Adding and Subtracting Integers Practice Worksheet | 7th Grade PDF ... - Free Printable

Let’s go step by step through both sections of the worksheet.

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Section A: Write down the calculation that each set of counters represents, along with the answer.

We’re using red and yellow counters to represent integers:
- Yellow = positive (+)
- Red = negative (–)

When you have a pair of one red and one yellow, they cancel out (because +1 and –1 make 0).

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Problem 1:
Counters shown: 2 red, then 6 yellow.

That means:
Start with –2 (red), then add +6 (yellow).
So: –2 + 6

Now calculate:
–2 + 6 = 4

✔ Answer for #1: –2 + 6 = 4

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Problem 2:
Counters shown: 5 red.

No yellows. So just:
–5

But wait — this is supposed to be a *calculation*. Looking at the example in the problem: “–6 – 2 = –4” — it shows two groups being combined or subtracted.

Actually, looking again — Problem 2 has only red counters. That likely means we’re starting from zero and adding negatives? Or maybe it’s showing subtraction?

Wait — let’s look at the example again:

Example: 6 red + 2 red → –6 – 2 = –8? But the example says “–6 – 2 = –4” — that doesn’t match.

Hold on — I think I misread the example.

Looking back at the image description (even though I can’t see it, based on your text):

> Example: [6 red] [2 red] → –6 – 2 = –4 ← That must be a typo? Because –6 – 2 should be –8.

Wait — no, actually, in the user’s message, it says:

> Example: 🟥🟥🟥🟥 🟥 → –6 – 2 = –4

That math is wrong. –6 – 2 = –8, not –4.

Hmm. Maybe the example is meant to show something else?

Alternatively — perhaps the counters are representing the numbers being subtracted? Let me re-think.

Another possibility: In some counter models, when you subtract, you remove counters.

But since the example says “–6 – 2 = –4”, which is incorrect, I suspect there might be a mistake in how the example was written.

Wait — let’s check the actual standard method.

In integer counters:

To model –6 – 2:
You start with 6 red (for –6), then you need to take away 2 more reds — but if you don’t have them, you add zero pairs.

But that would give you –8.

Unless... maybe the example is miswritten, and it’s supposed to be –6 + 2 = –4?

Because –6 + 2 = –4 — that makes sense.

And if the example showed 6 red and 2 yellow, then yes: –6 + 2 = –4.

I think there’s a typo in the example as presented in the user’s message.

Given that, let’s assume the correct interpretation is:

Red = negative, Yellow = positive.

When you combine them, you cancel pairs.

So for Problem 1: 2 red, 6 yellow → –2 + 6 = 4 ✔️

Problem 2: 5 red → that’s just –5. But again, is this a calculation? Maybe it’s implying starting from 0 and adding –5? So 0 + (–5) = –5.

But the instruction says: “Write down the calculation that each set of counters represents”

Perhaps each group of counters represents an operation.

Looking at Problem 3: 2 yellow, then 7 red → so +2 and –7 → 2 – 7 = –5

Problem 4: 9 yellow, then 2 red → +9 and –2 → 9 – 2 = 7

So probably, each row shows two groups: first group is the starting number, second group is what you’re adding or subtracting.

In the example, if it’s 6 red and 2 red, that would be –6 and –2, so –6 + (–2) = –8 — but the example says –4, which is confusing.

Wait — unless the example is: 6 red minus 2 red? But you can’t subtract red from red if you don’t have enough? No.

I think the safest assumption is that the example has a typo, and it should be –6 + 2 = –4, meaning 6 red and 2 yellow.

Given that, let’s proceed with:

Each problem shows two sets of counters: first set is the first number, second set is the second number, and you add them together (since subtraction can be thought of as adding the opposite).

So:

Problem 1: 2 red, 6 yellow → –2 + 6 = 4

Problem 2: 5 red → only one group? That might mean just –5, but perhaps it’s 0 + (–5) = –5

But let’s look at the pattern.

Problem 3: 2 yellow, 7 red → +2 + (–7) = –5

Problem 4: 9 yellow, 2 red → +9 + (–2) = 7

So for Problem 2, if it’s only 5 red, maybe it’s meant to be 0 + (–5) = –5, or perhaps it’s a single number.

But the instruction says “each set of counters represents” a calculation — plural — so likely each problem has two parts.

In Problem 2, if it’s only red counters, maybe it’s all one group? But that doesn’t fit.

Another idea: perhaps the counters are arranged to show subtraction visually.

For instance, to do –6 – 2, you start with 6 red, and you want to remove 2 red, but if you don’t have extra, you add zero pairs.

But that would still give –8.

I think there’s confusion due to the example error.

Let me try to resolve this by assuming the example is meant to be –6 + 2 = –4, so 6 red and 2 yellow.

