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Term 1 Number System Exercise Solutions | KalviGavani

TN Class 7 Maths Term 1 Number System exercise solutions — integers fractions decimals rational numbers, MCQ and step-by-step answers.

Updated 12 June 202632 min read

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These are complete solutions for Samacheer Kalvi 7th Maths (Term 1) Chapter 1 — Number System. For every problem, show all steps: Identify the operation → Apply the rule → Calculate → State the final answer. Solve each exercise on your own first, then check the method below.

Key Concepts (Quick Recap)

  • Integers: The set of whole numbers and their negatives: {..., -3, -2, -1, 0, 1, 2, 3, ...}
  • Addition rules: Same sign → add magnitudes, keep sign. Different signs → subtract magnitudes, keep sign of larger absolute value.
  • Subtraction rule: Subtracting an integer = adding its additive inverse. a - b = a + (-b).
  • Multiplication rules: Positive x Positive = Positive; Positive x Negative = Negative; Negative x Negative = Positive.
  • Division rules: Same sign as multiplication — same signs give positive, different signs give negative. Division by zero is undefined.
  • Additive Identity: 0 — adding 0 to any integer gives the same integer.
  • Additive Inverse: For every integer a, its additive inverse is -a. a + (-a) = 0.
  • Properties of Integers under Addition: Closure (yes), Commutative (yes), Associative (yes).
  • Properties of Integers under Subtraction: Closure (yes), Commutative (no), Associative (no).
  • Properties of Integers under Multiplication: Closure (yes), Commutative (yes), Associative (yes), Distributive over addition (yes).
  • Properties of Integers under Division: Closure (no — 5 ÷ 2 is not an integer), Commutative (no), Associative (no).
  • BODMAS rule: Brackets → Orders → Division → Multiplication → Addition → Subtraction.

Exercise 1.1 — Addition of Integers

Q1. Malar's temperature was 102°F at noon. It dropped by 3°F by the evening. Find her evening temperature.

Solution
Given: Initial temperature = 102°F Temperature dropped by 3°F → we add -3 Evening temperature = 102 + (-3) = 102 - 3 = 99°F
Answer99°F

Q2. An elevator starts on the 20th floor, goes down 11 floors, then goes up 5 floors. Which floor is it on now?

Solution
Starting floor = 20 Goes down 11 floors → add -11 After going down: 20 + (-11) = 9th floor Goes up 5 floors → add +5 Current floor: 9 + 5 = 14th floor
Answer14th floor

Q3. 16 + ___ = 16. Which property is demonstrated?

Solution
We need a number that when added to 16 gives 16 itself. 16 + 0 = 16 This demonstrates the Additive Identity Property. The number 0 is the additive identity — adding 0 to any integer does not change its value.
Answer0 (Additive Identity Property)

Q4. Fill in the blanks:

(i) (-4) + (+3) = ___

(-4) + (+3) = -(4 - 3) = -1
Answer-1

(ii) (-4) + (-3) = ___

(-4) + (-3) = -(4 + 3) = -7
Answer-7

(iii) (+4) + (-3) = ___

(+4) + (-3) = +(4 - 3) = +1
Answer+1

Q5. Complete the properties table for integers under addition:

PropertyTrue/FalseExplanation
ClosureYesSum of any two integers is always an integer
CommutativeYesa + b = b + a for all integers
AssociativeYes(a + b) + c = a + (b + c) for all integers
AnswerClosure — Yes, Commutative — Yes, Associative — Yes

Q6. Find the values:

(i) 7 + (-5)

7 + (-5) = +(7 - 5) = +2
Answer+2

(ii) (-6) + (-13)

(-6) + (-13) = -(6 + 13) = -19
Answer-19

(iii) 25 + 9

25 + 9 = 34
Answer34

(iv) (-12) + 4

(-12) + 4 = -(12 - 4) = -8
Answer-8

Q7. Fill in the blanks using the commutative property of addition:

(i) 20 + (-11) = (-11) + ___

By commutative property: a + b = b + a 20 + (-11) = (-11) + 20
Answer20

(ii) (-5) + (-8) = (-8) + ___

(-5) + (-8) = (-8) + (-5)
Answer(-5)

(iii) (-3) + 12 = 12 + ___

(-3) + 12 = 12 + (-3)
Answer(-3)

Q8. True or False:

(i) (-11) + (-8) = (-8) + (-11)

