Integer Worksheet-Fill in the Sign (C) - Mr. R.s World of Math - Free Printable
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Step-by-step solution for: Integer Worksheet-Fill in the Sign (C) - Mr. R.s World of Math
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Step-by-step solution for: Integer Worksheet-Fill in the Sign (C) - Mr. R.s World of Math
Let’s solve each problem one by one. We need to place +, -, ×, or ÷ between the four digits on the left so that the equation equals the number on the right. Remember: follow order of operations (multiplication and division before addition and subtraction).
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A: 8 5 2 6 = 36
Try:
8 × 5 = 40 → too big?
What if we do: 8 + 5 × 2 + 6?
→ 5 × 2 = 10 → 8 + 10 + 6 = 24 ✘
Try: 8 × 5 - 2 - 6 = 40 - 2 - 6 = 32 ✘
Try: 8 + 5 + 2 × 6 = 8 + 5 + 12 = 25 ✘
Try: 8 × 2 + 5 + 6 = 16 + 5 + 6 = 27 ✘
Wait — what about: 8 × 5 - 2 - 6? Still 32.
Hmm… try: 8 + 5 × 6 - 2? But digits are 8,5,2,6 — must keep order!
So only between them: 8 _ 5 _ 2 _ 6
Try: 8 × 5 - 2 - 6 = 40 - 8 = 32 ✘
Try: 8 + 5 × 2 + 6 = 8+10+6=24 ✘
Try: 8 × 2 + 5 + 6 = 16+11=27 ✘
Wait — maybe: 8 + 5 + 2 × 6 = 8+5+12=25 ✘
What if: (8 + 5) × 2 + 6? But no parentheses allowed — just operators between.
Hold on — let’s try: 8 × 5 - 2 - 6 = 32 — close but not 36.
Wait — what about: 8 + 5 × 6 - 2? Again, wrong digit order.
Digits must stay in order: 8, then 5, then 2, then 6.
Try: 8 × 2 + 5 + 6 — again, skips order.
Actually — let me try: 8 + 5 + 2 × 6 = 8+5+12=25 ✘
Wait — here’s an idea: 8 × 5 - 2 - 6 is 32 — too low.
What if: 8 × 5 - (2 + 6)? No parentheses.
Maybe I’m missing something.
Try: 8 + 5 × 2 + 6 = 24 ✘
Wait — what if: 8 × 2 + 5 × 6? That would be 16 + 30 = 46 — too big, and also uses two multiplications — but allowed? Yes, as long as order of operations followed.
But digits are 8,5,2,6 — so 8 × 5 × 2 × 6 is way too big.
Wait — perhaps: 8 + 5 × 6 - 2 — but again, 6 comes after 2 — can’t rearrange.
I think I made a mistake — let’s list all possibilities systematically.
Possible combinations:
Option 1: 8 + 5 + 2 + 6 = 21 ✘
Option 2: 8 + 5 + 2 - 6 = 9 ✘
Option 3: 8 + 5 - 2 + 6 = 17 ✘
Option 4: 8 + 5 - 2 - 6 = 5 ✘
Option 5: 8 - 5 + 2 + 6 = 11 ✘
... this will take forever.
Better approach: since target is 36, which is fairly large, likely involves multiplication.
Try: 8 × 5 = 40 → then subtract 4 to get 36 → can we make 4 from 2 and 6? 6 - 2 = 4 → yes!
So: 8 × 5 - (6 - 2) — but again, no parentheses, and digits must be in order: 8,5,2,6 — so it would be 8 × 5 - 2 - 6 = 32, or 8 × 5 - 2 + 6 = 44.
Wait — what if: 8 × 5 - 2 - 6 = 32 — still not 36.
Another idea: 5 × 6 = 30, plus 8 - 2 = 6 → 36 — but again, order: 8,5,2,6 — so 8 _ 5 _ 2 _ 6.
What if: 8 + 5 × 6 - 2 — but 6 is last, 2 is third — so expression would be 8 + 5 × 2 × 6? Too big.
Wait — perhaps: 8 × 2 + 5 + 6 — but that’s using 8,2,5,6 — not in order.
I think I found it: 8 + 5 × 2 + 6 = 8 + 10 + 6 = 24 — no.
Wait — let's calculate 8 × 5 = 40, then 40 - 4 = 36, and 6 - 2 = 4, so if we could do 8 × 5 - (6 - 2), but we can't because 2 comes before 6.
Unless... what if we do: 8 × 5 - 6 + 2? That would be 40 - 6 + 2 = 36! And digits are 8,5,6,2 — but wait, the digits are given as 8,5,2,6 — so 2 comes before 6.
So 8 _ 5 _ 2 _ 6 — so after 5 is 2, then 6.
So 8 × 5 - 2 + 6 = 40 - 2 + 6 = 44 ✘
8 × 5 + 2 - 6 = 40 +2 -6 = 36 ✔ YES!
Check: 8 × 5 = 40, then +2 = 42, then -6 = 36. Perfect.
And order of operations: multiplication first, then left to right for + and -.
So: 8 × 5 + 2 - 6 = 40 + 2 - 6 = 36.
Yes! So A is: 8 × 5 + 2 - 6 = 36
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B: 5 7 8 3 = 58
Target 58.
Try: 5 × 7 = 35, 8 × 3 = 24, 35+24=59 — close.
5 × 8 = 40, 7 × 3 = 21, 40+21=61 — too big.
5 + 7 × 8 + 3 = 5 + 56 + 3 = 64 ✘
5 × 7 + 8 × 3 = 35 + 24 = 59 ✘
5 × 7 + 8 + 3 = 35+8+3=46 ✘
5 + 7 + 8 × 3 = 5+7+24=36 ✘
What if: 5 × 8 + 7 + 3 = 40+10=50 ✘
Wait — 5 × 7 = 35, need 23 more — 8×3=24, too much.
Perhaps: 5 + 7 × 8 - 3 = 5 + 56 - 3 = 58 ✔ YES!
Check: 7 × 8 = 56, then 5 + 56 = 61, minus 3 = 58.
Order: 5 + 7 × 8 - 3 — multiplication first: 7×8=56, then 5+56=61, then 61-3=58.
Perfect. Digits in order: 5,7,8,3.
So B: 5 + 7 × 8 - 3 = 58
---
C: 8 8 8 4 = 32
Target 32.
Try: 8 × 4 = 32, so maybe use that.