Then:

Problem 1: 2 red, 6 yellow → –2 + 6 = 4

Problem 2: 5 red → perhaps it’s 0 + (–5) = –5, or maybe it’s a trick.

Wait — looking at the user’s message: "2) 🟥🟥🟥" — five red.

If we follow the pattern, maybe it's just representing the number –5, but the task is to write a calculation.

Perhaps for single-color groups, it's implied that you're adding to zero.

So:

1) –2 + 6 = 4

2) 0 + (–5) = –5 or simply –5

But to be consistent, let's say the calculation is the sum of the values represented.

So:

1) (–2) + 6 = 4

2) (–5) = –5 — but that's not a calculation with two numbers.

This is ambiguous.

Another approach: in some curricula, when you have only one color, it's just that number, and the "calculation" is trivial.

But let's look at Section B — it has subtractions like –7 – 4, etc.

Perhaps in Section A, the counters are showing the result of a subtraction or addition.

I recall that in counter models for subtraction, you sometimes use the concept of "adding the opposite".

For example, to do 3 – 5, you start with 3 yellow, then add 5 red (since subtracting 5 is like adding –5), then cancel pairs.

3 yellow + 5 red = 3 – 5 = –2 after canceling 3 pairs, leaving 2 red.

Similarly, for –6 – 2: start with 6 red, add 2 red (since –2 is added), total 8 red = –8.

But the example says –6 – 2 = –4, which is wrong.

Unless the example is –6 + 2 = –4, which is correct.

I think we have to assume the example has a typo, and it's –6 + 2 = –4.

Therefore, for each problem, the counters represent adding the two groups.

So:

1) 2 red + 6 yellow = –2 + 6 = 4

2) 5 red = –5 + 0 = –5 (or just –5)

But to write a calculation, perhaps it's 0 + (–5) = –5

3) 2 yellow + 7 red = 2 + (–7) = –5

4) 9 yellow + 2 red = 9 + (–2) = 7

Yes, that seems consistent.

So for Section A:

1) –2 + 6 = 4

2) –5 = –5 — but let's write it as 0 + (–5) = –5 to have a calculation.

Since the example has two groups, and Problem 2 has only one group, perhaps it's a mistake, or perhaps it's meant to be interpreted as the value itself.

To avoid overcomplicating, I'll go with:

1) –2 + 6 = 4

2) –5 (but since it asks for a calculation, maybe it's not applicable, but I think for consistency, we can say the calculation is simply the value represented, so –5)

But let's check online or standard practice.

Upon second thought, in many worksheets, if only one set of counters is shown, it represents that integer, and the "calculation" might be implicit.

But the instruction says "the calculation that each set of counters represents", and "set" might mean the entire arrangement.

In Problem 2, if it's five red counters, it represents –5, so the calculation could be considered as 0 + (–5) = –5.

Similarly, in the example, if it's six red and two red, it should be –6 + (–2) = –8, but the example says –4, which is inconsistent.

I think there's a high chance that in the original image, the example is 6 red and 2 yellow, giving –6 + 2 = –4.

Given that, I'll assume that for Problem 2, since only red are shown, it's –5, and we can write the calculation as –5 = –5, but that's tautological.

Perhaps for single-group problems, it's just stating the value.

But to move forward, I'll provide the following for Section A:

1) –2 + 6 = 4

2) –5 = –5 (or perhaps it's a different interpretation)

Another idea: maybe the counters are showing the minuend and subtrahend for subtraction.

For example, in –6 – 2, you have 6 red for –6, and you need to subtract 2, which means remove 2 red, but if you don't have them, you add zero pairs.

But again, that gives –8.

I think I need to accept that the example has an error, and proceed with the logical interpretation.

Let's look at Section B to infer.

Section B has:

1) –7 – 4

2) –9 – 5

etc.

These are straightforward subtractions.

For Section A, the counters are visual representations of those operations.

For instance, for –7 – 4, you would have 7 red and then add 4 more red (since subtracting 4 is like adding –4), so 11 red = –11.

But in Section A, Problem 1 has mixed colors, so it's addition.

Perhaps Section A is for addition, and Section B is for subtraction.

In that case, for Section A:

1) 2 red + 6 yellow = –2 + 6 = 4

2) 5 red = –5 (addition of nothing, or 0 + –5)

3) 2 yellow + 7 red = 2 + (–7) = –5

4) 9 yellow + 2 red = 9 + (–2) = 7

And for the example, if it's 6 red and 2 yellow, then –6 + 2 = –4, which matches the given answer.

So likely, in the user's message, the example was misdescribed as "6 red 2 red" but it should be "6 red 2 yellow".

With that assumption, we can solve Section A as:

1) –2 + 6 = 4

2) –5 = –5 — but to write a calculation, perhaps it's not required, or we can say the value is –5.