LHS = (-11) + (-8) = -(11 + 8) = -19 RHS = (-8) + (-11) = -(8 + 11) = -19 LHS = RHS → True (Commutative property)
AnswerTrue ✓

(ii) -7 + 2 = 2 + (-7)

LHS = -7 + 2 = -(7 - 2) = -5 RHS = 2 + (-7) = -(7 - 2) = -5 LHS = RHS → True
AnswerTrue ✓

(iii) (-33) + 8 = 8 + (-33)

LHS = (-33) + 8 = -(33 - 8) = -25 RHS = 8 + (-33) = -(33 - 8) = -25 LHS = RHS → True
AnswerTrue ✓

Q9. Verify the associative property of addition with (-3), (-7) and (+6).

Solution
Let a = -3, b = -7, c = +6 LHS: (a + b) + c = (-3 + (-7)) + 6 = (-10) + 6 = -4 RHS: a + (b + c) = -3 + ((-7) + 6) = -3 + (-1) = -4 LHS = RHS = -4 Associative property verified.
Answer(a + b) + c = a + (b + c) = -4. Verified. ✓

Q10. What is the additive identity for integers? Verify with examples.

Solution
The additive identity for integers is 0. Adding 0 to any integer gives the same integer. Verification: (i) 0 + (-95) = -95 (ii) -611 + 0 = -611
Answer0 is the additive identity. Verified. ✓

Q11. What is the additive inverse? Find the additive inverse of (i) -603 (ii) 9847.

Solution
The additive inverse of an integer a is -a, such that a + (-a) = 0. (i) Additive inverse of -603: -603 + 603 = 0 Additive inverse of -603 is 603. (ii) Additive inverse of 9847: 9847 + (-9847) = 0 Additive inverse of 9847 is -9847.
Answer(i) 603 (ii) -9847

Exercise 1.2 — Subtraction of Integers

Q1. Fill in the blanks:

(i) (-7) - (-15) = ___

(-7) - (-15) = (-7) + 15 [subtracting negative = adding positive] = +(15 - 7) = +8
Answer+8

(ii) 12 - (-7) = ___

12 - (-7) = 12 + 7 [subtracting negative = adding positive] = 19
Answer19

(iii) (-4) - (-5) = ___

(-4) - (-5) = (-4) + 5 [subtracting negative = adding positive] = +(5 - 4) = +1
Answer+1

Q2. Compare using > or <:

(i) 15 - 12 ___ 12 - 15

LHS: 15 - 12 = 3 RHS: 12 - 15 = -(15 - 12) = -3 3 > -3
Answer3 > -3, so 15 - 12 > 12 - 15

(ii) (-21) - 32 ___ (-32) - (-21)

LHS: (-21) - 32 = -21 - 32 = -53 RHS: (-32) - (-21) = -32 + 21 = -(32 - 21) = -11 -53 < -11
Answer(-21) - 32 < (-32) - (-21)

Q3. Is subtraction associative? Verify with an example.

Solution
Let us check whether (a - b) - c = a - (b - c) Take a = 1, b = 2, c = 3 LHS: (1 - 2) - 3 = (-1) - 3 = -4 RHS: 1 - (2 - 3) = 1 - (-1) = 1 + 1 = 2 LHS = -4 ≠ 2 = RHS Subtraction is NOT associative.
AnswerNo, subtraction is not associative. Example: (1-2)-3 = -4 but 1-(2-3) = 2.

Q4. The Roman civilization began in 509 BC and ended in 476 AD. How long did the Roman civilization last?

Solution
509 BC is represented as -509 476 AD is represented as +476 Duration = 476 - (-509) = 476 + 509 = 985 years
Answer985 years

Q5. A submarine is at a depth of -450 feet. It descends another 300 feet. What is its new position?

Solution
Current position = -450 ft Descends 300 ft → subtract 300 (or add -300) New position = -450 + (-300) = -(450 + 300) = -750 ft
Answer-750 feet

Q6. The temperature at noon was 90°F. By midnight, it was -2°F. Find the change in temperature.

