Class 7th NCERT Math Solutions to Exercise 1.4 on Integers

Class 7th NCERT Math Solutions to Exercise 1.4 from the mathematics chapter on integers.

Question 1: Evaluate Each Expression

Compute the following:

• (a) (−30) ÷ 10:
  • Solution: (−30) ÷ 10 = −3
  • Answer: −3
• (b) 50 ÷ (−5):
  • Solution: 50 ÷ (−5) = −10
  • Answer: −10
• (c) (−36) ÷ (−9):
  • Solution: (−36) ÷ (−9) = 36 ÷ 9 = 4
  • Answer: 4
• (d) (−49) ÷ 49:
  • Solution: (−49) ÷ 49 = −1
  • Answer: −1
• (e) 13 ÷ [(−2) + 1]:
  • Solution: (−2) + 1 = −1, 13 ÷ (−1) = −13
  • Answer: −13
• (f) 0 ÷ (−12):
  • Solution: 0 ÷ (−12) = 0
  • Answer: 0
• (g) (−31) ÷ [(−30) + (−1)]:
  • Solution: (−30) + (−1) = −31, (−31) ÷ (−31) = 1
  • Answer: 1
• (h) [(−36) ÷ 12] ÷ 3:
  • Solution: (−36) ÷ 12 = −3, −3 ÷ 3 = −1
  • Answer: −1
• (i) [(−6) + 5] ÷ [(−2) + 1]:
  • Solution: (−6) + 5 = −1, (−2) + 1 = −1, −1 ÷ (−1) = 1
  • Answer: 1

Question 2: Verify Non-Distributivity

Verify a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for:

• (a) a = 12, b = −4, c = 2:
  • Solution:
    • 12 ÷ [(−4) + 2] = 12 ÷ (−2) = −6
    • (12 ÷ (−4)) + (12 ÷ 2) = (−3) + 6 = 3
    • −6 ≠ 3
  • Answer: Verified
• (b) a = −10, b = 1, c = 1:
  • Solution:
    • (−10) ÷ (1 + 1) = (−10) ÷ 2 = −5
    • ((−10) ÷ 1) + ((−10) ÷ 1) = (−10) + (−10) = −20
    • −5 ≠ −20
  • Answer: Verified

Question 3: Fill in the Blanks

Complete the statements:

• (a) 369 ÷ ? = 369:
  • Solution: 369 ÷ x = 369 ⇒ x = 1
  • Answer: 1
• (b) (−75) ÷ ? = −1:
  • Solution: (−75) ÷ x = −1 ⇒ x = (−75) ÷ (−1) = 75
  • Answer: 75
• (c) (−206) ÷ ? = 1:
  • Solution: (−206) ÷ x = 1 ⇒ x = (−206) ÷ 1 = −206
  • Answer: −206
• (d) −87 ÷ ? = 87:
  • Solution: −87 ÷ x = 87 ⇒ x = (−87) ÷ 87 = −1
  • Answer: −1
• (e) ? ÷ 1 = −87:
  • Solution: x ÷ 1 = −87 ⇒ x = −87
  • Answer: −87
• (f) ? ÷ 48 = −1:
  • Solution: x ÷ 48 = −1 ⇒ x = (−1) × 48 = −48
  • Answer: −48
• (g) 20 ÷ ? = −2:
  • Solution: 20 ÷ x = −2 ⇒ x = 20 ÷ (−2) = −10
  • Answer: −10
• (h) ? ÷ 4 = −3:
  • Solution: x ÷ 4 = −3 ⇒ x = (−3) × 4 = −12
  • Answer: −12

Question 4: Pairs of Integers

Find five pairs (a, b26, b) such that a ÷ b = −3. One pair is (6, −2).

• Solution:
  • 6 ÷ (−2) = −3
  • −9 ÷ 3 = −3
  • 12 ÷ (−4) = −3
  • −15 ÷ 5 = −3
  • 18 ÷ (−6) = −3
• Answer: (6, −2), (−9, 3), (12, −4), (−15, 5), (18, −6)

Question 5: Temperature Change

Temperature at 12 noon is 10°C, decreasing at 2°C/hour until midnight. Find the time when temperature is −8°C and the temperature at midnight.

• Solution:
  • Initial: 10°C
  • Decrease: 2°C/hour
  • To reach −8°C: 10 − (−8) = 18°C
    • Time: 18 ÷ 2 = 9 hours
    • From 12 noon: 12 + 9 = 21:00 (9:00 PM)
  • Midnight (12 hours): 10 − (2 × 12) = 10 − 24 = −14°C
• Answer: 9:00 PM, −14°C

Question 6: Class Test Scores

Test: +3 marks for correct, −2 for incorrect, 0 for unattempted.

• (i) Radhika: score 20, 12 correct. Find incorrect.
  • Solution:
    • Correct: 12 × 3 = 36
    • Score: 20, incorrect marks: 20 − 36 = −16
    • Incorrect: −16 ÷ (−2) = 8
  • Answer: 8
• (ii) Mohini: score −5, 7 correct. Find incorrect.
  • Solution:
    • Correct: 7 × 3 = 21
    • Score: −5, incorrect marks: −5 − 21 = −26
    • Incorrect: −26 ÷ (−2) = 13
  • Answer: 13

Question 7: Elevator Descent

Elevator descends at 6 m/min from 10 m above ground to −350 m. Find time.

• Solution:
  • Distance: 10 − (−350) = 360 m
  • Time: 360 ÷ 6 = 60 min
• Answer: 60 min (1 hour)

Question 8: Integer Division Property

Show that (−a) ÷ (−b) = a ÷ b for a = 24, b = 6.

• Solution:
  • Left side: (−24) ÷ (−6) = 24 ÷ 6 = 4
  • Right side: 24 ÷ 6 = 4
  • Since (−24) ÷ (−6) = 24 ÷ 6 = 4, the property holds.
• Answer: Verified

Question 9: Debt Repayment

A person has a debt of −1200 dollars and repays it at a rate of 150 dollars per month. Find the number of months required to fully repay the debt.

• Solution:
  • Initial debt: −1200 dollars
  • Repayment rate: 150 dollars/month
  • Months needed: (−1200) ÷ (−150) = 1200 ÷ 150 = 8
• Answer: 8 months

This completes Exercise 1.4 solutions up to Question 9 using PDF symbols. For further assistance or additional exercises, please provide details!