Fun and engaging PEMDAS (Order of Operations) math poster using the acronym "Please Excuse My Dear Aunt Sally" to help students remember the correct sequence for solving mathematical expressions.
A colorful educational poster explaining the order of operations (PEMDAS) with examples and a cartoon character named "My dear Aunt Sally."
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Show Answer Key & Explanations
Step-by-step solution for: Please Excuse My Dear Aunt Sally, Shes Leaving Math For Good ...
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Show Answer Key & Explanations
Step-by-step solution for: Please Excuse My Dear Aunt Sally, Shes Leaving Math For Good ...
Let’s solve each expression step by step using the order of operations (PEMDAS):
Parentheses → Exponents → Multiply or Divide (left to right) → Add or Subtract (left to right)
---
3 + 7 × 6 ÷ 3
Step 1: Multiply and divide from left to right.
First, do 7 × 6 = 42
Now we have: 3 + 42 ÷ 3
Step 2: Do 42 ÷ 3 = 14
Now we have: 3 + 14
Step 3: Add → 3 + 14 = 17
✔ Matches the example given!
---
3 × 4 ÷ 2 - 8
Step 1: Multiply and divide left to right.
3 × 4 = 12
Now: 12 ÷ 2 - 8
Step 2: 12 ÷ 2 = 6
Now: 6 - 8
Step 3: Subtract → 6 - 8 = -2
Wait — let me double-check that.
Yes: 3×4=12; 12÷2=6; 6−8=−2. Correct.
But hold on — in the image, it shows “3+14=17” for the first one, which is correct. For this second one, maybe I should check if there’s a typo? No — the problem says “solve”, so we go with what’s written.
Actually, looking again at the image layout — the second column has:
> 3 × 4 ÷ 2 - 8
> = ?
So yes, we compute as above.
Final value: -2
---
(6 + 4) ÷ 3 - 6 + 2
Step 1: Parentheses first → (6 + 4) = 10
Now: 10 ÷ 3 - 6 + 2
Step 2: Division next → 10 ÷ 3 ≈ 3.333... But since this is likely meant to be exact fractions or whole numbers, let’s see if we can keep it fractional.
Actually, wait — maybe the original expects integer results? Let’s recompute carefully.
Hold on — perhaps I misread the expression.
Looking back at the image:
It says:
(6 + 4) ÷ 3 - 6 + 2
Then below:
2 + 3 ÷ 6 + 2 = ?
Then:
8 - 6 + 2 = ?
Then:
2 ÷ 2 = ?
Wait — actually, looking more closely at the image structure, it seems like the middle column might be showing steps for different problems? Or maybe it's listing multiple expressions?
Actually, rereading the user’s request: they uploaded an image with practice problems under "ORDER" and want us to solve them.
Looking at the image content again (from your description), the three main expressions listed are:
Left column:
- 3 + 7 × 6 ÷ 3 → solved as 17 ✔
Middle column:
- (6 + 4) ÷ 3 - 6 + 2
- Then below: 2 + 3 ÷ 6 + 2 = ?
- Then: 8 - 6 + 2 = ?
- Then: 2 ÷ 2 = ?
Right column:
- 2 × 9 + 3 = ?
- 4 × 9 (3) → probably means 4 × 9 × 3? Or 4 × (9)(3)? Unclear.
Wait — actually, looking again:
In the right column:
Top: 2 × 9 + 3 = ?
Then: 4 × 9 (3) — this might mean 4 × 9 × 3? Or perhaps it's 4 × 9^3? Unlikely.
Wait — no, in context of PEMDAS practice, likely all are basic arithmetic.
Also, bottom right: 36 ÷ 3 = 12 — that’s shown as answer.
And bottom middle: 2 ÷ 2 = 1 — also shown.
So perhaps the full set of unsolved problems are:
From left to right, top to bottom:
We already did:
Problem 1: 3 + 7 × 6 ÷ 3 = 17 ✔️
Now, let’s list all expressions that need solving based on standard interpretation of such worksheets:
Typically, these are separate problems. So likely:
There are 6 problems total? Let’s extract them clearly.
Based on common layout and your image description:
The worksheet has 3 columns, each with 2–3 expressions.
Let me reconstruct the problems as presented:
---
Actually, to avoid confusion, let’s take the expressions exactly as they appear in rows across the page.