Solution
Change = Final temperature - Initial temperature = (-2) - 90 = -(2 + 90) = -92°F The temperature dropped by 92°F.
AnswerThe temperature decreased by 92°F (or the change is -92°F)

Q7. Using the number line, find:

(i) (-3) - 2

Start at -3 on the number line. Move 2 units to the left (subtracting 2). -3 → -4 → -5 Answer: -5

(ii) 4 - (-3)

Start at 4 on the number line. Subtracting -3 means moving 3 units to the right. 4 → 5 → 6 → 7 Answer: 7

(iii) (-5) - (-4)

Start at -5 on the number line. Subtracting -4 means moving 4 units to the right. -5 → -4 → -3 → -2 → -1 Answer: -1

Q8 (MCQ). The additive inverse of (-7) is:

(i) -7 (ii) 7 (iii) 0 (iv) 1

Additive inverse of a is the number that gives 0 when added to a. (-7) + 7 = 0 Additive inverse of -7 is 7.
Answer(ii) 7 ✓

Q9 (MCQ). (-3) - (-9) = ___

(i) -12 (ii) 6 (iii) -6 (iv) 12

(-3) - (-9) = (-3) + 9 = +(9 - 3) = +6
Answer(ii) 6 ✓

Q10 (MCQ). Which of the following is not equivalent to 15 - (-8)?

(i) 15 + 8 (ii) 23 (iii) 15 - 8 (iv) None of these

15 - (-8) = 15 + 8 = 23 (i) 15 + 8 = 23 ✓ (ii) 23 ✓ (iii) 15 - 8 = 7 ✗ (not equivalent)
Answer(iii) 15 - 8 ✓

Exercise 1.3 — Multiplication of Integers

Q1. Fill in the blanks:

(i) -80 × 1 = ___

Any integer × 1 = the same integer -80 × 1 = -80
Answer-80

(ii) (-10) × (-2) = ___

Negative × Negative = Positive (-10) × (-2) = +20
Answer+20

(iii) 100 × (-5) = ___

Positive × Negative = Negative 100 × (-5) = -500
Answer-500

(iv) 5 × (-9) = ___

Positive × Negative = Negative 5 × (-9) = -45
Answer-45

(v) 0 × 75 = ___

Any integer × 0 = 0 0 × 75 = 0
Answer0

Q2. True or False:

(i) (-15) × 5 = 75

Negative × Positive = Negative (-15) × 5 = -75 ≠ 75
AnswerFalse ✗. The correct answer is -75.

(ii) (-100) × 0 × 20 = 0

Any number multiplied by 0 gives 0. (-100) × 0 = 0; then 0 × 20 = 0
AnswerTrue ✓

(iii) 8 × (-4) = 32

Positive × Negative = Negative 8 × (-4) = -32 ≠ 32
AnswerFalse ✗. The correct answer is -32.

Q3. What will be the sign of the product when:

(i) 16 negative integers are multiplied?

When an even number of negative integers are multiplied, the product is positive. 16 is even → Product is Positive.
AnswerPositive

(ii) 29 negative integers are multiplied?

When an odd number of negative integers are multiplied, the product is negative. 29 is odd → Product is Negative.
AnswerNegative

Q4. Find the product:

(i) (-35) × 22

(-35) × 22 = -(35 × 22) 35 × 22 = 35 × 20 + 35 × 2 = 700 + 70 = 770 (-35) × 22 = -770
Answer-770

(ii) (-10) × 12 × (-9)

Step 1: (-10) × 12 = -120 Step 2: (-120) × (-9) = +1080 Alternatively: (-10) × (-9) = +90 90 × 12 = 1080
Answer+1080

(iii) (-9) × (-8) × (-7) × (-6)

Step 1: (-9) × (-8) = +72 Step 2: (-7) × (-6) = +42 Step 3: 72 × 42 = 3024 Alternatively: Four negatives → even number → product is positive 9 × 8 × 7 × 6 = 3024
Answer+3024

(iv) (-25) × 0 × 45 × 90

Any number multiplied by 0 is 0. (-25) × 0 = 0
Answer0

(v) (-2) × (+50) × (-25) × 4

Step 1: (-2) × (+50) = -100 Step 2: (-25) × 4 = -100 Step 3: (-100) × (-100) = +10000 Alternatively: Two negatives → product is positive 2 × 50 × 25 × 4 = 2 × 50 × 100 = 10000
Answer+10000

Q5. Check whether the following are equal:

(i) (8 - 13) × 7 and 8 - (13 × 7)

LHS: (8 - 13) × 7 = (-5) × 7 = -35 RHS: 8 - (13 × 7) = 8 - 91 = -83 -35 ≠ -83
AnswerNot equal

(ii) Verify the distributive property: a × (b + c) = a × b + a × c with a = -3, b = 4, c = -6

LHS: a × (b + c) = (-3) × (4 + (-6)) = (-3) × (-2) = +6 RHS: a × b + a × c = (-3) × 4 + (-3) × (-6) = -12 + 18 = +6 LHS = RHS = 6. Distributive property verified.
AnswerDistributive property verified. ✓

Q6. The water level in a tank decreases by 2 inches every week. By how much does the water level change in 6 weeks?

