 + 6 - 2 = 12 — not matching.

Let’s move on and return later.

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Problem 3:

> □ + 36 ÷ 9 = 18

Step 1: Do division first:
36 ÷ 9 = 4

So:
□ + 4 = 18

Step 2: Subtract 4:
□ = 18 - 4 = 14

✔ Answer: 14

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Problem 4:

> □ - 10 + 20 = 100

Step 1: Combine constants:
-10 + 20 = 10

So:
□ + 10 = 100

Step 2: Subtract 10:
□ = 90

✔ Answer: 90

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Problem 5:

> (25 - 3) ÷ 4 + □ = 27

Step 1: Parentheses first:
25 - 3 = 22

Then divide:
22 ÷ 4 = 5.5

So:
5.5 + □ = 27

Step 2: Subtract 5.5:
□ = 27 - 5.5 = 21.5

✔ Answer: 21.5 (or 43/2)

Again, decimal — but correct.

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Problem 6:

> 24 + □ - 18 ÷ 6 = 30

Step 1: Division first:
18 ÷ 6 = 3

So:
24 + □ - 3 = 30

Simplify:
21 + □ = 30

Step 2: Subtract 21:
□ = 9

✔ Answer: 9

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Problem 7:

> □ + 16 ÷ 8 × 3 = 14

Step 1: Division and multiplication left to right:
16 ÷ 8 = 2
2 × 3 = 6

So:
□ + 6 = 14

Step 2: Subtract 6:
□ = 8

✔ Answer: 8

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Problem 8:

> 60 ÷ □ × 5 + 7 = 49

Step 1: Isolate the division/multiplication part.

Let’s denote □ as x.

Equation:
(60 ÷ x) × 5 + 7 = 49

Subtract 7:
(60 ÷ x) × 5 = 42

Divide both sides by 5:
60 ÷ x = 8.4

Now solve:
x = 60 ÷ 8.4 = ?

Convert 8.4 to fraction: 84/10 = 42/5

So:
x = 60 ÷ (42/5) = 60 × (5/42) = 300 / 42 = 50 / 7 ≈ 7.14

Again, not a whole number.

Check:
If x = 5: 60÷5=12, 12×5=60, 60+7=67 → too big
x = 10: 60÷10=6, 6×5=30, 30+7=37 → too small
x = 6: 60÷6=10, 10×5=50, 50+7=57
x = 7: 60÷7≈8.57, ×5≈42.86, +7≈49.86 — close to 49!

Wait — 60 ÷ 7 × 5 + 7 = ?

60/7 ≈ 8.571
×5 = 42.857
+7 = 49.857 — not 49.

What if x = 60/8.4 = 600/84 = 100/14 = 50/7 ≈ 7.142857

Check: 60 ÷ (50/7) = 60 × 7/50 = 420/50 = 8.4
8.4 × 5 = 42
42 + 7 = 49 ✔

So exact answer is 50/7

✔ Answer: 50/7

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Problem 9:

> (12 × 5 - 18) + □ × 3 = 52

Step 1: Parentheses first:
12 × 5 = 60
60 - 18 = 42

So:
42 + (□ × 3) = 52

Step 2: Subtract 42:
□ × 3 = 10

Step 3: Divide by 3:
□ = 10/3 ≈ 3.333...

✔ Answer: 10/3

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Problem 10:

> □ - 61 + 80 = 2

Step 1: Combine constants:
-61 + 80 = 19

So:
□ + 19 = 2

Step 2: Subtract 19:
□ = 2 - 19 = -17

✔ Answer: -17

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## 🧾 Final Answers:

1. 34
2. 64/9 (≈7.11) — *possibly a typo*
3. 14
4. 90
5. 21.5
6. 9
7. 8
8. 50/7 (≈7.14)
9. 10/3 (≈3.33)
10. -17

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## 💡 Notes:
- Most problems involve applying order of operations (PEMDAS).
- Some answers are fractions or decimals, which may be unexpected for elementary worksheets — possibly indicating typos or advanced level.
- Problem 2 and 8 might have intended different numbers (e.g., 63 instead of 64, or 60 instead of 49).

If you suspect a typo in any problem, feel free to share the corrected version!

Let me know if you want these rewritten with boxes filled in visually or as a completed worksheet.