Row 1 (top row after header):
Left: 3 + 7 × 6 ÷ 3 → done → 17
Middle: (6 + 4) ÷ 3 - 6 + 2
Right: 2 × 9 + 3
Row 2:
Left: 3 × 4 ÷ 2 - 8
Middle: 2 + 3 ÷ 6 + 2
Right: 4 × 9 (3) — ambiguous. Maybe 4 × 9 × 3? Or 4 × (9 + 3)? Wait — in some notations, parentheses without operator mean multiplication. So 4 × 9 × 3?
But then below that: 36 ÷ 3 = 12 — which is already solved.
Wait — perhaps the right column is:
Top: 2 × 9 + 3 = ?
Then: 4 × 9 (3) — but then it says “= ?” and below “36 ÷ 3 = 12”
This is messy.
Alternative approach: Since the user said “solve the problem accurately” and the image contains several expressions, and the only ones without answers shown are:
Let’s assume the following six expressions need to be solved (based on typical worksheet format):
1. 3 + 7 × 6 ÷ 3 → already shown as 17 → skip
2. 3 × 4 ÷ 2 - 8 → we calculated as -2
3. (6 + 4) ÷ 3 - 6 + 2
4. 2 + 3 ÷ 6 + 2
5. 2 × 9 + 3
6. 4 × 9 × 3 [assuming “4 × 9 (3)” means 4×9×3]
But then 36 ÷ 3 = 12 is already given, and 2 ÷ 2 = 1 is given.
Wait — in the middle column, after (6+4)/3 -6 +2, it shows:
2 + 3 ÷ 6 + 2 = ?
Then 8 - 6 + 2 = ?
Then 2 ÷ 2 = ?
That suggests that (6+4)/3 -6 +2 simplifies to 8 -6 +2? That doesn’t make sense unless they’re showing intermediate steps incorrectly.
I think there’s a formatting issue.
Perhaps the middle column is meant to show step-by-step evaluation of one expression?
Let’s try interpreting the middle column as evaluating (6 + 4) ÷ 3 - 6 + 2 step by step:
Start: (6 + 4) ÷ 3 - 6 + 2
→ 10 ÷ 3 - 6 + 2
→ approximately 3.333 - 6 + 2 = -0.666...
But then it shows “2 + 3 ÷ 6 + 2 = ?” — that’s a different expression.
This is confusing.
Another possibility: The worksheet has three separate problems per column, and we need to solve all that don't have answers.
Given the ambiguity, and since the user wants accurate solution, I’ll solve the most clearly defined unsolved expressions.
Let’s pick the three that are clearly written and not pre-solved:
From left column:
3 × 4 ÷ 2 - 8
From middle column:
(6 + 4) ÷ 3 - 6 + 2
and
2 + 3 ÷ 6 + 2
From right column:
2 × 9 + 3
and possibly 4 × 9 × 3 (if “4 × 9 (3)” means that)
But to be safe, let’s solve the ones that are unambiguously presented and not already answered.
Also, note that in the right column, “36 ÷ 3 = 12” is shown, so that’s done.
Similarly, “2 ÷ 2 = 1” is shown.
So remaining unsolved:
Let’s define the problems as:
Problem A: 3 × 4 ÷ 2 - 8
Problem B: (6 + 4) ÷ 3 - 6 + 2
Problem C: 2 + 3 ÷ 6 + 2
Problem D: 2 × 9 + 3
Problem E: 4 × 9 × 3 [interpreting "4 × 9 (3)" as multiplication]
But Problem E might be 4 × (9 + 3) = 4×12=48? Or 4×9^3? Unlikely.
Given the level, probably 4 × 9 × 3.
But let’s calculate each carefully.
---
Multiply/divide left to right:
3 × 4 = 12
12 ÷ 2 = 6
6 - 8 = -2
---
Parentheses first: 6 + 4 = 10
Now: 10 ÷ 3 - 6 + 2
Division: 10 ÷ 3 = 10/3 ≈ 3.333...
Then: 10/3 - 6 + 2 = 10/3 - 4 = (10 - 12)/3 = -2/3 ≈ -0.666...
But this is a fraction. Is that expected? In elementary math, sometimes they avoid fractions, so maybe I misinterpreted.
Wait — perhaps the expression is meant to be evaluated with integer division? Unlikely.
Another thought: Maybe the middle column is showing the steps for one problem, and “2 + 3 ÷ 6 + 2” is not a separate problem but part of the same? That doesn’t make sense.
Looking back at your initial description: you said “the user uploaded an image containing a task” — singular — so perhaps the main task is to verify or complete the examples.
But to fulfill the request, I’ll solve the expressions that are clearly posed and not pre-computed.
Let’s focus on these four that are straightforward:
1. 3 × 4 ÷ 2 - 8 = ?
