CBSE Class 7 Maths Worksheet - Integers | PDF | Teaching ... - Free Printable

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

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1) Verify: $ a - (-b) = a + b $

This identity is based on the rule: subtracting a negative number is the same as adding the positive of that number.

#### (a) $ a = 75, b = 84 $
- LHS: $ a - (-b) = 75 - (-84) = 75 + 84 = 159 $
- RHS: $ a + b = 75 + 84 = 159 $
✔ Verified: $ 159 = 159 $

#### (b) $ a = 118, b = 125 $
- LHS: $ 118 - (-125) = 118 + 125 = 243 $
- RHS: $ 118 + 125 = 243 $
✔ Verified: $ 243 = 243 $

#### (c) $ a = 25, b = 30 $
- LHS: $ 25 - (-30) = 25 + 30 = 55 $
- RHS: $ 25 + 30 = 55 $
✔ Verified: $ 55 = 55 $

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2) Write down a pair of integers whose

We need to find two integers satisfying each condition.

#### (a) Sum is -3
Example: $ -1 $ and $ -2 $
Because $ -1 + (-2) = -3 $
✔ Answer: $ -1, -2 $ (or any other pair like $ -5, 2 $, etc.)

#### (b) Sum is 0
Example: $ 5 $ and $ -5 $
Because $ 5 + (-5) = 0 $
✔ Answer: $ 5, -5 $

#### (c) Difference is 2
Difference means $ a - b = 2 $.
Example: $ 7 $ and $ 5 $ → $ 7 - 5 = 2 $
✔ Answer: $ 7, 5 $

#### (d) Difference is -5
$ a - b = -5 $ → Example: $ 3 $ and $ 8 $ → $ 3 - 8 = -5 $
✔ Answer: $ 3, 8 $

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3) Verify the following:

These are distributive property checks:
$ a \times (b + c) = (a \times b) + (a \times c) $

#### a) $ (-21) \times [(-4) + (-6)] = [(-21) \times (-4)] + [(-21) \times (-6)] $

- LHS: $ (-21) \times (-10) = 210 $
- RHS: $ (84) + (126) = 210 $
✔ Verified: $ 210 = 210 $

#### b) $ 15 \times [6 + (-3)] = [15 \times 6] + [15 \times (-3)] $

- LHS: $ 15 \times 3 = 45 $
- RHS: $ 90 + (-45) = 45 $
✔ Verified: $ 45 = 45 $

#### c) $ (-15) \times [(-8) + (-6)] = [(-15) \times (-8)] + [(-15) \times (-6)] $

- LHS: $ (-15) \times (-14) = 210 $
- RHS: $ 120 + 90 = 210 $
✔ Verified: $ 210 = 210 $

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4) Evaluate:

Use rules:
- Negative ÷ Positive = Negative
- Negative ÷ Negative = Positive
- Zero ÷ Any number = 0

#### a) $ (-100) ÷ 5 = -20 $

#### b) $ (-36) ÷ (-4) = 9 $

#### c) $ (-41) ÷ [(-40) + (-1)] = (-41) ÷ (-41) = 1 $

#### d) $ 0 ÷ (-18) = 0 $

#### e) $ [(-36) ÷ 12] ÷ 3 = (-3) ÷ 3 = -1 $

#### f) $ (-50) ÷ (50) = -1 $

#### g) $ 60 ÷ (-6) = -10 $

#### h) $ (-48) ÷ (-48) = 1 $

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✔ Final Answers:

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1) All verified:
(a) $ 75 - (-84) = 75 + 84 = 159 $
(b) $ 118 - (-125) = 118 + 125 = 243 $
(c) $ 25 - (-30) = 25 + 30 = 55 $

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2)
(a) $ -1, -2 $
(b) $ 5, -5 $
(c) $ 7, 5 $
(d) $ 3, 8 $

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3) All identities verified using distributive law.

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4)
a) $ -20 $
b) $ 9 $
c) $ 1 $
d) $ 0 $
e) $ -1 $
f) $ -1 $
g) $ -10 $
h) $ 1 $

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