50+ Integers and Rational Numbers worksheets for 7th Grade on ... - Free Printable

Let’s go through each question one by one and solve them carefully.

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Question 1: Order from least to greatest –4, 3, –2, 0, 1

We need to arrange these numbers from smallest (most negative) to largest (most positive).

Negative numbers are smaller than zero, and among negatives, the more negative the number, the smaller it is.

So:
- –4 is the smallest
- Then –2
- Then 0
- Then 1
- Then 3

Order: –4, –2, 0, 1, 3

Looking at options:
A → 0, –4, –2, 1, 3 ✘
B → –4, –2, 0, 1, 3 ✔
C → –4, 0, 1, –2, 3 ✘
D → 0, 1, –2, 3, –4 ✘

✔ Correct answer: B

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Question 2: Order the integers from least to greatest 7, –6, 5, –8, –3

List: 7, –6, 5, –8, –3

Smallest to largest:
- –8 (most negative)
- –6
- –3
- 5
- 7

Order: –8, –6, –3, 5, 7

Options:
A → –3, –6, –8, 5, 7 ✘
B → 5, 7, –3, –6, –8 ✘
C → –3, 5, –6, 7, –8 ✘
D → –8, –6, –3, 5, 7 ✔

✔ Correct answer: D

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Question 3: Find the absolute value of |5²|

First, calculate 5² = 25
Then take absolute value: |25| = 25

Absolute value always gives a non-negative result.

Options:
A → -5 ✘
B → -25 ✘
C → 25 ✔
D → 5 ✘

✔ Correct answer: C

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Question 4: Find the absolute value of |–3²|

Important: Exponentiation comes before negation unless parentheses say otherwise.

So –3² means –(3²) = –9
Then |–9| = 9

Note: If it were (–3)², that would be 9, but here it’s written as –3², so it’s –(3²)

So: |–9| = 9

Options:
A → -9 ✘
B → 3 ✘
C → 9 ✔
D → -3 ✘

✔ Correct answer: C

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Question 5: Evaluate (b – a) for a = –3 and b = –7

Plug in:
b – a = (–7) – (–3)
Subtracting a negative is like adding:
= –7 + 3 = –4

Options:
A → 10 ✘
B → -10 ✘
C → 4 ✘
D → -4 ✔

✔ Correct answer: D

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Question 6: Evaluate (a + 2b) for a = –3 and b = –7

Plug in:
a + 2b = (–3) + 2×(–7)
First, 2 × (–7) = –14
Then: –3 + (–14) = –17

Options:
A → -17 ✔
B → -11 ✘
C → 11 ✘
D → 17 ✘

✔ Correct answer: A

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Question 7: Evaluate (ab) for a = –4 and b = –5

ab means a × b
(–4) × (–5) = 20
(Multiplying two negatives gives a positive)

But wait — looking at the image, question 7 is cut off. The options aren’t visible. However, based on standard problems, we can assume the answer is 20.

Since the user didn’t provide options for Q7, and the instruction says to answer what’s shown, I’ll note that.

But since the quiz only shows up to Q7 and no options are visible, perhaps it’s incomplete. But let’s assume we’re to compute it.

✔ Answer for Q7: 20

However, since the original image doesn’t show options for Q7, and the user might expect answers only for fully visible questions, I’ll include it but note that.

Actually, rechecking the image — yes, Q7 is there: “Evaluate expression (ab) for the values a = -4 and b = -5” — and no options shown below it in the crop. So perhaps it’s meant to be solved without multiple choice.

But since the format requires selecting from A-D for previous ones, and this one has no options, maybe it’s an error. Still, mathematically:

(–4)(–5) = 20

If forced to pick from hypothetical options, 20 would be correct.

But since no options are given, I’ll just state the value.

Wait — looking again at the original image text provided:

> 7. Evaluate expression (ab) for the values a = -4 and b = -5

And then it stops — no options listed. So perhaps in the actual quiz, options follow, but they’re not in the image. Since we must work with what’s given, and the instruction is to solve the problem, I’ll compute it.

Final Answer for Q7: 20

But since the response format expects a single final answer per question, and we have 7 questions, I should list all.

Actually, the user said “solve the problem” — plural — so likely expects all 7 answered.

But the response format says “Final Answer: [only the final correct answer]” — implying one answer? That doesn’t fit.

Re-reading the rules:

> Final Answer:
> [Provide only the final correct answer — this should come AFTER all explanations and reasoning.]

But if there are multiple questions, how to handle?

Looking back at the initial instruction: “You are an educational assistant helping a student solve homework problems.” and “Solve the problem accurately.”

The image contains 7 questions. Probably, the student wants all solved.

But the response format seems designed for a single problem. However, since the user uploaded an image with multiple questions, and didn’t specify which one, I think we should answer all.

Perhaps the “Final Answer” section should list all correct choices.

Alternatively, maybe the system expects one answer — but that doesn’t make sense.

Another thought: perhaps the user intended for us to solve all, and the “Final Answer” can be a list.

To be safe, I’ll provide all answers in the Final Answer section as a list.

But let’s see the example in the rules — it says “the final correct answer” singular. Hmm.

Perhaps for multi-question tasks, we list them.

I think it’s better to provide all.

So summarizing:

Q1: B
Q2: D
Q3: C
Q4: C
Q5: D
Q6: A
Q7: 20 (but no options, so perhaps omit or state)

For Q7, since no options are visible, and the calculation is straightforward, I’ll include it.

But to match the format, perhaps the Final Answer should be the selections for the multiple choice, and for Q7, since it’s not multiple choice in the image, maybe skip? No, the question is there.

Perhaps in the original quiz, Q7 has options, but they’re cut off. Since we can’t see them, I’ll compute the value.

I think for completeness, I’ll list all.

So Final Answers:

1. B
2. D
3. C
4. C
5. D
6. A
7. 20

But the format says “only the final correct answer” — perhaps for each question separately? But the response is one block.

Another idea: perhaps the user expects the answers in order, and the Final Answer is a string of letters/numbers.

I think that’s reasonable.

So: B, D, C, C, D, A, 20

But for Q7, since no options, maybe just the number.

To be precise, I’ll write the answers as per the questions.

Since the instruction is to solve the problems, and the image has 7, I’ll provide all.

In the Final Answer section, I’ll list them clearly.

But the rule says “only the final correct answer” — singular. This is ambiguous.

Looking at the user’s message: “Solve the problem accurately.” — and the image has multiple problems.

I think it’s acceptable to provide all.

Perhaps the “problem” refers to the entire quiz.

I’ll proceed.

So after reasoning, the answers are:

1. B
2. D
3. C
4. C
5. D
6. A
7. 20

For Q7, since it's not multiple choice in the visible part, but the expression is clear, 20 is correct.

Now, to box the final answers.

But the format says "Final Answer:" and then the answer.

Perhaps I can write:

Final Answer:
1. B
2. D
3. C
4. C
5. D
6. A
7. 20

That should be fine.

Since the user might expect only the letters for multiple choice, and for Q7 the value.

Yes.

So I'll go with that.