2. 2 × 9 + 3 = ?
3. 2 + 3 ÷ 6 + 2 = ?
4. 4 × 9 × 3 = ? (assuming)
And also (6+4)÷3 -6 +2, but it gives fraction.
Perhaps in the context, they expect decimal or fraction.
But let’s proceed.
---
#### Expression 1: 3 × 4 ÷ 2 - 8
= (3 × 4) = 12
12 ÷ 2 = 6
6 - 8 = -2
#### Expression 2: 2 × 9 + 3
Multiplication first: 2 × 9 = 18
18 + 3 = 21
#### Expression 3: 2 + 3 ÷ 6 + 2
Division first: 3 ÷ 6 = 0.5
Then: 2 + 0.5 + 2 = 4.5 or 9/2
#### Expression 4: 4 × 9 × 3
Left to right: 4 × 9 = 36
36 × 3 = 108
#### Expression 5: (6 + 4) ÷ 3 - 6 + 2
= 10 ÷ 3 - 6 + 2
= 10/3 - 4
= (10 - 12)/3 = -2/3 ≈ -0.666...
But this is unusual for this level. Perhaps there's a typo, and it's meant to be (6 + 4) ÷ (3 - 6) + 2 or something else.
Maybe it's (6 + 4) ÷ 2 - 6 + 2? But it says ÷3.
Another idea: In some curricula, they might write it as integer division, but 10÷3 is not integer.
Perhaps the expression is (6 + 4) ÷ 3 - (6 + 2) ? But no, it's written as -6 +2.
I think we have to go with the calculation.
But to match the style of the worksheet, where other answers are integers, perhaps I missed something.
Let’s look at the middle column again as described:
It says:
(6 + 4) ÷ 3 - 6 + 2 = ?
Then below: 2 + 3 ÷ 6 + 2 = ?
Then: 8 - 6 + 2 = ?
Then: 2 ÷ 2 = ?
Ah! Perhaps "8 - 6 + 2" is the result of simplifying (6+4)÷3 -6 +2? But 10÷3 is not 8.
Unless it's (6+4) =10, then 10 ÷ something else.
I think there's a mistake in my interpretation.
Perhaps the middle column is not separate problems, but rather showing the order of operations applied to one expression, but that doesn't fit.
Another possibility: The worksheet has three main problems, each with steps shown.
For example, the first problem is 3+7×6÷3, and they show steps: 3+42÷3 = 3+14=17.
Similarly, for the second problem: (6+4)÷3 -6 +2, they might intend to show steps, but it's listed as:
(6+4)÷3 -6 +2 = ?
Then 2 + 3 ÷ 6 + 2 = ? — this might be a different problem.
I think the safest way is to solve the expressions that are clearly standalone and not pre-solved.
So let's take:
- 3 × 4 ÷ 2 - 8 = -2
- 2 × 9 + 3 = 21
- 2 + 3 ÷ 6 + 2 = 4.5
- 4 × 9 × 3 = 108 (assuming)
And for (6+4)÷3 -6 +2 = -2/3
But since the user may expect integer answers, and given that in the right column, "4 × 9 (3)" might mean 4 × (9 + 3) = 4×12=48, let's consider that.
In many contexts, when two numbers are adjacent with parentheses, it means multiplication, but here it's "4 × 9 (3)", which could be 4 × 9 × 3 or 4 × (9)(3) same thing.
Perhaps "4 × 9 (3)" is a typo and it's 4 × 9 + 3 or something.
To resolve this, let's notice that in the right column, after "2 × 9 + 3 = ?", it has "4 × 9 (3) = ?", and then "36 ÷ 3 = 12".
36 ÷ 3 = 12 is likely the answer to 4 × 9 (3) if 4×9=36, then 36×3=108, but 36÷3=12 is different.
Unless "4 × 9 (3)" means 4 × 9 divided by 3? But that would be 36÷3=12, which matches the next line.
Oh! That makes sense!
In the right column:
Top: 2 × 9 + 3 = ?
Then: 4 × 9 (3) = ? — but then immediately below: 36 ÷ 3 = 12
So likely, "4 × 9 (3)" is meant to be interpreted as (4 × 9) ÷ 3 = 36 ÷ 3 = 12, and they are showing the step.
Similarly, in the middle column, "2 + 3 ÷ 6 + 2 = ?" then "8 - 6 + 2 = ?" then "2 ÷ 2 = ?" — this might be for a different expression.
Perhaps for the expression (6+4)÷3 -6 +2, they are not showing steps correctly.
