Class 7 Integers worksheet with questions on integer operations, multiple-choice answers, and fill-in-the-blank problems.

Let's solve each question step by step from the worksheet.

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(1) Find the value of the following expression:

#### A) $(-126) - (-14) - 76 - (-43) - 97 - (-109)$

We simplify step by step using the rule:
$-(-a) = +a$

So:
$$
= -126 + 14 - 76 + 43 - 97 + 109
$$

Now compute step by step:

- $-126 + 14 = -112$
- $-112 - 76 = -188$
- $-188 + 43 = -145$
- $-145 - 97 = -242$
- $-242 + 109 = -133$

✔ Answer A: -133

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#### B) $34 - 142 - 21 - (-181) - (-88) - (-41)$

Again, simplify signs:

$$
= 34 - 142 - 21 + 181 + 88 + 41
$$

Now compute:

- $34 - 142 = -108$
- $-108 - 21 = -129$
- $-129 + 181 = 52$
- $52 + 88 = 140$
- $140 + 41 = 181$

✔ Answer B: 181

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(2) An integer is divided by 8 giving a remainder of 3. The resulting quotient when divided by 7 gives a remainder of 2. The resulting quotient is then divided by 7 giving a quotient of 1 and a remainder of 6. What will be the final remainder if the order of the divisors is reversed?

Let’s break this down carefully.

Let the original integer be $ N $.

Step 1: $ N \div 8 $ → remainder 3
So:
$$
N = 8Q_1 + 3 \quad \text{(1)}
$$

Step 2: $ Q_1 \div 7 $ → remainder 2
So:
$$
Q_1 = 7Q_2 + 2 \quad \text{(2)}
$$

Step 3: $ Q_2 \div 7 $ → quotient 1, remainder 6
So:
$$
Q_2 = 7 \cdot 1 + 6 = 13
$$

Now substitute back:

From (2): $ Q_1 = 7 \cdot 13 + 2 = 91 + 2 = 93 $

From (1): $ N = 8 \cdot 93 + 3 = 744 + 3 = 747 $

So the original number is $ N = 747 $

Now, reverse the order of divisors: divide by 7 first, then by 8, then by 7 again? Wait — let's re-read.

> "What will be the final remainder if the order of the divisors is reversed?"

Original order: divide by 8 → 7 → 7
Reversed order: divide by 7 → 7 → 8?

But the process is:

- First division: by 8 → rem 3
- Then take quotient and divide by 7 → rem 2
- Then take that quotient and divide by 7 → q=1, r=6

So the sequence of divisions was:
$ N \to \text{div} 8 \to \text{div} 7 \to \text{div} 7 $

So reversed order would be:
$ N \to \text{div} 7 \to \text{div} 7 \to \text{div} 8 $

We are to find the final remainder after dividing in the reversed order.

So start with $ N = 747 $

Step 1: Divide 747 by 7

$$
747 \div 7 = 106 \times 7 = 742, \quad \text{remainder } 5
$$
→ Quotient = 106

Step 2: Divide 106 by 7

$$
106 \div 7 = 15 \times 7 = 105, \quad \text{remainder } 1
$$
→ Quotient = 15

Step 3: Divide 15 by 8

$$
15 \div 8 = 1 \times 8 = 8, \quad \text{remainder } 7
$$

✔ So the final remainder is 7

Answer: 7

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(3) Find how many integers are there between:

We need to count integers between two numbers (not including endpoints).

#### A) -5 and 6

Integers between: $-4, -3, -2, -1, 0, 1, 2, 3, 4, 5$ → total = 10

✔ 10 integers

#### B) -1 and 6

Between: $0, 1, 2, 3, 4, 5$ → total = 6

✔ 6 integers

#### C) -2 and 2

Between: $-1, 0, 1$ → total = 3

✔ 3 integers

#### D) -4 and 7

Between: $-3, -2, -1, 0, 1, 2, 3, 4, 5, 6$ → total = 10

✔ 10 integers

So answers:
- A: 10
- B: 6
- C: 3
- D: 10

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(4) A railway company makes a profit of Rs. 1671 per ticket of business class while loses Rs. 165 on every ticket in economy class. If the company sold 3865 tickets of business class and 45723 tickets of economy class in March, what would be the total profit or loss?

Profit from business class:
$$
3865 \times 1671
$$

Loss from economy class:
$$
45723 \times 165
$$

Total profit/loss = (Business profit) - (Economy loss)

Let’s compute both.

First, $3865 \times 1671$

Break it down:

$$
3865 \times 1671 = 3865 \times (1600 + 70 + 1)
= 3865 \times 1600 + 3865 \times 70 + 3865 \times 1
$$

- $3865 \times 1600 = 3865 \times 16 \times 100$

$3865 \times 16$:
$3865 \times 10 = 38650$
$3865 \times 6 = 23190$
Sum: $38650 + 23190 = 61840$ → times 100 = 6,184,000

- $3865 \times 70 = 3865 \times 7 \times 10 = (27055) \times 10 = 270,550$

- $3865 \times 1 = 3,865$

Add:
$$
6,184,000 + 270,550 = 6,454,550 + 3,865 = 6,458,415
$$

So business profit = Rs. 6,458,415

Now economy loss: $45723 \times 165$

Break 165 = 100 + 60 + 5

- $45723 \times 100 = 4,572,300$
- $45723 \times 60 = 45723 \times 6 \times 10 = 274,338 \times 10 = 2,743,380$
- $45723 \times 5 = 228,615$

Add:
$$
4,572,300 + 2,743,380 = 7,315,680 + 228,615 = 7,544,295
$$

So economy loss = Rs. 7,544,295

Now total net result:
$$
\text{Profit} - \text{Loss} = 6,458,415 - 7,544,295 = -1,085,880
$$

So net loss of Rs. 1,085,880

✔ Answer: c. -1085880

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(5) Choose the correct operator:

$$
-5 \quad \_\_\_\_\_\_\_\_ \quad -5
$$

We have to choose between <, >, or =

Clearly, $-5 = -5$, so the correct operator is =

But options are:

a. <
b. >
c. =
d. None of these

✔ Correct answer: c. =

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(6) $A + B = B + A$ represents the __________ property of addition.

This is the Commutative Property of addition.

✔ Answer: Commutative

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(7) What is the sum of the following series if the number of terms is 236?

Series: $6 + (-6) + 6 + (-6) + 6 + (-6) + \ldots$

Pattern: Alternating 6 and -6

Each pair: $6 + (-6) = 0$

Number of terms = 236 → even number

So number of pairs = $236 / 2 = 118$

Each pair sums to 0 → total sum = $118 \times 0 = 0$

✔ Answer: 0

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✔ Final Answers Summary:

(1)
A) $-133$
B) $181$

(2) Final remainder when order reversed: 7

(3) Number of integers between:
A) 10
B) 6
C) 3
D) 10

(4) Total profit/loss: c. -1085880

(5) Operator: c. =

(6) Property: Commutative

(7) Sum of series: 0

Let me know if you'd like these explained in simpler terms or with diagrams!