Solution
Decrease per week = 2 inches → represented as -2 Number of weeks = 6 Total change = 6 × (-2) = -12 inches The water level decreases by 12 inches.
AnswerThe water level changes by -12 inches (decreases by 12 inches).

Q7. Find all pairs of integers whose product is -50.

Solution
We need a × b = -50 where a and b are integers. One must be positive and one must be negative. Pairs: (-1) × 50 = -50 → (-1, 50) (1) × (-50) = -50 → (1, -50) (-2) × 25 = -50 → (-2, 25) (2) × (-25) = -50 → (2, -25) (-5) × 10 = -50 → (-5, 10) (5) × (-10) = -50 → (5, -10)
AnswerThe pairs are: (-1, 50), (1, -50), (-2, 25), (2, -25), (-5, 10), (5, -10)

Q8 (MCQ). (-8) × (-3) × (-2) = ___

(i) 48 (ii) -48 (iii) 14 (iv) -14

Three negatives → odd number → product is negative 8 × 3 × 2 = 48 (-8) × (-3) × (-2) = -48
Answer(ii) -48 ✓

Q9 (MCQ). The multiplicative identity for integers is:

(i) -1 (ii) 0 (iii) 1 (iv) None of these

Any integer × 1 = the same integer 1 is the multiplicative identity.
Answer(iii) 1 ✓

Q10 (MCQ). Which of the following is true?

(i) a × 1 = 1 × a = a (ii) a × 0 = 0 (iii) a × (-1) = -a (iv) All of these

(i) a × 1 = 1 × a = a — True (multiplicative identity) (ii) a × 0 = 0 — True (property of zero) (iii) a × (-1) = -a — True (multiplication by -1) All three are true.
Answer(iv) All of these ✓

Q11 (MCQ). The product of two integers is 180. If one integer is -12, find the other.

(i) -15 (ii) 15 (iii) -12 (iv) 12

Other integer = Product ÷ Given integer = 180 ÷ (-12) = -15
Answer(i) -15 ✓

Exercise 1.4 — Division of Integers

Q1. Fill in the blanks:

(i) (-40) ÷ (-1) = ___

Negative ÷ Negative = Positive (-40) ÷ (-1) = 40
Answer40

(ii) 25 ÷ (-5) = ___

Positive ÷ Negative = Negative 25 ÷ (-5) = -(25 ÷ 5) = -5
Answer-5

(iii) (-36) ÷ (-4) = ___

Negative ÷ Negative = Positive (-36) ÷ (-4) = +(36 ÷ 4) = +9
Answer+9

(iv) (-62) ÷ (-62) = ___

Any non-zero integer divided by itself equals 1. (-62) ÷ (-62) = 1
Answer1

Q2. True or False:

(i) (-30) ÷ (-6) = -6

(-30) ÷ (-6) = +(30 ÷ 6) = +5 5 ≠ -6
AnswerFalse ✗. The correct answer is +5.

(ii) (-64) ÷ (-64) = 0

(-64) ÷ (-64) = 1 (any number divided by itself is 1, not 0)
AnswerFalse ✗. The correct answer is 1.

Q3. Find the values:

(i) (-75) ÷ 5

Negative ÷ Positive = Negative (-75) ÷ 5 = -(75 ÷ 5) = -15
Answer-15

(ii) (-100) ÷ (-20)

Negative ÷ Negative = Positive (-100) ÷ (-20) = +(100 ÷ 20) = +5
Answer+5

(iii) 45 ÷ (-9)

Positive ÷ Negative = Negative 45 ÷ (-9) = -(45 ÷ 9) = -5
Answer-5

(iv) (-82) ÷ 82

(-82) ÷ 82 = -(82 ÷ 82) = -1
Answer-1

Q4. The product of two integers is -135. If one of them is -15, find the other.