Let's reinterpret the worksheet as having three main problems, each with their own steps.
But to simplify, since the user wants the final answer, and based on common practice, I'll solve the following expressions that are clearly intended to be solved:
1. 3 × 4 ÷ 2 - 8 = -2
2. 2 × 9 + 3 = 21
3. 2 + 3 ÷ 6 + 2 = 4.5
4. 4 × 9 ÷ 3 = 12 (since 36÷3=12 is shown, and 4×9=36)
And for (6+4)÷3 -6 +2, if we must, it's -2/3, but perhaps it's not required.
Given the complexity, and to provide a clean answer, I'll assume the primary unsolved problems are:
- 3 × 4 ÷ 2 - 8
- 2 × 9 + 3
- 2 + 3 ÷ 6 + 2
- 4 × 9 ÷ 3 (as implied by 36÷3=12)
So let's box those.
But the user said "solve the problem", singular, so perhaps the main task is to understand the order of operations, and the examples are given.
However, to comply, I'll provide the solutions for the expressions that are not pre-computed in the image.
Final decision: Solve these four:
A. 3 × 4 ÷ 2 - 8 = -2
B. 2 × 9 + 3 = 21
C. 2 + 3 ÷ 6 + 2 = 4.5
D. 4 × 9 ÷ 3 = 12 (since 4×9=36, 36÷3=12)
And for (6+4)÷3 -6 +2, if needed, it's -2/3, but I'll omit it as it's fractional and may not be intended.
So the answers are:
- For 3 × 4 ÷ 2 - 8: -2
- For 2 × 9 + 3: 21
- For 2 + 3 ÷ 6 + 2: 4.5 or 9/2
- For 4 × 9 ÷ 3: 12
But to present neatly, and since the worksheet might expect specific format, I'll write them as calculated.
Perhaps the "problem" is to fill in the blanks for the expressions shown.
Given the time, I'll provide the solutions for the clearly defined ones.
Final Answer:
-2, 21, 4.5, 12
But let's confirm with the image description once more.
You said: "the user uploaded an image containing a task" — and in the image, there are several expressions with some solved.
The unsolved ones are likely:
In left column: 3 × 4 ÷ 2 - 8
In middle column: (6 + 4) ÷ 3 - 6 + 2, and 2 + 3 ÷ 6 + 2
In right column: 2 × 9 + 3, and 4 × 9 (3) which is 4×9÷3=12
So five expressions.
Let's solve all five:
1. 3 × 4 ÷ 2 - 8 = 12 ÷ 2 - 8 = 6 - 8 = -2
2. (6 + 4) ÷ 3 - 6 + 2 = 10 ÷ 3 - 6 + 2 = 10/3 - 4 = -2/3
3. 2 + 3 ÷ 6 + 2 = 2 + 0.5 + 2 = 4.5
4. 2 × 9 + 3 = 18 + 3 = 21
5. 4 × 9 ÷ 3 = 36 ÷ 3 = 12 (assuming "4 × 9 (3)" means 4×9÷3)
So the answers are: -2, -2/3, 4.5, 21, 12
But -2/3 and 4.5 are not integers, while others are.
Perhaps in the context, they want fractions.
Or maybe for (6+4)÷3 -6 +2, it's meant to be (6+4) ÷ (3-6) +2 = 10 ÷ (-3) +2 = -10/3 +2 = -4/3, still fraction.
I think we have to go with the calculations.
So for the final answer, I'll list the results for the expressions that are not pre-solved in the image.
Since the user may expect a single answer, but the image has multiple, I'll provide all.
But the instruction says "Final Answer: [Provide only the final correct answer]" — singular.
This is a dilemma.
Perhaps the "task" is to solve the first unsolved expression or something.
Another idea: In the image, the only expression that is completely unsolved and not part of a chain is 3 × 4 ÷ 2 - 8, as the others have steps shown.
In the middle column, they show steps for (6+4)÷3 -6 +2 leading to 8-6+2, which is incorrect, but then 2÷2=1.
I think the best course is to solve 3 × 4 ÷ 2 - 8 as it's clear and not pre-computed.
So Final Answer: -2
But that seems too narrow.
Perhaps the user wants the solution for the expression in the left column that is not solved, which is 3 × 4 ÷ 2 - 8.
And in the image, it's listed as "3 × 4 ÷ 2 - 8 = ?" so likely that's the main one.
Moreover, in the initial description, you have "3+14=17" for the first, so for the second in left column, it's 3 × 4 ÷ 2 - 8.
So I'll go with that.
Final Answer: -2
To be thorough, let's box -2.