8 + 8 + 8 + 4 = 28 ✘
8 × 8 / 8 × 4 = ? 64 / 8 = 8, ×4=32 — but let's see: 8 × 8 ÷ 8 × 4
Order: left to right for same precedence: 8×8=64, ÷8=8, ×4=32 ✔
But is that allowed? Operators between: 8 _ 8 _ 8 _ 4
So: 8 × 8 ÷ 8 × 4 = 32
Yes.
Alternatively, simpler: 8 + 8 + 8 + 8? No, only three 8s and a 4.
8 × 4 = 32, and 8/8=1, but how to combine.
8 × (8 - 8/8)? No parentheses.
With order: 8 × 8 ÷ 8 × 4 = as above, works.
8 + 8 × 3? No 3.
Another way: 8 × 4 + 8 - 8 = 32 +0=32 — but digits are 8,8,8,4 — so 8 _ 8 _ 8 _ 4
If we do 8 × 4 + 8 - 8, but 4 is last, so it would be 8 _ 8 _ 8 _ 4 — so last operation with 4.
So 8 × 4 is not directly possible unless 4 is multiplied early.
In 8 × 8 ÷ 8 × 4, it works.
We can also do: 8 + 8 + 8 + 8? No.
Or: 8 × 8 - 8 × 4 = 64 - 32 = 32 — oh! That's better.
8 × 8 - 8 × 4
But order: multiplication first: 8×8=64, 8×4=32, then 64-32=32.
And digits: 8,8,8,4 — so positions: first 8, second 8, third 8, fourth 4.
So expression: 8 × 8 - 8 × 4
Is that valid? Between the digits: between first and second: ×, between second and third: -, between third and fourth: ×
So: 8 × 8 - 8 × 4
Yes, and by order of operations, both multiplications done before subtraction: 64 - 32 = 32.
Perfect.
So C: 8 × 8 - 8 × 4 = 32
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D: 5 7 6 3 = 10
Target 10.
Try: 5 + 7 - 6 + 3 = 9 ✘
5 + 7 - 6 - 3 = 3 ✘
5 × 2 = 10, but no 2.
7 + 3 = 10, so maybe 5 and 6 cancel.
5 - 5 =0, but no.
(5 + 7 + 6)/ something — no parentheses.
Try: 5 + 7 - 6 ÷ 3? 6÷3=2, 5+7-2=10 ✔
Check: 6 ÷ 3 = 2, then 5 + 7 = 12, minus 2 = 10.
Order: division first, then left to right: 5 + 7 - (6÷3) = 12 - 2 = 10.
Digits: 5,7,6,3 — so 5 + 7 - 6 ÷ 3
Yes.
So D: 5 + 7 - 6 ÷ 3 = 10
---
E: 6 6 7 8 = 56
Target 56.
56 is 7×8, so probably involve that.
6 + 6 + 7 × 8 = 6+6+56=68 ✘
6 × 6 + 7 + 8 = 36+15=51 ✘
6 × 7 + 6 + 8 = 42+14=56 ✔
Check: 6 × 7 = 42, then +6 = 48, +8=56.
Digits: 6,6,7,8 — so first 6, second 6, third 7, fourth 8.
Expression: 6 × 7 + 6 + 8 — but that would require skipping the second 6 or reordering.
No: the sequence is 6 _ 6 _ 7 _ 8
So if we do 6 × 6 + 7 + 8 = 36+15=51 ✘
6 + 6 × 7 + 8 = 6 + 42 + 8 = 56 ✔
Yes! Multiplication first: 6×7=42, then 6+42=48, +8=56.
Digits in order: 6,6,7,8 — so 6 + 6 × 7 + 8
Perfect.
So E: 6 + 6 × 7 + 8 = 56
---
F: 4 4 4 9 = 6
Target 6.
Small number, so probably division or subtraction.
4 + 4 + 4 - 9 = 12 - 9 = 3 ✘
4 × 4 - 4 - 9 = 16-4-9=3 ✘
(4 + 4 + 4)/2 = 6, but no 2.
9 - 4 - 4/4 = 9-4-1=4 ✘
4 + 4/4 - 9? 4+1-9=-4 ✘
What if: 4 × 4 - 4 - 6? No 6.
Another idea: 9 - 4 + 4/4 = 9-4+1=6 ✔
Check: 4/4=1, then 9-4=5, +1=6? Order: if expression is 9 - 4 + 4 ÷ 4
But digits are 4,4,4,9 — so must start with 4.
So 4 _ 4 _ 4 _ 9
Try: 4 + 4 - 4 + 9? 4+4-4+9=13 ✘
4 × 4 ÷ 4 - 9? 16÷4=4, -9=-5 ✘
(4 + 4 + 4) ÷ 2, no.
What if: 4 - 4 + 4 + 9? 0+4+9=13 ✘
Perhaps division: 4 ÷ 4 =1, then 4 + 1 =5, not 6.
9 - 3 =6, and 4 - 4/4 = 4-1=3, so 9 - (4 - 4/4) — but no parentheses, and order.
Try: 4 ÷ 4 + 4 + 9? 1+4+9=14 ✘
Another thought: 4 × 9 - 4 × 4? 36 - 16 = 20 ✘
Too big.
What if: (4 + 4) ÷ 4 × 3, no.
Let's think differently.
Suppose: 4 + 4 ÷ 4 - 9? 4+1-9=-4 ✘
4 - 4 ÷ 4 + 9? 4-1+9=12 ✘
Perhaps: 9 - 4 - 4/4 = 9-4-1=4 ✘
Wait — what if we do: 4 × 4 - 4 - 6, no.
Another idea: 6 = 24 ÷ 4, and 4×6=24, but no 6.
4 + 4 + 4 = 12, 12 ÷ 2 =6, but no 2.
9 - 3 =6, and 3 = 4 - 1, and 1=4/4.
So: 9 - (4 - 4/4) — but again, no parentheses.
In order: if we write 4 ÷ 4 =1, then 4 - 1 =3, then 9 - 3 =6, but the expression would be 9 - 4 + 4 ÷ 4? Let's calculate: 4÷4=1, then 9-4=5, 5+1=6 — oh! 9 - 4 + 4 ÷ 4 = 5 + 1 =6.
But digits are 4,4,4,9 — so we need to start with 4.
So perhaps: 4 ÷ 4 + 9 - 4? That would be 1 + 9 - 4 = 6 ✔
Check: 4 ÷ 4 =1, then 1 + 9 =10, then 10 - 4 =6.
Digits: first 4, second 4, third 9, fourth 4? But the digits are 4,4,4,9 — so third is 4, fourth is 9.