Solution
Product = -135 One integer = -15 Other integer = Product ÷ Given integer = (-135) ÷ (-15) = +(135 ÷ 15) = +9 Verification: (-15) × 9 = -135 ✓
Answer9

Q5. The temperature dropped 24°C over 8 hours. What is the average rate of temperature change per hour?

Solution
Total drop = 24°C Time = 8 hours Rate = 24 ÷ 8 = 3°C per hour (drop) Since the temperature dropped, the change is -24°C over 8 hours: -24 ÷ 8 = -3°C per hour
AnswerThe temperature drops at an average rate of 3°C per hour (change of -3°C/hour).

Q6. An elevator starts at 15 m above ground and descends to -250 m. It travels at 5 m per minute. How long does the descent take?

Solution
Start = +15 m End = -250 m Total distance = 15 - (-250) = 15 + 250 = 265 m Speed = 5 m/min Time = 265 ÷ 5 = 53 minutes
Answer53 minutes

Q7. A person consumes 4800 calories in 30 days. What is the average calorie consumption per day?

Solution
Total calories = 4800 Number of days = 30 Average per day = 4800 ÷ 30 = 160 calories/day
Answer160 calories per day

Q8. Given that 168 × 32 = 5376, find (-5376) ÷ (-32).

Solution
168 × 32 = 5376 Therefore: 5376 ÷ 32 = 168 Now: (-5376) ÷ (-32) = +(5376 ÷ 32) = +168 Negative ÷ Negative = Positive
Answer168

Q9. Find the quotient: (-256) ÷ 16

Negative ÷ Positive = Negative (-256) ÷ 16 = -(256 ÷ 16) = -16
Answer-16

Q10. Find the quotient: (-144) ÷ (-12)

Negative ÷ Negative = Positive (-144) ÷ (-12) = +(144 ÷ 12) = +12
Answer+12

Q11 (MCQ). (-1) ÷ (-1) = ___

(i) -1 (ii) 0 (iii) 1 (iv) None of these

(-1) ÷ (-1) = +(1 ÷ 1) = 1
Answer(iii) 1 ✓

Q12 (MCQ). 0 ÷ (-7) = ___

(i) -7 (ii) 0 (iii) 7 (iv) Not defined

0 divided by any non-zero integer = 0 0 ÷ (-7) = 0
Answer(ii) 0 ✓

Q13 (MCQ). Which is not defined?

(i) 0 ÷ 5 (ii) 5 ÷ 1 (iii) 5 ÷ 0 (iv) 0 ÷ (-5)

Division by zero is not defined. 5 ÷ 0 is undefined.
Answer(iii) 5 ÷ 0 ✓

Q14 (MCQ). If a ÷ (-1) = -8, then a = ___

(i) 8 (ii) -8 (iii) 1 (iv) 0

a ÷ (-1) = -8 a = -8 × (-1) = 8
Answer(i) 8 ✓

Exercise 1.5 — Fractions and Decimals (Rational Numbers)

Q1. Ani is scuba diving. She descends 5 feet below sea level, then descends the same distance 4 more times. What is her final elevation?

Solution
First descent = -5 ft Then 4 more descents of the same distance = 4 × (-5) = -20 ft Total descent = -5 + (-20) = -25 ft Alternatively: Total descents = 5 times 5 ft each Final position = 5 × (-5) = -25 ft
Answer25 feet below sea level (elevation = -25 ft)

Q2. The price of a plant reduced by ₹6 per week for 7 weeks. By how much did the price change over 7 weeks?

Solution
Weekly reduction = ₹6 (represented as -6) Number of weeks = 7 Total change = 7 × (-6) = -₹42 The price decreased by ₹42 over 7 weeks.
AnswerThe price changed by -₹42 (decreased by ₹42)

Q3. The product of three integers is -3. Determine all possible sets of values for the three integers.

Solution
We need a × b × c = -3, where a, b, c are integers. The product is negative, so either 1 or 3 of the integers must be negative. Possible combinations (order matters): (1) × (1) × (-3) = -3 (1) × (-1) × (3) = -3 (-1) × (1) × (3) = -3 (1) × (-3) × (1) = -3 (-3) × (1) × (1) = -3 (-1) × (-1) × (-3) = -3 Key distinct factor sets (ignoring order): {1, 1, -3}, {1, -1, 3}, {-1, -1, -3}
AnswerPossible sets include (1, 1, -3), (1, -1, 3), and (-1, -1, -3)

Exercise 1.6 — BODMAS and Properties

Q1. Simplify using suitable properties:

(a) (-1650) × (-2) + (-1650) × (-98)

Solution
Using distributive property: a × b + a × c = a × (b + c) = (-1650) × [(-2) + (-98)] = (-1650) × (-100) = 1650 × 100 = 1,65,000
Answer1,65,000

(b) (9150 × 405) - (8150 × 405)

Solution
Using distributive property: a × c - b × c = (a - b) × c = 405 × (9150 - 8150) = 405 × 1000 = 4,05,000
Answer4,05,000

Q2. Which is greater: (9 + 7) × 1000 or 9 + 7 × 1000?