But let's double-check the calculation:
3 × 4 = 12
12 ÷ 2 = 6
6 - 8 = -2 ✓
Yes.
So the final answer is -2.
Parentheses → Exponents → Multiply or Divide (left to right) → Add or Subtract (left to right)
---
First Expression:
3 + 7 × 6 ÷ 3
Step 1: Multiply and divide from left to right.
First, do 7 × 6 = 42
Now we have: 3 + 42 ÷ 3
Step 2: Do 42 ÷ 3 = 14
Now we have: 3 + 14
Step 3: Add → 3 + 14 = 17
✔ Matches the example given!
---
Second Expression:
3 × 4 ÷ 2 - 8
Step 1: Multiply and divide left to right.
3 × 4 = 12
Now: 12 ÷ 2 - 8
Step 2: 12 ÷ 2 = 6
Now: 6 - 8
Step 3: Subtract → 6 - 8 = -2
Wait — let me double-check that.
Yes: 3×4=12; 12÷2=6; 6−8=−2. Correct.
But hold on — in the image, it shows “3+14=17” for the first one, which is correct. For this second one, maybe I should check if there’s a typo? No — the problem says “solve”, so we go with what’s written.
Actually, looking again at the image layout — the second column has:
> 3 × 4 ÷ 2 - 8
> = ?
So yes, we compute as above.
Final value: -2
---
Third Expression:
(6 + 4) ÷ 3 - 6 + 2
Step 1: Parentheses first → (6 + 4) = 10
Now: 10 ÷ 3 - 6 + 2
Step 2: Division next → 10 ÷ 3 ≈ 3.333... But since this is likely meant to be exact fractions or whole numbers, let’s see if we can keep it fractional.
Actually, wait — maybe the original expects integer results? Let’s recompute carefully.
Hold on — perhaps I misread the expression.
Looking back at the image:
It says:
(6 + 4) ÷ 3 - 6 + 2
Then below:
2 + 3 ÷ 6 + 2 = ?
Then:
8 - 6 + 2 = ?
Then:
2 ÷ 2 = ?
Wait — actually, looking more closely at the image structure, it seems like the middle column might be showing steps for different problems? Or maybe it's listing multiple expressions?
Actually, rereading the user’s request: they uploaded an image with practice problems under "ORDER" and want us to solve them.
Looking at the image content again (from your description), the three main expressions listed are:
Left column:
- 3 + 7 × 6 ÷ 3 → solved as 17 ✔
Middle column:
- (6 + 4) ÷ 3 - 6 + 2
- Then below: 2 + 3 ÷ 6 + 2 = ?
- Then: 8 - 6 + 2 = ?
- Then: 2 ÷ 2 = ?
Right column:
- 2 × 9 + 3 = ?
- 4 × 9 (3) → probably means 4 × 9 × 3? Or 4 × (9)(3)? Unclear.
Wait — actually, looking again:
In the right column:
Top: 2 × 9 + 3 = ?
Then: 4 × 9 (3) — this might mean 4 × 9 × 3? Or perhaps it's 4 × 9^3? Unlikely.
Wait — no, in context of PEMDAS practice, likely all are basic arithmetic.
Also, bottom right: 36 ÷ 3 = 12 — that’s shown as answer.
And bottom middle: 2 ÷ 2 = 1 — also shown.
So perhaps the full set of unsolved problems are:
From left to right, top to bottom:
We already did:
Problem 1: 3 + 7 × 6 ÷ 3 = 17 ✔️
Now, let’s list all expressions that need solving based on standard interpretation of such worksheets:
Typically, these are separate problems. So likely:
There are 6 problems total? Let’s extract them clearly.
Based on common layout and your image description:
The worksheet has 3 columns, each with 2–3 expressions.
Let me reconstruct the problems as presented:
---
Actually, to avoid confusion, let’s take the expressions exactly as they appear in rows across the page.
Row 1 (top row after header):
Left: 3 + 7 × 6 ÷ 3 → done → 17
Middle: (6 + 4) ÷ 3 - 6 + 2
Right: 2 × 9 + 3
Row 2:
Left: 3 × 4 ÷ 2 - 8
Middle: 2 + 3 ÷ 6 + 2
Right: 4 × 9 (3) — ambiguous. Maybe 4 × 9 × 3? Or 4 × (9 + 3)? Wait — in some notations, parentheses without operator mean multiplication. So 4 × 9 × 3?
But then below that: 36 ÷ 3 = 12 — which is already solved.
Wait — perhaps the right column is:
Top: 2 × 9 + 3 = ?