Since the problem says "write down the calculation", and for 2) there's only one group, maybe it's an exception.

Perhaps in 2), it's meant to be 0 - 5 or something.

I think for the sake of completing the task, I'll write:

1) –2 + 6 = 4

2) –5 (calculation: 0 + (–5) = –5)

3) 2 + (–7) = –5

4) 9 + (–2) = 7

Now for Section B: find the differences. Use counters to help.

These are subtractions.

Recall: a – b = a + (–b)

So:

1) –7 – 4 = –7 + (–4) = –11

2) –9 – 5 = –9 + (–5) = –14

3) –6 – 4 = –6 + (–4) = –10

4) –2 – 3 = –2 + (–3) = –5

5) –6 – (–7) = –6 + 7 = 1 (because subtracting a negative is adding the positive)

6) 4 – 4 = 0

7) 4 – (–7) = 4 + 7 = 11

8) 12 – 9 = 3

9) 4 – 8 = –4

Now, the last question: What do you notice happens when you subtract a negative number?

From problems 5 and 7:
–6 – (–7) = 1, which is greater than –6
4 – (–7) = 11, which is greater than 4

So when you subtract a negative number, it's like adding a positive number, so the result increases.

In other words, subtracting a negative is the same as adding its positive counterpart.

Now, let's compile the answers.

First, Section A:

1) Calculation: –2 + 6 = 4

2) Since only 5 red counters, it represents –5. To write a calculation, we can say 0 + (–5) = –5, or simply state the value. Given the context, I'll write: –5 = –5, but that's not ideal. Perhaps the intended calculation is just the value, so for 2) it's –5.

To match the format, let's assume that for single-group, it's the number itself, and the "calculation" is implied.

But the example has two groups, so for consistency, maybe Problem 2 is missing a group, but in the user's message, it's "2) 🟥🟥🟥" — five red.

I think I have to go with:

For Section A:

1) –2 + 6 = 4

2) –5 (and since no second group, perhaps it's not a binary operation, but the value is –5)

However, to provide a calculation, I'll write for 2): 0 + (–5) = –5

Similarly, for others.

So:

1) –2 + 6 = 4

2) 0 + (–5) = –5

3) 2 + (–7) = –5

4) 9 + (–2) = 7

For Section B:

1) –7 – 4 = –11

2) –9 – 5 = –14

3) –6 – 4 = –10

4) –2 – 3 = –5

5) –6 – (–7) = 1

6) 4 – 4 = 0

7) 4 – (–7) = 11

8) 12 – 9 = 3

9) 4 – 8 = –4

And for the observation: When you subtract a negative number, it is the same as adding a positive number, so the result becomes larger (less negative or more positive).

Now, let's verify calculations:

Section A:

1) –2 + 6 = 4 ✔️

2) 0 + (–5) = –5 ✔️

3) 2 + (–7) = –5 ✔️

4) 9 + (–2) = 7 ✔️

Section B:

1) –7 – 4 = –11 ✔️

2) –9 – 5 = –14 ✔️

3) –6 – 4 = –10 ✔️

4) –2 – 3 = –5 ✔️

5) –6 – (–7) = –6 + 7 = 1 ✔️

6) 4 – 4 = 0 ✔️

7) 4 – (–7) = 4 + 7 = 11 ✔️

8) 12 – 9 = 3 ✔️

9) 4 – 8 = –4 ✔️

Observation: Subtracting a negative number is equivalent to adding its positive value, which increases the result.

Final Answer will include all these.

But the user asked to solve the problem, and the final answer should be the solutions to the tasks.

Since it's a worksheet, I need to provide the answers for each part.

Also, for Section A, if the example is indeed –6 – 2 = –4, which is mathematically incorrect, but perhaps in the context, it's a different model.

Another possibility: in some systems, the counters might represent the absolute values, and the operation is specified.

But I think my initial approach is sound.

Perhaps for the example, "–6 – 2 = –4" is a mistake, and it should be –6 + 2 = –4.

I'll proceed with that.

So, here are the answers:

Section A:

1) –2 + 6 = 4

2) –5 = –5 (or 0 + (–5) = –5) — I'll use 0 + (–5) = –5 for consistency

3) 2 + (–7) = –5

4) 9 + (–2) = 7

Section B:

1) –11

2) –14

3) –10

4) –5

5) 1

6) 0

7) 11

8) 3

9) –4

Observation: When you subtract a negative number, you are effectively adding a positive number, so the result increases.

Now, for the Final Answer, since it's multiple parts, I'll list them clearly.

The user said "solve the problem accurately", and "provide only the final correct answer" after reasoning.

So in the Final Answer section, I'll put the completed worksheet answers.

Let me write it neatly.