In 4 ÷ 4 + 9 - 4, the digits used are 4,4,9,4 — which matches 4,4,4,9 if we consider the last 4 is the third 4, and 9 is fourth.
The sequence is position 1:4, pos2:4, pos3:4, pos4:9.
In expression 4 ÷ 4 + 9 - 4, we have: first 4, second 4, then 9, then 4 — but the third digit should be 4, not 9. Here we have 9 as third operand, but it should be the fourth digit.
Mistake.
The expression must use the digits in order: digit1 _ digit2 _ digit3 _ digit4
So for F: 4 _ 4 _ 4 _ 9
So options like 4 ÷ 4 + 4 - 9 = 1 + 4 - 9 = -4 ✘
4 + 4 ÷ 4 - 9 = 4 + 1 - 9 = -4 ✘
4 - 4 ÷ 4 + 9 = 4 - 1 + 9 = 12 ✘
4 × 4 ÷ 4 - 9 = 4 - 9 = -5 ✘
(4 + 4) ÷ 4 * 3, no.
Another idea: 9 - 4 - 4/4, but again, order.
Perhaps: 4 + 4 - 4 + 9? 4+4-4+9=13 ✘
Let's calculate 4 * 9 = 36, too big.
What if: (4 * 4 + 4) / 4 = 20/4=5, not 6.
4! / 4 = 24/4=6, but no factorial.
Perhaps I missed something.
Try: 4 ÷ 4 =1, then 4 + 1 =5, not 6.
9 - 3 =6, and 3 = 12/4, but no.
Another thought: 6 = 18 / 3, but no 3 or 18.
Let's list possible combinations.
Suppose we do division first.
4 ÷ 4 =1, then we have 1,4,9 to combine with operators.
But must be in sequence.
Expression: 4 op1 4 op2 4 op3 9
Try op1=+, op2=÷, op3=- : 4 + 4 ÷ 4 - 9 = 4 + 1 - 9 = -4 ✘
op1=-, op2=÷, op3=+ : 4 - 4 ÷ 4 + 9 = 4 - 1 + 9 = 12 ✘
op1=×, op2=÷, op3=- : 4 × 4 ÷ 4 - 9 = 4 - 9 = -5 ✘
op1=+, op2=+, op3=- : 4+4+4-9=3 ✘
op1=×, op2=-, op3=- : 4×4-4-9=16-4-9=3 ✘
op1=-, op2=+, op3=+ : 4-4+4+9=13 ✘
What if op2 is × or ÷.
Another idea: 4 + 4 + 4 = 12, 12 - 6 =6, but no 6.
9 - 3 =6, and 3 = 4 - 1, 1=4/4, so if we can do 9 - (4 - 4/4), but in linear order without parentheses, it might work if we arrange the operations properly.
Suppose: 4 ÷ 4 =1, then 4 - 1 =3, then 9 - 3 =6, but the expression would be 9 - 4 + 4 ÷ 4, which is 9 - 4 + 1 =6, but as before, the digits are not in order; we have 9 first, but it should be last.
Unless we do: 4 ÷ 4 + 9 - 4, but again, the third digit is 9, but it should be the third 4.
The digits are fixed: first 4, second 4, third 4, fourth 9.
So the expression is A op B op C op D with A=B=C=4, D=9.
So perhaps: 4 - 4 + 4 + 9? 0+4+9=13 ✘
4 * 4 - 4 - 6, no.
Let's try: (4 + 4) * 4 / 8, no.
Another thought: 6 = 24 / 4, and 4*6=24, but no 6.
4! =24, but not allowed.
Perhaps: 4 + 4/4 =5, then 5 +1=6, but no 1.
9/3=3, but no 3.
Let's calculate 4 * 9 = 36, 36 / 6 =6, but no 6.
36 / (4 + 2), no.
Perhaps: 4 * 9 - 4 * 7.5, no.
I recall that sometimes they use concatenation, but the instruction says place +,-,x,/ between digits, so probably not.
Another idea: 4 + 4 - 4/4 = 4+4-1=7 ✘
4 - 4/4 + 4 = 4-1+4=7 ✘
(4*4 + 8)/4 = 24/4=6, but no 8.
Let's think outside the box.
What if: 4 ÷ 4 =1, then 1 * 6 =6, but no 6.
9 - 3 =6, and 3 = 12/4, 12=4*3, circular.
Perhaps: 9 - 4 - 4/4 = 9-4-1=4 ✘
Wait — what if we do: 4 + 4 ÷ 4 = 5, then 5 +1=6, but no.
Let's try: 4 * 4 = 16, 16 - 10 =6, 10=9+1, 1=4/4, so 4*4 - (9 + 4/4) — but no parentheses, and order.
In sequence: 4 * 4 - 9 + 4 ÷ 4? Let's calculate: 4*4=16, 4÷4=1, then 16 - 9 =7, +1=8 ✘
4 * 4 - 9 - 4 ÷ 4 = 16 - 9 - 1 =6 ✔
Check: multiplication and division first: 4*4=16, 4÷4=1, then 16 - 9 =7, then 7 - 1 =6.
Digits: 4,4,9,4 — but the digits are 4,4,4,9 — so third digit is 4, fourth is 9.
In this expression: 4 * 4 - 9 - 4 ÷ 4, we have five numbers: 4,4,9,4,4 — too many.
Mistake.
The expression has three operators, so four numbers: digit1 op1 digit2 op2 digit3 op3 digit4
So for F: 4 op1 4 op2 4 op3 9
So only four numbers.
So 4 * 4 - 9 - 4 ÷ 4 is invalid because it has five numbers.
Must be exactly four numbers with three operators between them.
So back to square one.
Try: 4 + 4 + 4 - 9 = 3 ✘
4 * 4 - 4 - 9 = 16-4-9=3 ✘
4 - 4 + 4 * 9 = 0 + 36 = 36 ✘
4 * 9 - 4 * 4 = 36 - 16 = 20 ✘
(4 + 4) * 4 / 8, no.
Another idea: 6 = 30 / 5, but no.
Perhaps division: 4 / 4 =1, then 4 + 1 =5, not 6.
9 / 1.5 =6, but no 1.5.
Let's calculate 4 + 4/4 =5, then if we had another 1, but we have 9.
9 - 3 =6, and 3 = 4 - 1, 1=4/4, so if we can do 9 - (4 - 4/4), but in linear order, if we write 4/4 first, then 4 - that, then 9 - that.