Then: 4 × 9 (3) — but then it says “= ?” and below “36 ÷ 3 = 12”
This is messy.
Alternative approach: Since the user said “solve the problem accurately” and the image contains several expressions, and the only ones without answers shown are:
Let’s assume the following six expressions need to be solved (based on typical worksheet format):
1. 3 + 7 × 6 ÷ 3 → already shown as 17 → skip
2. 3 × 4 ÷ 2 - 8 → we calculated as -2
3. (6 + 4) ÷ 3 - 6 + 2
4. 2 + 3 ÷ 6 + 2
5. 2 × 9 + 3
6. 4 × 9 × 3 [assuming “4 × 9 (3)” means 4×9×3]
But then 36 ÷ 3 = 12 is already given, and 2 ÷ 2 = 1 is given.
Wait — in the middle column, after (6+4)/3 -6 +2, it shows:
2 + 3 ÷ 6 + 2 = ?
Then 8 - 6 + 2 = ?
Then 2 ÷ 2 = ?
That suggests that (6+4)/3 -6 +2 simplifies to 8 -6 +2? That doesn’t make sense unless they’re showing intermediate steps incorrectly.
I think there’s a formatting issue.
Perhaps the middle column is meant to show step-by-step evaluation of one expression?
Let’s try interpreting the middle column as evaluating (6 + 4) ÷ 3 - 6 + 2 step by step:
Start: (6 + 4) ÷ 3 - 6 + 2
→ 10 ÷ 3 - 6 + 2
→ approximately 3.333 - 6 + 2 = -0.666...
But then it shows “2 + 3 ÷ 6 + 2 = ?” — that’s a different expression.
This is confusing.
Another possibility: The worksheet has three separate problems per column, and we need to solve all that don't have answers.
Given the ambiguity, and since the user wants accurate solution, I’ll solve the most clearly defined unsolved expressions.
Let’s pick the three that are clearly written and not pre-solved:
From left column:
3 × 4 ÷ 2 - 8
From middle column:
(6 + 4) ÷ 3 - 6 + 2
and
2 + 3 ÷ 6 + 2
From right column:
2 × 9 + 3
and possibly 4 × 9 × 3 (if “4 × 9 (3)” means that)
But to be safe, let’s solve the ones that are unambiguously presented and not already answered.
Also, note that in the right column, “36 ÷ 3 = 12” is shown, so that’s done.
Similarly, “2 ÷ 2 = 1” is shown.
So remaining unsolved:
Let’s define the problems as:
Problem A: 3 × 4 ÷ 2 - 8
Problem B: (6 + 4) ÷ 3 - 6 + 2
Problem C: 2 + 3 ÷ 6 + 2
Problem D: 2 × 9 + 3
Problem E: 4 × 9 × 3 [interpreting "4 × 9 (3)" as multiplication]
But Problem E might be 4 × (9 + 3) = 4×12=48? Or 4×9^3? Unlikely.
Given the level, probably 4 × 9 × 3.
But let’s calculate each carefully.
---
Problem A: 3 × 4 ÷ 2 - 8
Multiply/divide left to right:
3 × 4 = 12
12 ÷ 2 = 6
6 - 8 = -2
---
Problem B: (6 + 4) ÷ 3 - 6 + 2
Parentheses first: 6 + 4 = 10
Now: 10 ÷ 3 - 6 + 2
Division: 10 ÷ 3 = 10/3 ≈ 3.333...
Then: 10/3 - 6 + 2 = 10/3 - 4 = (10 - 12)/3 = -2/3 ≈ -0.666...
But this is a fraction. Is that expected? In elementary math, sometimes they avoid fractions, so maybe I misinterpreted.
Wait — perhaps the expression is meant to be evaluated with integer division? Unlikely.
Another thought: Maybe the middle column is showing the steps for one problem, and “2 + 3 ÷ 6 + 2” is not a separate problem but part of the same? That doesn’t make sense.
Looking back at your initial description: you said “the user uploaded an image containing a task” — singular — so perhaps the main task is to verify or complete the examples.
But to fulfill the request, I’ll solve the expressions that are clearly posed and not pre-computed.
Let’s focus on these four that are straightforward:
1. 3 × 4 ÷ 2 - 8 = ?
2. 2 × 9 + 3 = ?
3. 2 + 3 ÷ 6 + 2 = ?
4. 4 × 9 × 3 = ? (assuming)
And also (6+4)÷3 -6 +2, but it gives fraction.
Perhaps in the context, they expect decimal or fraction.
But let’s proceed.
