Class VII Mathematics worksheet focusing on integers, with fill-in-the-blank exercises covering identities, operations, and problem-solving.

Let's solve the worksheet step by step.

Worksheet: Integers

#### Fill in the Blanks

1. ________ is the additive identity and ________ is the multiplicative identity of integers.
- The additive identity is 0 because adding 0 to any integer does not change its value.
- The multiplicative identity is 1 because multiplying any integer by 1 does not change its value.
- Answer: 0, 1

2. (-1) x even number of times = ________
- Multiplying \(-1\) an even number of times results in a positive number because the negative signs cancel out.
- For example, \((-1) \times (-1) = 1\), \((-1) \times (-1) \times (-1) \times (-1) = 1\).
- Answer: 1

3. (-1) x odd number of times = ________
- Multiplying \(-1\) an odd number of times results in a negative number because there will be an unpaired negative sign.
- For example, \((-1) \times (-1) \times (-1) = -1\).
- Answer: -1

4. 38 ÷ 0 = ________
- Division by zero is undefined in mathematics.
- Answer: Undefined

5. 0 ÷ 11 = ________
- Dividing 0 by any non-zero number results in 0.
- Answer: 0

6. 13 ÷ 1 + ________ = ________
- First, calculate \(13 \div 1 = 13\).
- The equation becomes \(13 + \_\_\_\_ = \_\_\_\_\). Since no specific result is given, we assume the question is incomplete or missing information. However, if we assume the result is 0 (as a common placeholder), then:
\[
13 + (-13) = 0
\]
- Answer: -13 (assuming the result is 0)

7. 55 + ________ = 0
- To find the missing number, solve for \(x\) in the equation \(55 + x = 0\):
\[
x = 0 - 55 = -55
\]
- Answer: -55

8. (-31) + ________ = 0
- To find the missing number, solve for \(x\) in the equation \(-31 + x = 0\):
\[
x = 0 - (-31) = 31
\]
- Answer: 31

9. (-55) + ________ = -89
- To find the missing number, solve for \(x\) in the equation \(-55 + x = -89\):
\[
x = -89 - (-55) = -89 + 55 = -34
\]
- Answer: -34

10. (-33) + ________ = 79
- To find the missing number, solve for \(x\) in the equation \(-33 + x = 79\):
\[
x = 79 - (-33) = 79 + 33 = 112
\]
- Answer: 112

11. 1000 + ________ = -1000
- To find the missing number, solve for \(x\) in the equation \(1000 + x = -1000\):
\[
x = -1000 - 1000 = -2000
\]
- Answer: -2000

12. [(-7) + 9] + (______) = 9 + [-7 + 4]
- Simplify both sides:
\[
[(-7) + 9] = 2 \quad \text{and} \quad [-7 + 4] = -3
\]
So the equation becomes:
\[
2 + x = 9 + (-3)
\]
Simplify the right side:
\[
9 + (-3) = 6
\]
So:
\[
2 + x = 6
\]
Solve for \(x\):
\[
x = 6 - 2 = 4
\]
- Answer: 4

13. (-6) + 2 = 2 (________)
- Simplify the left side:
\[
(-6) + 2 = -4
\]
So the equation becomes:
\[
-4 = 2 \times x
\]
Solve for \(x\):
\[
x = \frac{-4}{2} = -2
\]
- Answer: -2

14. 251 ÷ ________ = 1
- To find the missing number, solve for \(x\) in the equation \(251 \div x = 1\):
\[
x = 251
\]
- Answer: 251

15. (-70) ÷ ________ = 5
- To find the missing number, solve for \(x\) in the equation \((-70) \div x = 5\):
\[
x = \frac{-70}{5} = -14
\]
- Answer: -14

Final Answers:

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

\boxed{
\begin{array}{l}
1. 0, 1 \\
2. 1 \\
3. -1 \\
4. \text{Undefined} \\
5. 0 \\
6. -13 \\
7. -55 \\
8. 31 \\
9. -34 \\
10. 112 \\
11. -2000 \\
12. 4 \\
13. -2 \\
14. 251 \\
15. -14 \\
\end{array}
}