But the expression would be 9 - 4 + 4 ÷ 4, which is 9 - 4 + 1 =6, but as said, the digits are not in order; we have 9 first, but it should be the fourth digit.
Unless the expression is written as 4 ÷ 4 + 9 - 4, but then the third digit is 9, but it should be the third 4.
The only way is if we use the digits in the given order: first 4, second 4, third 4, fourth 9.
So perhaps: 4 - 4/4 + 9? 4 - 1 + 9 = 12 ✘
4 + 4/4 - 9 = 4+1-9= -4 ✘
4 * 4 / 4 * 9 = 4*9=36 ✘
4 + 4 - 4/9? Not integer.
Perhaps: (4 * 4 + 8) / 4, no.
I recall that in some puzzles, they allow the operations to be placed, and order of operations applies.
Let me try: 4 ÷ 4 =1, then 1 * 6 =6, but no 6.
Another thought: 6 = 2*3, but no.
Let's search online or think differently.
Perhaps: 4 + 4 - 4 + 9? 4+4-4+9=13 ✘
4 * 9 / 6 =6, but no 6.
36 / 6 =6, and 4*9=36, so if we can divide by 6, but we have two 4's left.
4*9 / (4 + 2), no.
(4*9) / (4 + 2), but no 2.
4/4 =1, so 4*9 / (4/4 + 5), complicated.
Perhaps: 4 + 4/4 =5, then 5 +1=6, but no 1.
9/3=3, but no 3.
Let's calculate the difference.
Target 6, current sum 4+4+4+9=21, too big.
Product 4*4*4*9=576, too big.
Perhaps subtraction and division.
Try: 9 - 4 - 4/4 = 9-4-1=4 ✘
4 - 4/4 =3, then 9 - 3 =6, so if the expression is 9 - (4 - 4/4), but to write it without parentheses, and in order, it might be 4/4 - 4 + 9 or something.
Let's try: 4 ÷ 4 - 4 + 9 = 1 - 4 + 9 = 6 ✔
Calculate: 4 ÷ 4 =1, then 1 - 4 = -3, then -3 + 9 =6.
Yes! And digits: first 4, second 4, third 4, fourth 9 — so 4 ÷ 4 - 4 + 9
Order of operations: division first: 4÷4=1, then left to right: 1 - 4 = -3, then -3 + 9 =6.
Perfect.
So F: 4 ÷ 4 - 4 + 9 = 6
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G: 8 2 9 5 = 180
Target 180.
Large number, so likely multiplication.
8 × 2 = 16, 9 × 5 = 45, 16×45=720, too big.
8 × 9 = 72, 2 × 5 = 10, 72×10=720, still big.
8 × 5 = 40, 2 × 9 = 18, 40×18=720.
180 = 18 × 10, or 9 × 20, etc.
8 × 2 × 9 × 5 = 720, too big.
Perhaps (8 + 2) × (9 + 9), no.
8 × 2 = 16, 16 × 11.25 = 180, not integer.
9 × 20 = 180, and 20 = 8 + 2 + 10, no.
5 × 36 = 180, 36 = 8 × 4.5, no.
Another idea: 8 × 9 = 72, 72 × 2.5 = 180, 2.5 = 5/2, so 8 × 9 × 5 / 2
Check: 8 × 9 = 72, ×5 = 360, /2 = 180.
Digits: 8,2,9,5 — so 8 × 9 × 5 / 2
But order: 8 _ 2 _ 9 _ 5
So if we do 8 × 9 × 5 / 2, but 2 is second digit, 9 is third, 5 is fourth.
So expression: 8 × 2 × 9 × 5 / something, too many.
With three operators: 8 op1 2 op2 9 op3 5
Try: 8 × 2 × 9 × 5 = 720, too big.
8 × 9 × 5 / 2 = 360 / 2 = 180, but how to arrange with digits in order.
If we do 8 × 9 × 5 / 2, but 2 is before 9 and 5 in the sequence.
Sequence is 8,2,9,5 — so after 8 is 2, then 9, then 5.
So perhaps: 8 × 2 × 9 × 5 / 2, but extra 2.
No.
Another way: 180 = 90 × 2, 90 = 9 × 10, 10 = 5 × 2, but duplicate.
8 + 2 = 10, 9 × 5 = 45, 10 × 45 = 450, too big.
(8 + 2) × 9 × 2, no.
Let's try: 8 × 5 = 40, 40 × 4.5 = 180, 4.5 = 9/2, so 8 × 5 × 9 / 2
Same as before.
So 8 × 5 × 9 / 2 = 360 / 2 = 180.
Now, with digits 8,2,9,5 — so if we can do 8 × 5 × 9 / 2, but 2 is second, 5 is fourth.
So perhaps: 8 / 2 × 9 × 5
Calculate: 8 / 2 = 4, then 4 × 9 = 36, then 36 × 5 = 180 ✔
Yes! And digits in order: 8,2,9,5 — so 8 ÷ 2 × 9 × 5
Order: division and multiplication left to right: 8÷2=4, 4×9=36, 36×5=180.
Perfect.
So G: 8 ÷ 2 × 9 × 5 = 180
---
H: 4 3 8 2 = 3
Target 3.
Small number.
Try: 4 + 3 - 8 + 2 = 1 ✘
4 - 3 + 8 - 2 = 7 ✘
4 × 3 - 8 - 2 = 12-8-2=2 ✘
4 + 3 - 8 ÷ 2 = 4+3-4=3 ✔
Check: 8 ÷ 2 = 4, then 4 + 3 = 7, then 7 - 4 = 3.
Digits: 4,3,8,2 — so 4 + 3 - 8 ÷ 2
Order: division first: 8÷2=4, then 4+3=7, then 7-4=3.
Yes.
So H: 4 + 3 - 8 ÷ 2 = 3
---
Now, summarize all answers:
A: 8 × 5 + 2 - 6 = 36
B: 5 + 7 × 8 - 3 = 58
C: 8 × 8 - 8 × 4 = 32
D: 5 + 7 - 6 ÷ 3 = 10
E: 6 + 6 × 7 + 8 = 56
F: 4 ÷ 4 - 4 + 9 = 6
G: 8 ÷ 2 × 9 × 5 = 180
H: 4 + 3 - 8 ÷ 2 = 3
All verified.
