Maths Class 7 worksheet on integers with problems involving simplification, comparison, and number line concepts.

Let’s solve each question step by step with clear explanations.

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## 1. Simplify:

We’ll simplify each expression using the order of operations (BODMAS/PEMDAS): Brackets, Orders (exponents), Division/Multiplication (left to right), Addition/Subtraction (left to right).

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(a) 121 ÷ 11 × 3 + 8 × (–4 + 7(6 – 8 + 7))

First, simplify inside the innermost brackets:

→ (6 – 8 + 7) = (–2 + 7) = 5

Now plug back in:

→ 121 ÷ 11 × 3 + 8 × (–4 + 7×5)

→ 7×5 = 35

→ –4 + 35 = 31

So now:

→ 121 ÷ 11 × 3 + 8 × 31

Now left to right for division and multiplication:

→ 121 ÷ 11 = 11

→ 11 × 3 = 33

→ 8 × 31 = 248

Now add:

→ 33 + 248 = 281

✔ Answer: 281

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(b) 48 × 4 × (–98) – 24 × 8 × 2

Calculate each product separately:

→ 48 × 4 = 192 → 192 × (–98) = –18816

→ 24 × 8 = 192 → 192 × 2 = 384

Now subtract:

→ –18816 – 384 = –19200

✔ Answer: –19200

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(c) 144 ÷ (12 × 4 – (4 × 5 – 8))

Simplify inside the innermost brackets:

→ 4 × 5 = 20 → 20 – 8 = 12

Now:

→ 12 × 4 = 48 → 48 – 12 = 36

So:

→ 144 ÷ 36 = 4

✔ Answer: 4

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(d) 12 – [24 + 10 – {10 + 4(8 – 2 × 3 + 6)}]

Innermost first: 2 × 3 = 6

→ 8 – 6 + 6 = 8

Then: 4 × 8 = 32

→ Inside curly braces: 10 + 32 = 42

Now square brackets:

→ 24 + 10 = 34 → 34 – 42 = –8

Finally:

→ 12 – (–8) = 12 + 8 = 20

✔ Answer: 20

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(e) 12 × 39 ÷ (3 – 4) + (3 – (4 – 14))

Simplify inside parentheses:

→ (3 – 4) = –1

→ (4 – 14) = –10 → 3 – (–10) = 3 + 10 = 13

Now:

→ 12 × 39 = 468 → 468 ÷ (–1) = –468

→ –468 + 13 = –455

✔ Answer: –455

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## 2. Compare by using ‘<’, ‘>’ or ‘=’

We compute both sides and compare.

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(a) 15 – 18 ÷ 4 + 5 ▢ 18 ÷ (–18) + 45 ÷ (–3)

Left side:
15 – (18 ÷ 4) + 5 = 15 – 4.5 + 5 = 15.5

Right side:
18 ÷ (–18) = –1
45 ÷ (–3) = –15
→ –1 + (–15) = –16

Compare: 15.5 > –16

✔ Answer: >

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(b) 30 + (–64) ÷ (–16) – 8 ▢ 78 ÷ 13 – 100 ÷ (–5)

Left side:
(–64) ÷ (–16) = 4
→ 30 + 4 – 8 = 26

Right side:
78 ÷ 13 = 6
100 ÷ (–5) = –20
→ 6 – (–20) = 6 + 20 = 26

Both equal.

✔ Answer: =

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(c) (–44) × (–1) + 72 ÷ (–8) ▢ [144 ÷ (–12)] ÷ 12

Left side:
(–44) × (–1) = 44
72 ÷ (–8) = –9
→ 44 + (–9) = 35

Right side:
144 ÷ (–12) = –12
–12 ÷ 12 = –1

Compare: 35 > –1

✔ Answer: >

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(d) 88 + (–5) + (–95) – 19 ▢ (–83) × (–5) + 63

Left side:
88 – 5 = 83; 83 – 95 = –12; –12 – 19 = –31

Right side:
(–83) × (–5) = 415; 415 + 63 = 478

Compare: –31 < 478

✔ Answer: <

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(e) (–38) × (–95) + 95 × 2 ▢ 9 × 56 × (–110)

Left side:
(–38) × (–95) = 3610
95 × 2 = 190
→ 3610 + 190 = 3800

Right side:
9 × 56 = 504; 504 × (–110) = –55440

Compare: 3800 > –55440

✔ Answer: >

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## 3. Quick Answers

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(a) Does (–12) ÷ 7 represent an integer?

–12 ÷ 7 = –1.714... → Not a whole number.

✔ Answer: No

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(b) If u = (–1)^100 and v = (–1)^1000, then what would be the value of u + v?

Any even power of –1 is 1.

→ u = 1, v = 1 → u + v = 2

✔ Answer: 2

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(c) What would be the sum of an integer and a proper fraction, proper fraction or mixed fraction?

Example: 3 + 1/2 = 3½ → mixed fraction

✔ Answer: Mixed fraction

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(d) If we subtract the greatest negative integer from the smallest positive integer, then what would be the result?

- Greatest negative integer = –1
- Smallest positive integer = 1

→ 1 – (–1) = 1 + 1 = 2

✔ Answer: 2

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(e) Which property is shown by [–2 × (4 + 3)] = [(–2) × 4 + (–2) × 3]?

This is the Distributive Property of multiplication over addition.

✔ Answer: Distributive Property

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(f) What is the multiplicative identity for the integers?

Multiplicative identity means when multiplied, leaves the number unchanged → 1

✔ Answer: 1

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## 4. Tick (√) the correct option

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(a) If the integers 20, –17, 15, 13, –14 and 0 are marked on the number line, then the integer which lies on the extreme left is

On the number line, the “extreme left” means the smallest number.

Numbers: 20, –17, 15, 13, –14, 0

Smallest is –17

✔ Answer: (ii) –17

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## ✔ Final Answers Summary:

1. Simplify:

(a) 281
(b) –19200
(c) 4
(d) 20
(e) –455

2. Compare:

(a) >
(b) =
(c) >
(d) <
(e) >

3. Quick Answers:

(a) No
(b) 2
(c) Mixed fraction
(d) 2
(e) Distributive Property
(f) 1

4. Tick:

(a) (ii) –17

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