Solution
First expression: (9 + 7) × 1000 = 16 × 1000 = 16,000 Second expression: 9 + 7 × 1000 = 9 + 7000 = 7,009 (BODMAS: multiplication before addition) Since 16,000 > 7,009
Answer(9 + 7) × 1000 is greater

Q3. Simplify: 80 ÷ [240 ÷ (-24)] + 7

Solution
Step 1: Solve the inner bracket first 240 ÷ (-24) = -10 Step 2: Now solve the outer division 80 ÷ (-10) = -8 Step 3: Add 7 -8 + 7 = -1
Answer-1

Q4. The temperature at 6 AM was -5°C. By noon, it rose to 9°C. What was the increase in temperature?

Solution
Initial temperature = -5°C Final temperature = 9°C Increase = Final - Initial = 9 - (-5) = 9 + 5 = 14°C
Answer14°C increase

Q5. An atom has 9 protons (positive charges) and 10 electrons (negative charges). What is the net charge?

Solution
Positive charges = +9 Negative charges = -10 Net charge = (+9) + (-10) = -(10 - 9) = -1
AnswerNet charge = -1 (one negative unit)

Q6. The boiling point of water is 100°C and the melting point of ice is 0°C. Express these in Kelvin scale.

Solution
Kelvin = °C + 273 Boiling point = 100 + 273 = 373 K Melting point = 0 + 273 = 273 K
AnswerBoiling point = 373 K, Melting point = 273 K

Q7. Reena's bank account shows a balance of ₹2500. She deposits ₹1500 and then withdraws ₹4200. What is her new balance?

Solution
Opening balance = +₹2500 Deposit = +₹1500 Withdrawal = -₹4200 New balance = 2500 + 1500 + (-4200) = 4000 - 4200 = -₹200
Answer-₹200 (overdraft of ₹200)

Q8. Poet Tamizh Nambi wrote a book of 150 pages. He lost pages 21-30 and pages 61-70. How many pages remain?

Solution
Total pages = 150 Pages lost: Pages 21-30 = 10 pages (21, 22, 23, 24, 25, 26, 27, 28, 29, 30) Pages 61-70 = 10 pages (61, 62, 63, 64, 65, 66, 67, 68, 69, 70) Total lost = 10 + 10 = 20 pages Pages remaining = 150 - 20 = 130 pages
Answer130 pages remain

Q9. I added 2 to a number, multiplied the result by 5, subtracted 10, and divided by 4. The final result was 15. Find the original number.

Solution
Working backwards from the result: Final result = 15 Before division by 4: 15 × 4 = 60 Before subtracting 10: 60 + 10 = 70 Before multiplying by 5: 70 ÷ 5 = 14 Before adding 2: 14 - 2 = 12 Verification: ((12 + 2) × 5 - 10) ÷ 4 = (14 × 5 - 10) ÷ 4 = (70 - 10) ÷ 4 = 60 ÷ 4 = 15 ✓
AnswerThe original number is 12.

Q10. Kamatchi sells 30 idlis at ₹8 each and 50 dosas at ₹5 each. The cost of making each idli is ₹6 and each dosa is ₹8. Find her overall profit or loss.

Solution
Revenue from idlis = 30 × ₹8 = ₹240 Revenue from dosas = 50 × ₹5 = ₹250 Total revenue = ₹240 + ₹250 = ₹490 Cost of idlis = 30 × ₹6 = ₹180 Cost of dosas = 50 × ₹8 = ₹400 Total cost = ₹180 + ₹400 = ₹580 Profit/Loss = Revenue - Cost = ₹490 - ₹580 = -₹90 Since the result is negative, it is a loss.
AnswerKamatchi incurred a loss of ₹90.

Q11. A reservoir's water level decreases by 3 inches each week during a drought. How much does the water level change in 6 weeks?