Final Answer:
A: 8 × 5 + 2 - 6 = 36
B: 5 + 7 × 8 - 3 = 58
C: 8 × 8 - 8 × 4 = 32
D: 5 + 7 - 6 ÷ 3 = 10
E: 6 + 6 × 7 + 8 = 56
F: 4 ÷ 4 - 4 + 9 = 6
G: 8 ÷ 2 × 9 × 5 = 180
H: 4 + 3 - 8 ÷ 2 = 3
---
A: 8 5 2 6 = 36
Try:
8 × 5 = 40 → too big?
What if we do: 8 + 5 × 2 + 6?
→ 5 × 2 = 10 → 8 + 10 + 6 = 24 ✘
Try: 8 × 5 - 2 - 6 = 40 - 2 - 6 = 32 ✘
Try: 8 + 5 + 2 × 6 = 8 + 5 + 12 = 25 ✘
Try: 8 × 2 + 5 + 6 = 16 + 5 + 6 = 27 ✘
Wait — what about: 8 × 5 - 2 - 6? Still 32.
Hmm… try: 8 + 5 × 6 - 2? But digits are 8,5,2,6 — must keep order!
So only between them: 8 _ 5 _ 2 _ 6
Try: 8 × 5 - 2 - 6 = 40 - 8 = 32 ✘
Try: 8 + 5 × 2 + 6 = 8+10+6=24 ✘
Try: 8 × 2 + 5 + 6 = 16+11=27 ✘
Wait — maybe: 8 + 5 + 2 × 6 = 8+5+12=25 ✘
What if: (8 + 5) × 2 + 6? But no parentheses allowed — just operators between.
Hold on — let’s try: 8 × 5 - 2 - 6 = 32 — close but not 36.
Wait — what about: 8 + 5 × 6 - 2? Again, wrong digit order.
Digits must stay in order: 8, then 5, then 2, then 6.
Try: 8 × 2 + 5 + 6 — again, skips order.
Actually — let me try: 8 + 5 + 2 × 6 = 8+5+12=25 ✘
Wait — here’s an idea: 8 × 5 - 2 - 6 is 32 — too low.
What if: 8 × 5 - (2 + 6)? No parentheses.
Maybe I’m missing something.
Try: 8 + 5 × 2 + 6 = 24 ✘
Wait — what if: 8 × 2 + 5 × 6? That would be 16 + 30 = 46 — too big, and also uses two multiplications — but allowed? Yes, as long as order of operations followed.
But digits are 8,5,2,6 — so 8 × 5 × 2 × 6 is way too big.
Wait — perhaps: 8 + 5 × 6 - 2 — but again, 6 comes after 2 — can’t rearrange.
I think I made a mistake — let’s list all possibilities systematically.
Possible combinations:
Option 1: 8 + 5 + 2 + 6 = 21 ✘
Option 2: 8 + 5 + 2 - 6 = 9 ✘
Option 3: 8 + 5 - 2 + 6 = 17 ✘
Option 4: 8 + 5 - 2 - 6 = 5 ✘
Option 5: 8 - 5 + 2 + 6 = 11 ✘
... this will take forever.
Better approach: since target is 36, which is fairly large, likely involves multiplication.
Try: 8 × 5 = 40 → then subtract 4 to get 36 → can we make 4 from 2 and 6? 6 - 2 = 4 → yes!
So: 8 × 5 - (6 - 2) — but again, no parentheses, and digits must be in order: 8,5,2,6 — so it would be 8 × 5 - 2 - 6 = 32, or 8 × 5 - 2 + 6 = 44.
Wait — what if: 8 × 5 - 2 - 6 = 32 — still not 36.
Another idea: 5 × 6 = 30, plus 8 - 2 = 6 → 36 — but again, order: 8,5,2,6 — so 8 _ 5 _ 2 _ 6.
What if: 8 + 5 × 6 - 2 — but 6 is last, 2 is third — so expression would be 8 + 5 × 2 × 6? Too big.
Wait — perhaps: 8 × 2 + 5 + 6 — but that’s using 8,2,5,6 — not in order.
I think I found it: 8 + 5 × 2 + 6 = 8 + 10 + 6 = 24 — no.
Wait — let's calculate 8 × 5 = 40, then 40 - 4 = 36, and 6 - 2 = 4, so if we could do 8 × 5 - (6 - 2), but we can't because 2 comes before 6.
Unless... what if we do: 8 × 5 - 6 + 2? That would be 40 - 6 + 2 = 36! And digits are 8,5,6,2 — but wait, the digits are given as 8,5,2,6 — so 2 comes before 6.
So 8 _ 5 _ 2 _ 6 — so after 5 is 2, then 6.
So 8 × 5 - 2 + 6 = 40 - 2 + 6 = 44 ✘
8 × 5 + 2 - 6 = 40 +2 -6 = 36 ✔ YES!
Check: 8 × 5 = 40, then +2 = 42, then -6 = 36. Perfect.
And order of operations: multiplication first, then left to right for + and -.
So: 8 × 5 + 2 - 6 = 40 + 2 - 6 = 36.
Yes! So A is: 8 × 5 + 2 - 6 = 36
---
B: 5 7 8 3 = 58
Target 58.
Try: 5 × 7 = 35, 8 × 3 = 24, 35+24=59 — close.
5 × 8 = 40, 7 × 3 = 21, 40+21=61 — too big.
5 + 7 × 8 + 3 = 5 + 56 + 3 = 64 ✘
5 × 7 + 8 × 3 = 35 + 24 = 59 ✘
5 × 7 + 8 + 3 = 35+8+3=46 ✘
5 + 7 + 8 × 3 = 5+7+24=36 ✘
What if: 5 × 8 + 7 + 3 = 40+10=50 ✘
Wait — 5 × 7 = 35, need 23 more — 8×3=24, too much.
Perhaps: 5 + 7 × 8 - 3 = 5 + 56 - 3 = 58 ✔ YES!
Check: 7 × 8 = 56, then 5 + 56 = 61, minus 3 = 58.
Order: 5 + 7 × 8 - 3 — multiplication first: 7×8=56, then 5+56=61, then 61-3=58.
Perfect. Digits in order: 5,7,8,3.
So B: 5 + 7 × 8 - 3 = 58
---
C: 8 8 8 4 = 32
Target 32.
Try: 8 × 4 = 32, so maybe use that.
8 + 8 + 8 + 4 = 28 ✘
8 × 8 / 8 × 4 = ? 64 / 8 = 8, ×4=32 — but let's see: 8 × 8 ÷ 8 × 4
Order: left to right for same precedence: 8×8=64, ÷8=8, ×4=32 ✔
But is that allowed? Operators between: 8 _ 8 _ 8 _ 4
So: 8 × 8 ÷ 8 × 4 = 32
Yes.
