Class VII Mathematics worksheet focusing on integers, with fill-in-the-blank exercises covering additive and multiplicative identities, operations with negative numbers, and basic arithmetic.

Let’s go through each problem one by one. I’ll solve them step by step so you can understand how to get the right answer.

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1.
We need to fill in: “______ is the additive identity and ______ is the multiplicative identity of integers.”

- Additive identity means: when you add it to any number, the number doesn’t change → that’s 0.
Example: 5 + 0 = 5
- Multiplicative identity means: when you multiply it by any number, the number doesn’t change → that’s 1.
Example: 5 × 1 = 5

✔ So: 0 is the additive identity and 1 is the multiplicative identity.

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2.
(-1) × even number of times = ?

Think: If you multiply (-1) an even number of times, like 2 times: (-1) × (-1) = 1
4 times: [(-1)×(-1)] × [(-1)×(-1)] = 1 × 1 = 1
So always positive 1.

✔ Answer: 1

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3.
(-1) × odd number of times = ?

Example: 1 time → -1
3 times → (-1)×(-1)×(-1) = 1 × (-1) = -1
Always negative.

✔ Answer: -1

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4.
38 ÷ 0 = ?

Division by zero is undefined — you cannot divide any number by zero. It’s not allowed in math.

✔ Answer: Undefined (or sometimes written as “not possible”)

But since this is a worksheet for Class VII, they might expect you to write “undefined” or leave it blank? But let’s check standard answers — usually we say undefined.

Wait — actually, in many school worksheets, they may accept “not defined” or just leave it. But technically, it’s undefined.

However, looking at other problems, maybe they want a numerical answer? But no — division by zero has no answer.

I think safest is to write: undefined

But let me double-check with common curriculum — yes, in CBSE/ICSE Class 7, they teach that division by zero is undefined.

✔ Final: undefined

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5.
0 ÷ 11 = ?

Zero divided by any non-zero number is zero.

Because: 0 ÷ 11 = 0 → because 11 × 0 = 0

✔ Answer: 0

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6.
13 ÷ 1 + _______

This seems incomplete? Wait — look again:

It says: “13 ÷ 1 + ___________”

Probably meant to be equal to something? But there’s no equals sign. Maybe typo?

Wait — looking back at original image description — question 6 is:
“13 ÷ 1 + ___________”

That’s all? That doesn’t make sense unless it’s part of a pattern or missing RHS.

Wait — perhaps it’s supposed to be “13 ÷ 1 = ___”? But it says “+”.

Alternatively, maybe it’s “13 ÷ 1 + 0” or something? But no.

Hold on — let me re-read the user input.

User wrote:
"6. 13 ÷ 1 + ___________"

No equals sign. That must be a mistake. Perhaps it’s meant to be “13 ÷ 1 = ___”? Because otherwise it’s incomplete.

Looking at context — questions 4,5 are divisions, 7 onwards are equations.

Maybe it’s a typo and should be “13 ÷ 1 = ___”

Because 13 ÷ 1 = 13

If it’s “13 ÷ 1 + ___”, then without RHS, we can’t solve.

But wait — perhaps it’s “13 ÷ 1 + 0” to show identity? Unlikely.

Another possibility: maybe it’s “13 ÷ 1 = ___” and the “+” is a formatting error.

Given that, and since 13 ÷ 1 = 13, I’ll assume it’s meant to be equality.

✔ Let’s go with 13

(If it’s really “+”, then it’s incomplete — but for worksheet purposes, likely 13)

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7.
55 + ________ = 0

What number added to 55 gives 0? That’s the additive inverse → -55

Because 55 + (-55) = 0

✔ Answer: -55

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8.
(-31) + ________ = 0

Same idea — what adds to -31 to give 0? → +31

Because -31 + 31 = 0

✔ Answer: 31

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9.
(-55) + ________ = -89

Let the blank be x.

So: -55 + x = -89

Add 55 to both sides: x = -89 + 55 = -34

Check: -55 + (-34) = -89 → yes.

✔ Answer: -34

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10.
(-33) + ________ = 79

Let x be the blank.

-33 + x = 79

Add 33 to both sides: x = 79 + 33 = 112

Check: -33 + 112 = 79 → yes.

✔ Answer: 112

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11.
1000 + ________ = -1000

Let x be blank.

1000 + x = -1000

Subtract 1000: x = -1000 - 1000 = -2000

Check: 1000 + (-2000) = -1000 → yes.

✔ Answer: -2000

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12.
[ (-7) + 9 ] + (___) = 9 + [ -7 + 4 ]

First, simplify left side inside brackets: (-7) + 9 = 2

Right side: -7 + 4 = -3, then 9 + (-3) = 6

So equation becomes: 2 + (___) = 6

Therefore, blank = 6 - 2 = 4

Check: Left: [(-7)+9] + 4 = 2 + 4 = 6
Right: 9 + [-7+4] = 9 + (-3) = 6 → matches.

✔ Answer: 4

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13.
(-6) + 2 = 2 (_________)

Left side: -6 + 2 = -4

So: -4 = 2 × (blank)

Divide both sides by 2: blank = -4 ÷ 2 = -2

Check: 2 × (-2) = -4 → yes.

✔ Answer: -2

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14.
251 ÷ ________ = 1

What number divides 251 to give 1? Only itself.

Because any number ÷ itself = 1 (except 0)

So: 251 ÷ 251 = 1

✔ Answer: 251

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15.
(-70) ÷ ________ = 5

Let blank be x.

So: -70 ÷ x = 5

Which means: -70 / x = 5

Multiply both sides by x: -70 = 5x

Divide by 5: x = -70 ÷ 5 = -14

Check: -70 ÷ (-14) = 5 → because negative ÷ negative = positive, and 70÷14=5 → yes.

✔ Answer: -14

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Now, compiling all final answers:

1. 0, 1
2. 1
3. -1
4. undefined
5. 0
6. 13 (assuming typo, meant = instead of +)
7. -55
8. 31
9. -34
10. 112
11. -2000
12. 4
13. -2
14. 251
15. -14

For #6, if strictly as written “13 ÷ 1 + ___”, it’s incomplete. But given context, likely meant to be “13 ÷ 1 = ___”, so 13 is correct.

Also for #4, “undefined” is correct, though some worksheets might write “not defined” — same thing.

Final Answer:
1. 0, 1
2. 1
3. -1
4. undefined
5. 0
6. 13
7. -55
8. 31
9. -34
10. 112
11. -2000
12. 4
13. -2
14. 251
15. -14