Solution
Decrease per week = -3 inches Number of weeks = 6 Total change = 6 × (-3) = -18 inches The water level decreases by 18 inches.
AnswerThe water level changes by -18 inches (decreases by 18 inches).

Q12. Buddha was born in 563 BC and died in 483 BC. Was he alive in 500 BC? How many years did he live?

Solution
Born: 563 BC → represented as -563 Died: 483 BC → represented as -483 (i) Was he alive in 500 BC (-500)? -563 < -500 < -483 Yes, Buddha was alive in 500 BC. (ii) Number of years he lived: = 563 - 483 = 80 years Verification: (-483) - (-563) = -483 + 563 = 80 years
AnswerYes, Buddha was alive in 500 BC. He lived for 80 years.

Objective Type Questions (MCQs)

Q1. Which of the following is the additive identity for integers?

(i) 1 (ii) -1 (iii) 0 (iv) None of these

The additive identity is the number which when added to any integer gives the same integer. 0 + a = a for all integers a.
Answer(iii) 0 ✓

Q2. The sum of two integers is -15. If one of them is 9, the other is:

(i) -6 (ii) 24 (iii) -24 (iv) 6

9 + x = -15 x = -15 - 9 = -24
Answer(iii) -24 ✓

Q3. On a number line, when we add a positive integer, we move:

(i) To the left (ii) To the right (iii) Up (iv) Down

Adding a positive integer means moving to the right on the number line.
Answer(ii) To the right ✓

Q4. The integer which is its own additive inverse is:

(i) 1 (ii) -1 (iii) 0 (iv) None of these

A number is its own additive inverse if a + (-a) = 0 and a = -a. This is only true for 0, since 0 = -0.
Answer(iii) 0 ✓

Q5. The product of two integers is 180. If one integer is -12, find the other.

(i) -15 (ii) 15 (iii) -12 (iv) 12

Other integer = Product ÷ Given integer = 180 ÷ (-12) = -15
Answer(i) -15 ✓

Q6. Which of the following statements is true?

(i) Integers are closed under division (ii) Integers are commutative under subtraction (iii) Integers are associative under addition (iv) Integers are closed under subtraction but not commutative

(i) False: 5 ÷ 2 = 2.5 is not an integer (ii) False: 3 - 5 ≠ 5 - 3 (iii) True: (a + b) + c = a + (b + c) for all integers (iv) True but (iii) is also true and is more fundamental
Answer(iii) Integers are associative under addition ✓

Q7. What is the value of (-1) × (-1) × (-1) × ... × (-1) (2024 times)?

(i) 1 (ii) -1 (iii) 0 (iv) Cannot determine

2024 is an even number. Product of an even number of negative integers is positive. (-1) raised to an even power = 1.
Answer(i) 1 ✓

Q8. If a and b are integers such that a > b, then which is always true?

(i) a + b > a (ii) a - b > 0 (iii) a × b > a (iv) a ÷ b > 1

If a > b, then a - b > 0 is always true. Example: 5 > 3 → 5 - 3 = 2 > 0 Example: -2 > -5 → -2 - (-5) = 3 > 0
Answer(ii) a - b > 0 ✓

True or False (with corrections)

1. The sum of two negative integers is always a positive integer.

AnswerFalse ✗. The sum of two negative integers is always negative. Example: (-3) + (-5) = -8.

2. Subtraction of integers is commutative.

AnswerFalse ✗. Subtraction is not commutative. Example: 5 - 3 = 2, but 3 - 5 = -2.

3. Division by zero is not defined.

AnswerTrue ✓. There is no number that when multiplied by 0 gives a non-zero dividend.

4. The product of a positive integer and a negative integer is always negative.

AnswerTrue ✓. Positive × Negative = Negative. Example: 3 × (-4) = -12.

5. The integer 0 has no predecessor.

AnswerFalse ✗. The predecessor of 0 is -1. Every integer has both a predecessor and a successor.

6. a + b = b + a for all integers a and b.

AnswerTrue ✓. This is the commutative property of addition, which holds for all integers.

7. (a - b) - c = a - (b - c) for all integers a, b, c.

AnswerFalse ✗. Subtraction is not associative. Counterexample: (5 - 3) - 2 = 0, but 5 - (3 - 2) = 4.

8. Every integer has an additive inverse.

AnswerTrue ✓. For every integer a, the additive inverse -a exists and a + (-a) = 0.