Alternatively, simpler: 8 + 8 + 8 + 8? No, only three 8s and a 4.
8 × 4 = 32, and 8/8=1, but how to combine.
8 × (8 - 8/8)? No parentheses.
With order: 8 × 8 ÷ 8 × 4 = as above, works.
8 + 8 × 3? No 3.
Another way: 8 × 4 + 8 - 8 = 32 +0=32 — but digits are 8,8,8,4 — so 8 _ 8 _ 8 _ 4
If we do 8 × 4 + 8 - 8, but 4 is last, so it would be 8 _ 8 _ 8 _ 4 — so last operation with 4.
So 8 × 4 is not directly possible unless 4 is multiplied early.
In 8 × 8 ÷ 8 × 4, it works.
We can also do: 8 + 8 + 8 + 8? No.
Or: 8 × 8 - 8 × 4 = 64 - 32 = 32 — oh! That's better.
8 × 8 - 8 × 4
But order: multiplication first: 8×8=64, 8×4=32, then 64-32=32.
And digits: 8,8,8,4 — so positions: first 8, second 8, third 8, fourth 4.
So expression: 8 × 8 - 8 × 4
Is that valid? Between the digits: between first and second: ×, between second and third: -, between third and fourth: ×
So: 8 × 8 - 8 × 4
Yes, and by order of operations, both multiplications done before subtraction: 64 - 32 = 32.
Perfect.
So C: 8 × 8 - 8 × 4 = 32
---
D: 5 7 6 3 = 10
Target 10.
Try: 5 + 7 - 6 + 3 = 9 ✘
5 + 7 - 6 - 3 = 3 ✘
5 × 2 = 10, but no 2.
7 + 3 = 10, so maybe 5 and 6 cancel.
5 - 5 =0, but no.
(5 + 7 + 6)/ something — no parentheses.
Try: 5 + 7 - 6 ÷ 3? 6÷3=2, 5+7-2=10 ✔
Check: 6 ÷ 3 = 2, then 5 + 7 = 12, minus 2 = 10.
Order: division first, then left to right: 5 + 7 - (6÷3) = 12 - 2 = 10.
Digits: 5,7,6,3 — so 5 + 7 - 6 ÷ 3
Yes.
So D: 5 + 7 - 6 ÷ 3 = 10
---
E: 6 6 7 8 = 56
Target 56.
56 is 7×8, so probably involve that.
6 + 6 + 7 × 8 = 6+6+56=68 ✘
6 × 6 + 7 + 8 = 36+15=51 ✘
6 × 7 + 6 + 8 = 42+14=56 ✔
Check: 6 × 7 = 42, then +6 = 48, +8=56.
Digits: 6,6,7,8 — so first 6, second 6, third 7, fourth 8.
Expression: 6 × 7 + 6 + 8 — but that would require skipping the second 6 or reordering.
No: the sequence is 6 _ 6 _ 7 _ 8
So if we do 6 × 6 + 7 + 8 = 36+15=51 ✘
6 + 6 × 7 + 8 = 6 + 42 + 8 = 56 ✔
Yes! Multiplication first: 6×7=42, then 6+42=48, +8=56.
Digits in order: 6,6,7,8 — so 6 + 6 × 7 + 8
Perfect.
So E: 6 + 6 × 7 + 8 = 56
---
F: 4 4 4 9 = 6
Target 6.
Small number, so probably division or subtraction.
4 + 4 + 4 - 9 = 12 - 9 = 3 ✘
4 × 4 - 4 - 9 = 16-4-9=3 ✘
(4 + 4 + 4)/2 = 6, but no 2.
9 - 4 - 4/4 = 9-4-1=4 ✘
4 + 4/4 - 9? 4+1-9=-4 ✘
What if: 4 × 4 - 4 - 6? No 6.
Another idea: 9 - 4 + 4/4 = 9-4+1=6 ✔
Check: 4/4=1, then 9-4=5, +1=6? Order: if expression is 9 - 4 + 4 ÷ 4
But digits are 4,4,4,9 — so must start with 4.
So 4 _ 4 _ 4 _ 9
Try: 4 + 4 - 4 + 9? 4+4-4+9=13 ✘
4 × 4 ÷ 4 - 9? 16÷4=4, -9=-5 ✘
(4 + 4 + 4) ÷ 2, no.
What if: 4 - 4 + 4 + 9? 0+4+9=13 ✘
Perhaps division: 4 ÷ 4 =1, then 4 + 1 =5, not 6.
9 - 3 =6, and 4 - 4/4 = 4-1=3, so 9 - (4 - 4/4) — but no parentheses, and order.
Try: 4 ÷ 4 + 4 + 9? 1+4+9=14 ✘
Another thought: 4 × 9 - 4 × 4? 36 - 16 = 20 ✘
Too big.
What if: (4 + 4) ÷ 4 × 3, no.
Let's think differently.
Suppose: 4 + 4 ÷ 4 - 9? 4+1-9=-4 ✘
4 - 4 ÷ 4 + 9? 4-1+9=12 ✘
Perhaps: 9 - 4 - 4/4 = 9-4-1=4 ✘
Wait — what if we do: 4 × 4 - 4 - 6, no.
Another idea: 6 = 24 ÷ 4, and 4×6=24, but no 6.
4 + 4 + 4 = 12, 12 ÷ 2 =6, but no 2.
9 - 3 =6, and 3 = 4 - 1, and 1=4/4.
So: 9 - (4 - 4/4) — but again, no parentheses.
In order: if we write 4 ÷ 4 =1, then 4 - 1 =3, then 9 - 3 =6, but the expression would be 9 - 4 + 4 ÷ 4? Let's calculate: 4÷4=1, then 9-4=5, 5+1=6 — oh! 9 - 4 + 4 ÷ 4 = 5 + 1 =6.
But digits are 4,4,4,9 — so we need to start with 4.
So perhaps: 4 ÷ 4 + 9 - 4? That would be 1 + 9 - 4 = 6 ✔
Check: 4 ÷ 4 =1, then 1 + 9 =10, then 10 - 4 =6.
Digits: first 4, second 4, third 9, fourth 4? But the digits are 4,4,4,9 — so third is 4, fourth is 9.
In 4 ÷ 4 + 9 - 4, the digits used are 4,4,9,4 — which matches 4,4,4,9 if we consider the last 4 is the third 4, and 9 is fourth.
The sequence is position 1:4, pos2:4, pos3:4, pos4:9.