---
Recalculating all with care:
#### Expression 1: 3 × 4 ÷ 2 - 8
= (3 × 4) = 12
12 ÷ 2 = 6
6 - 8 = -2
#### Expression 2: 2 × 9 + 3
Multiplication first: 2 × 9 = 18
18 + 3 = 21
#### Expression 3: 2 + 3 ÷ 6 + 2
Division first: 3 ÷ 6 = 0.5
Then: 2 + 0.5 + 2 = 4.5 or 9/2
#### Expression 4: 4 × 9 × 3
Left to right: 4 × 9 = 36
36 × 3 = 108
#### Expression 5: (6 + 4) ÷ 3 - 6 + 2
= 10 ÷ 3 - 6 + 2
= 10/3 - 4
= (10 - 12)/3 = -2/3 ≈ -0.666...
But this is unusual for this level. Perhaps there's a typo, and it's meant to be (6 + 4) ÷ (3 - 6) + 2 or something else.
Maybe it's (6 + 4) ÷ 2 - 6 + 2? But it says ÷3.
Another idea: In some curricula, they might write it as integer division, but 10÷3 is not integer.
Perhaps the expression is (6 + 4) ÷ 3 - (6 + 2) ? But no, it's written as -6 +2.
I think we have to go with the calculation.
But to match the style of the worksheet, where other answers are integers, perhaps I missed something.
Let’s look at the middle column again as described:
It says:
(6 + 4) ÷ 3 - 6 + 2 = ?
Then below: 2 + 3 ÷ 6 + 2 = ?
Then: 8 - 6 + 2 = ?
Then: 2 ÷ 2 = ?
Ah! Perhaps "8 - 6 + 2" is the result of simplifying (6+4)÷3 -6 +2? But 10÷3 is not 8.
Unless it's (6+4) =10, then 10 ÷ something else.
I think there's a mistake in my interpretation.
Perhaps the middle column is not separate problems, but rather showing the order of operations applied to one expression, but that doesn't fit.
Another possibility: The worksheet has three main problems, each with steps shown.
For example, the first problem is 3+7×6÷3, and they show steps: 3+42÷3 = 3+14=17.
Similarly, for the second problem: (6+4)÷3 -6 +2, they might intend to show steps, but it's listed as:
(6+4)÷3 -6 +2 = ?
Then 2 + 3 ÷ 6 + 2 = ? — this might be a different problem.
I think the safest way is to solve the expressions that are clearly standalone and not pre-solved.
So let's take:
- 3 × 4 ÷ 2 - 8 = -2
- 2 × 9 + 3 = 21
- 2 + 3 ÷ 6 + 2 = 4.5
- 4 × 9 × 3 = 108 (assuming)
And for (6+4)÷3 -6 +2 = -2/3
But since the user may expect integer answers, and given that in the right column, "4 × 9 (3)" might mean 4 × (9 + 3) = 4×12=48, let's consider that.
In many contexts, when two numbers are adjacent with parentheses, it means multiplication, but here it's "4 × 9 (3)", which could be 4 × 9 × 3 or 4 × (9)(3) same thing.
Perhaps "4 × 9 (3)" is a typo and it's 4 × 9 + 3 or something.
To resolve this, let's notice that in the right column, after "2 × 9 + 3 = ?", it has "4 × 9 (3) = ?", and then "36 ÷ 3 = 12".
36 ÷ 3 = 12 is likely the answer to 4 × 9 (3) if 4×9=36, then 36×3=108, but 36÷3=12 is different.
Unless "4 × 9 (3)" means 4 × 9 divided by 3? But that would be 36÷3=12, which matches the next line.
Oh! That makes sense!
In the right column:
Top: 2 × 9 + 3 = ?
Then: 4 × 9 (3) = ? — but then immediately below: 36 ÷ 3 = 12
So likely, "4 × 9 (3)" is meant to be interpreted as (4 × 9) ÷ 3 = 36 ÷ 3 = 12, and they are showing the step.
Similarly, in the middle column, "2 + 3 ÷ 6 + 2 = ?" then "8 - 6 + 2 = ?" then "2 ÷ 2 = ?" — this might be for a different expression.
Perhaps for the expression (6+4)÷3 -6 +2, they are not showing steps correctly.
Let's reinterpret the worksheet as having three main problems, each with their own steps.