Fill in the Blanks

1. The additive inverse of -18 is ___

Additive inverse of -18 is 18, since (-18) + 18 = 0
Answer18

2. (-7) + ___ = 0

We need x such that -7 + x = 0 x = 7
Answer7

3. The product of three negative integers is ___

Three negatives → odd number → product is negative. Example: (-2) × (-3) × (-4) = -(2 × 3 × 4) = -24
Answernegative

4. 0 ÷ (-5) = ___

0 divided by any non-zero integer is 0.
Answer0

5. The additive identity for integers is ___

Adding 0 to any integer gives the same integer.
Answer0

6. a × (b + c) = a × b + a × c is called the ___ property

This is the distributive property of multiplication over addition.
Answerdistributive

7. (-6) ÷ ___ = 2

(-6) ÷ x = 2 x = (-6) ÷ 2 = -3 Verification: (-6) ÷ (-3) = 2 ✓
Answer-3

8. The predecessor of -7 is ___

The predecessor of an integer n is n - 1. Predecessor of -7 = -7 - 1 = -8
Answer-8

9. The successor of -10 is ___

The successor of an integer n is n + 1. Successor of -10 = -10 + 1 = -9
Answer-9

10. On a number line, the integer to the right of -3 is ___

Moving right on the number line increases the value. The integer to the right of -3 is -2.
Answer-2

Common Mistakes

1. Adding magnitudes and keeping the wrong sign: When adding (-8) + (+3), some students write 11 instead of -5. Rule: different signs → subtract the smaller absolute value from the larger, keep the sign of the larger absolute value.

2. Forgetting that subtracting a negative equals adding: 5 - (-3) = 5 + 3 = 8, not 2. Convert every subtraction a - (-b) to a + b before calculating.

3. Confusing multiplication sign rules: Negative × Negative = Positive (not negative). Example: (-6) × (-4) = +24, not -24. Memorize: same signs → positive product; different signs → negative product.

4. Not applying BODMAS correctly in mixed operations: In expressions like (-3) + 4 × (-2), multiplication comes before addition: first calculate 4 × (-2) = -8, then (-3) + (-8) = -11. Do not simply go left to right.

5. Treating division as commutative: a ÷ b is NOT equal to b ÷ a. For example, (-10) ÷ 2 = -5, but 2 ÷ (-10) = -1/5. These are different results. Division is not commutative.

6. Forgetting that any number multiplied by 0 equals 0: Some students write (-25) × 0 × 45 × 90 = -25 or some other non-zero number. Any product involving 0 equals 0, regardless of how many other factors there are.

7. Assuming subtraction is associative: It is NOT. (8 - 13) × 7 = -35, but 8 - (13 × 7) = -83. Always use brackets to clarify the order of operations.

Exam Checklist

  • [ ] I can add integers correctly, choosing the right sign based on absolute values.
  • [ ] I can subtract integers by converting to addition of the additive inverse.
  • [ ] I can multiply integers with correct sign rules (same sign → positive, different sign → negative).
  • [ ] I can divide integers with correct sign rules (same sign → positive, different sign → negative).
  • [ ] I know the properties: closure, commutative, associative for each operation and can identify which do NOT hold (subtraction is not commutative or associative; division is not commutative or associative).
  • [ ] I know the additive identity (0) and additive inverse of any integer.
  • [ ] I can represent integers on a number line and perform operations visually.
  • [ ] I can solve word problems involving temperature, elevation, profit/loss, and time periods (BC/AD).
  • [ ] I apply BODMAS correctly when solving mixed-operation expressions.
  • [ ] I remember that division by zero is undefined and 0 ÷ any non-zero integer = 0.
  • [ ] I can identify and use the distributive property to simplify calculations: a × (b + c) = a × b + a × c.

Internal Links

  • [Class 7 Maths (Term 1) Number System — Chapter Guide](/school/tamil-nadu-state-board/class/7/maths/term-1-number-system)
  • [All Class 7 Maths Solutions](/school/tamil-nadu-state-board/class/7/maths/solutions)
  • [Class 7 Maths Subject Guide](/school/tamil-nadu-state-board/class/7/maths)

Frequently Asked Questions

Integers are the set of whole numbers and their negatives: {..., -3, -2, -1, 0, 1, 2, 3, ...}. They include all positive whole numbers, zero, and all negative whole numbers.