In expression 4 ÷ 4 + 9 - 4, we have: first 4, second 4, then 9, then 4 — but the third digit should be 4, not 9. Here we have 9 as third operand, but it should be the fourth digit.
Mistake.
The expression must use the digits in order: digit1 _ digit2 _ digit3 _ digit4
So for F: 4 _ 4 _ 4 _ 9
So options like 4 ÷ 4 + 4 - 9 = 1 + 4 - 9 = -4 ✘
4 + 4 ÷ 4 - 9 = 4 + 1 - 9 = -4 ✘
4 - 4 ÷ 4 + 9 = 4 - 1 + 9 = 12 ✘
4 × 4 ÷ 4 - 9 = 4 - 9 = -5 ✘
(4 + 4) ÷ 4 * 3, no.
Another idea: 9 - 4 - 4/4, but again, order.
Perhaps: 4 + 4 - 4 + 9? 4+4-4+9=13 ✘
Let's calculate 4 * 9 = 36, too big.
What if: (4 * 4 + 4) / 4 = 20/4=5, not 6.
4! / 4 = 24/4=6, but no factorial.
Perhaps I missed something.
Try: 4 ÷ 4 =1, then 4 + 1 =5, not 6.
9 - 3 =6, and 3 = 12/4, but no.
Another thought: 6 = 18 / 3, but no 3 or 18.
Let's list possible combinations.
Suppose we do division first.
4 ÷ 4 =1, then we have 1,4,9 to combine with operators.
But must be in sequence.
Expression: 4 op1 4 op2 4 op3 9
Try op1=+, op2=÷, op3=- : 4 + 4 ÷ 4 - 9 = 4 + 1 - 9 = -4 ✘
op1=-, op2=÷, op3=+ : 4 - 4 ÷ 4 + 9 = 4 - 1 + 9 = 12 ✘
op1=×, op2=÷, op3=- : 4 × 4 ÷ 4 - 9 = 4 - 9 = -5 ✘
op1=+, op2=+, op3=- : 4+4+4-9=3 ✘
op1=×, op2=-, op3=- : 4×4-4-9=16-4-9=3 ✘
op1=-, op2=+, op3=+ : 4-4+4+9=13 ✘
What if op2 is × or ÷.
Another idea: 4 + 4 + 4 = 12, 12 - 6 =6, but no 6.
9 - 3 =6, and 3 = 4 - 1, 1=4/4, so if we can do 9 - (4 - 4/4), but in linear order without parentheses, it might work if we arrange the operations properly.
Suppose: 4 ÷ 4 =1, then 4 - 1 =3, then 9 - 3 =6, but the expression would be 9 - 4 + 4 ÷ 4, which is 9 - 4 + 1 =6, but as before, the digits are not in order; we have 9 first, but it should be last.
Unless we do: 4 ÷ 4 + 9 - 4, but again, the third digit is 9, but it should be the third 4.
The digits are fixed: first 4, second 4, third 4, fourth 9.
So the expression is A op B op C op D with A=B=C=4, D=9.
So perhaps: 4 - 4 + 4 + 9? 0+4+9=13 ✘
4 * 4 - 4 - 6, no.
Let's try: (4 + 4) * 4 / 8, no.
Another thought: 6 = 24 / 4, and 4*6=24, but no 6.
4! =24, but not allowed.
Perhaps: 4 + 4/4 =5, then 5 +1=6, but no 1.
9/3=3, but no 3.
Let's calculate 4 * 9 = 36, 36 / 6 =6, but no 6.
36 / (4 + 2), no.
Perhaps: 4 * 9 - 4 * 7.5, no.
I recall that sometimes they use concatenation, but the instruction says place +,-,x,/ between digits, so probably not.
Another idea: 4 + 4 - 4/4 = 4+4-1=7 ✘
4 - 4/4 + 4 = 4-1+4=7 ✘
(4*4 + 8)/4 = 24/4=6, but no 8.
Let's think outside the box.
What if: 4 ÷ 4 =1, then 1 * 6 =6, but no 6.
9 - 3 =6, and 3 = 12/4, 12=4*3, circular.
Perhaps: 9 - 4 - 4/4 = 9-4-1=4 ✘
Wait — what if we do: 4 + 4 ÷ 4 = 5, then 5 +1=6, but no.
Let's try: 4 * 4 = 16, 16 - 10 =6, 10=9+1, 1=4/4, so 4*4 - (9 + 4/4) — but no parentheses, and order.
In sequence: 4 * 4 - 9 + 4 ÷ 4? Let's calculate: 4*4=16, 4÷4=1, then 16 - 9 =7, +1=8 ✘
4 * 4 - 9 - 4 ÷ 4 = 16 - 9 - 1 =6 ✔
Check: multiplication and division first: 4*4=16, 4÷4=1, then 16 - 9 =7, then 7 - 1 =6.
Digits: 4,4,9,4 — but the digits are 4,4,4,9 — so third digit is 4, fourth is 9.
In this expression: 4 * 4 - 9 - 4 ÷ 4, we have five numbers: 4,4,9,4,4 — too many.
Mistake.
The expression has three operators, so four numbers: digit1 op1 digit2 op2 digit3 op3 digit4
So for F: 4 op1 4 op2 4 op3 9
So only four numbers.
So 4 * 4 - 9 - 4 ÷ 4 is invalid because it has five numbers.
Must be exactly four numbers with three operators between them.
So back to square one.
Try: 4 + 4 + 4 - 9 = 3 ✘
4 * 4 - 4 - 9 = 16-4-9=3 ✘
4 - 4 + 4 * 9 = 0 + 36 = 36 ✘
4 * 9 - 4 * 4 = 36 - 16 = 20 ✘
(4 + 4) * 4 / 8, no.
Another idea: 6 = 30 / 5, but no.
Perhaps division: 4 / 4 =1, then 4 + 1 =5, not 6.
9 / 1.5 =6, but no 1.5.
Let's calculate 4 + 4/4 =5, then if we had another 1, but we have 9.
9 - 3 =6, and 3 = 4 - 1, 1=4/4, so if we can do 9 - (4 - 4/4), but in linear order, if we write 4/4 first, then 4 - that, then 9 - that.
But the expression would be 9 - 4 + 4 ÷ 4, which is 9 - 4 + 1 =6, but as said, the digits are not in order; we have 9 first, but it should be the fourth digit.
Unless the expression is written as 4 ÷ 4 + 9 - 4, but then the third digit is 9, but it should be the third 4.