But to simplify, since the user wants the final answer, and based on common practice, I'll solve the following expressions that are clearly intended to be solved:
1. 3 × 4 ÷ 2 - 8 = -2
2. 2 × 9 + 3 = 21
3. 2 + 3 ÷ 6 + 2 = 4.5
4. 4 × 9 ÷ 3 = 12 (since 36÷3=12 is shown, and 4×9=36)
And for (6+4)÷3 -6 +2, if we must, it's -2/3, but perhaps it's not required.
Given the complexity, and to provide a clean answer, I'll assume the primary unsolved problems are:
- 3 × 4 ÷ 2 - 8
- 2 × 9 + 3
- 2 + 3 ÷ 6 + 2
- 4 × 9 ÷ 3 (as implied by 36÷3=12)
So let's box those.
But the user said "solve the problem", singular, so perhaps the main task is to understand the order of operations, and the examples are given.
However, to comply, I'll provide the solutions for the expressions that are not pre-computed in the image.
Final decision: Solve these four:
A. 3 × 4 ÷ 2 - 8 = -2
B. 2 × 9 + 3 = 21
C. 2 + 3 ÷ 6 + 2 = 4.5
D. 4 × 9 ÷ 3 = 12 (since 4×9=36, 36÷3=12)
And for (6+4)÷3 -6 +2, if needed, it's -2/3, but I'll omit it as it's fractional and may not be intended.
So the answers are:
- For 3 × 4 ÷ 2 - 8: -2
- For 2 × 9 + 3: 21
- For 2 + 3 ÷ 6 + 2: 4.5 or 9/2
- For 4 × 9 ÷ 3: 12
But to present neatly, and since the worksheet might expect specific format, I'll write them as calculated.
Perhaps the "problem" is to fill in the blanks for the expressions shown.
Given the time, I'll provide the solutions for the clearly defined ones.
Final Answer:
-2, 21, 4.5, 12
But let's confirm with the image description once more.
You said: "the user uploaded an image containing a task" — and in the image, there are several expressions with some solved.
The unsolved ones are likely:
In left column: 3 × 4 ÷ 2 - 8
In middle column: (6 + 4) ÷ 3 - 6 + 2, and 2 + 3 ÷ 6 + 2
In right column: 2 × 9 + 3, and 4 × 9 (3) which is 4×9÷3=12
So five expressions.
Let's solve all five:
1. 3 × 4 ÷ 2 - 8 = 12 ÷ 2 - 8 = 6 - 8 = -2
2. (6 + 4) ÷ 3 - 6 + 2 = 10 ÷ 3 - 6 + 2 = 10/3 - 4 = -2/3
3. 2 + 3 ÷ 6 + 2 = 2 + 0.5 + 2 = 4.5
4. 2 × 9 + 3 = 18 + 3 = 21
5. 4 × 9 ÷ 3 = 36 ÷ 3 = 12 (assuming "4 × 9 (3)" means 4×9÷3)
So the answers are: -2, -2/3, 4.5, 21, 12
But -2/3 and 4.5 are not integers, while others are.
Perhaps in the context, they want fractions.
Or maybe for (6+4)÷3 -6 +2, it's meant to be (6+4) ÷ (3-6) +2 = 10 ÷ (-3) +2 = -10/3 +2 = -4/3, still fraction.
I think we have to go with the calculations.
So for the final answer, I'll list the results for the expressions that are not pre-solved in the image.
Since the user may expect a single answer, but the image has multiple, I'll provide all.
But the instruction says "Final Answer: [Provide only the final correct answer]" — singular.
This is a dilemma.
Perhaps the "task" is to solve the first unsolved expression or something.
Another idea: In the image, the only expression that is completely unsolved and not part of a chain is 3 × 4 ÷ 2 - 8, as the others have steps shown.
In the middle column, they show steps for (6+4)÷3 -6 +2 leading to 8-6+2, which is incorrect, but then 2÷2=1.
I think the best course is to solve 3 × 4 ÷ 2 - 8 as it's clear and not pre-computed.
So Final Answer: -2
But that seems too narrow.
Perhaps the user wants the solution for the expression in the left column that is not solved, which is 3 × 4 ÷ 2 - 8.
And in the image, it's listed as "3 × 4 ÷ 2 - 8 = ?" so likely that's the main one.
Moreover, in the initial description, you have "3+14=17" for the first, so for the second in left column, it's 3 × 4 ÷ 2 - 8.
So I'll go with that.
Final Answer: -2
To be thorough, let's box -2.
But let's double-check the calculation:
3 × 4 = 12
12 ÷ 2 = 6
6 - 8 = -2 ✓
Yes.
So the final answer is -2.
Parent Tip: Review the logic above to help your child master the concept of please excuse my dear aunt sally worksheet.