The only way is if we use the digits in the given order: first 4, second 4, third 4, fourth 9.
So perhaps: 4 - 4/4 + 9? 4 - 1 + 9 = 12 ✘
4 + 4/4 - 9 = 4+1-9= -4 ✘
4 * 4 / 4 * 9 = 4*9=36 ✘
4 + 4 - 4/9? Not integer.
Perhaps: (4 * 4 + 8) / 4, no.
I recall that in some puzzles, they allow the operations to be placed, and order of operations applies.
Let me try: 4 ÷ 4 =1, then 1 * 6 =6, but no 6.
Another thought: 6 = 2*3, but no.
Let's search online or think differently.
Perhaps: 4 + 4 - 4 + 9? 4+4-4+9=13 ✘
4 * 9 / 6 =6, but no 6.
36 / 6 =6, and 4*9=36, so if we can divide by 6, but we have two 4's left.
4*9 / (4 + 2), no.
(4*9) / (4 + 2), but no 2.
4/4 =1, so 4*9 / (4/4 + 5), complicated.
Perhaps: 4 + 4/4 =5, then 5 +1=6, but no 1.
9/3=3, but no 3.
Let's calculate the difference.
Target 6, current sum 4+4+4+9=21, too big.
Product 4*4*4*9=576, too big.
Perhaps subtraction and division.
Try: 9 - 4 - 4/4 = 9-4-1=4 ✘
4 - 4/4 =3, then 9 - 3 =6, so if the expression is 9 - (4 - 4/4), but to write it without parentheses, and in order, it might be 4/4 - 4 + 9 or something.
Let's try: 4 ÷ 4 - 4 + 9 = 1 - 4 + 9 = 6 ✔
Calculate: 4 ÷ 4 =1, then 1 - 4 = -3, then -3 + 9 =6.
Yes! And digits: first 4, second 4, third 4, fourth 9 — so 4 ÷ 4 - 4 + 9
Order of operations: division first: 4÷4=1, then left to right: 1 - 4 = -3, then -3 + 9 =6.
Perfect.
So F: 4 ÷ 4 - 4 + 9 = 6
---
G: 8 2 9 5 = 180
Target 180.
Large number, so likely multiplication.
8 × 2 = 16, 9 × 5 = 45, 16×45=720, too big.
8 × 9 = 72, 2 × 5 = 10, 72×10=720, still big.
8 × 5 = 40, 2 × 9 = 18, 40×18=720.
180 = 18 × 10, or 9 × 20, etc.
8 × 2 × 9 × 5 = 720, too big.
Perhaps (8 + 2) × (9 + 9), no.
8 × 2 = 16, 16 × 11.25 = 180, not integer.
9 × 20 = 180, and 20 = 8 + 2 + 10, no.
5 × 36 = 180, 36 = 8 × 4.5, no.
Another idea: 8 × 9 = 72, 72 × 2.5 = 180, 2.5 = 5/2, so 8 × 9 × 5 / 2
Check: 8 × 9 = 72, ×5 = 360, /2 = 180.
Digits: 8,2,9,5 — so 8 × 9 × 5 / 2
But order: 8 _ 2 _ 9 _ 5
So if we do 8 × 9 × 5 / 2, but 2 is second digit, 9 is third, 5 is fourth.
So expression: 8 × 2 × 9 × 5 / something, too many.
With three operators: 8 op1 2 op2 9 op3 5
Try: 8 × 2 × 9 × 5 = 720, too big.
8 × 9 × 5 / 2 = 360 / 2 = 180, but how to arrange with digits in order.
If we do 8 × 9 × 5 / 2, but 2 is before 9 and 5 in the sequence.
Sequence is 8,2,9,5 — so after 8 is 2, then 9, then 5.
So perhaps: 8 × 2 × 9 × 5 / 2, but extra 2.
No.
Another way: 180 = 90 × 2, 90 = 9 × 10, 10 = 5 × 2, but duplicate.
8 + 2 = 10, 9 × 5 = 45, 10 × 45 = 450, too big.
(8 + 2) × 9 × 2, no.
Let's try: 8 × 5 = 40, 40 × 4.5 = 180, 4.5 = 9/2, so 8 × 5 × 9 / 2
Same as before.
So 8 × 5 × 9 / 2 = 360 / 2 = 180.
Now, with digits 8,2,9,5 — so if we can do 8 × 5 × 9 / 2, but 2 is second, 5 is fourth.
So perhaps: 8 / 2 × 9 × 5
Calculate: 8 / 2 = 4, then 4 × 9 = 36, then 36 × 5 = 180 ✔
Yes! And digits in order: 8,2,9,5 — so 8 ÷ 2 × 9 × 5
Order: division and multiplication left to right: 8÷2=4, 4×9=36, 36×5=180.
Perfect.
So G: 8 ÷ 2 × 9 × 5 = 180
---
H: 4 3 8 2 = 3
Target 3.
Small number.
Try: 4 + 3 - 8 + 2 = 1 ✘
4 - 3 + 8 - 2 = 7 ✘
4 × 3 - 8 - 2 = 12-8-2=2 ✘
4 + 3 - 8 ÷ 2 = 4+3-4=3 ✔
Check: 8 ÷ 2 = 4, then 4 + 3 = 7, then 7 - 4 = 3.
Digits: 4,3,8,2 — so 4 + 3 - 8 ÷ 2
Order: division first: 8÷2=4, then 4+3=7, then 7-4=3.
Yes.
So H: 4 + 3 - 8 ÷ 2 = 3
---
Now, summarize all answers:
A: 8 × 5 + 2 - 6 = 36
B: 5 + 7 × 8 - 3 = 58
C: 8 × 8 - 8 × 4 = 32
D: 5 + 7 - 6 ÷ 3 = 10
E: 6 + 6 × 7 + 8 = 56
F: 4 ÷ 4 - 4 + 9 = 6
G: 8 ÷ 2 × 9 × 5 = 180
H: 4 + 3 - 8 ÷ 2 = 3
All verified.
Final Answer:
A: 8 × 5 + 2 - 6 = 36
B: 5 + 7 × 8 - 3 = 58
C: 8 × 8 - 8 × 4 = 32
D: 5 + 7 - 6 ÷ 3 = 10
E: 6 + 6 × 7 + 8 = 56
F: 4 ÷ 4 - 4 + 9 = 6
G: 8 ÷ 2 × 9 × 5 = 180
H: 4 + 3 - 8 ÷ 2 = 3
Parent Tip: Review the logic above to help your child master the concept of integer operations worksheet.