Students can Download Class 7 Maths Chapter 1 Integers Ex 1.4 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 7 Maths helps you to revise the complete Karnataka State Board Syllabus and to clear all their doubts, score well in final exams.
Karnataka State Syllabus Class 7 Maths Chapter 1 Integers Ex 1.4
Question 1.
Evaluate each of the following
a) (- 30) ÷ 10
Solution:
(- 30) ÷ 10 = – 3
b) 50 ÷ (- 5)
Solution:
\(\frac{50}{-5}=-10\)
c) (- 36) ÷ (- 9)
Solution:
\(\frac{-36}{-9}=4\)
= 4
d) (- 49) ÷ (49)
Solution:
\(\frac{-49}{+49}=-1\)
= – 1
e) 13 ÷ [(- 2) + 1]
Solution:
= 13 ÷ (- 2 + 10)
= 13 ÷ (- 1)
= -13
f) 0 ÷ (- 12)
= 0
g) (- 31) ÷ [(- 30) + (- 1)]
= (- 31) ÷ [- 30 – 1]
= (- 31) ÷ (- 31)
\(\frac{-31}{-31}=+1\)
= 1
h) [(- 36) ÷ 12] ÷ 3
Solution:
= -1
i) [(- 6) + 5] ÷ [(- 2) + 1]
=[- 6 + 5] ÷ [- 2 + 1]
= (- 1) ÷ (- 1)
= 1
Question 2.
Verify that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) for each of the following values of a, b and c.
a) a = 12, b = – 4, c = 2
Solution:
a) a = 12, b = – 4, c = 2
To verify a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)
⇒ 12 ÷ (- 4 + 2) ≠ [12 ÷ (- 4)] + (12 ÷ 2 )
⇒ 12 ÷ (- 2) ≠ – 3 + 6
⇒ – 6 ≠ 3
b) a = (-10), b = 1, c = 1
⇒ (- 10) ÷ (1 + 1) ≠ [(- 10) ÷ 1] + (- 10 ÷ 1)
⇒ – 10 ÷ 2 ≠ – 10 + (-10)
⇒ – 5 ≠ – 20
Question 3.
Fill in the blanks :
a) 369 ÷ ___ = 369
369 ÷ 1 = 369
b) (- 75) ÷ ___ = – 1
(- 75) ÷ 75 = – 1
c) (- 206) ÷ ___ = 1
(- 206) ÷ – 206 = 1
d) – 87 ÷ ___ = 87
– 87 ÷ – 1 = 87
e) ___ ÷ 1 = – 87
87 ÷ 1 = – 87
f) ___ ÷ 48 = – 1
48 ÷ 48 = – 1
g) 20 ÷ ___ = – 2
20 ÷ – 10 = (- 2)
h) __ ÷ (4) = – 3
– 12 ÷ (4) = – 3
Question 4.
Write five pairs of integers (a, b) such that a – b = – 3. One such pair is (6, – 2) because 6 ÷ (- 2) = (- 3)
Solution:
a ÷ b = – 3
∴ The other five pairs are (- 6, 2), (- 3, 1), (- 9, 3), (- 12, 4), (- 15, 5)
Question 5.
The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night?
Solution:
Temperature at 12pm = 10°C
Temperature decreases at 2°C per hour
we need to find, time when temperature is 8°C below zero, ie., – 8°C
∴ Total decrease = Final temperature – initial temperature = – 8°C – 10°C
= – 8 – 10 = -18°C
Now,
Temperature decrease in 1 hour × Total number of hours = Total decrease
So, temperature becomes – 8°C = 9 hours
∴ Temperature is -8°C at 9PM
Now,
We need to find temperature at mid – night temperature at 12AM = Temperature at 12PM
Temperature change in 12 hours
Temperature change in 1 hour = – 2°C
Temperature change in 12 hour = – 2 × 12°C = – 24°C
Now,
Temperature at 12AM – Temperature at 12PM = Temperature change in 12 hours. Temperature at 12AM – 10°C = – 24°C
Temperature at 12AM = – 24°C + 10°C
Temperature at 12 AM = – 14°C
∴ Temperature at Mid – night = – 14°C
Question 6.
In a class test (+ 3) marks are given for every correct answer and (- 2) marks are given for every incorrect answer and no marks for not attempting any question.
Solution:
Marks given for correct answer = + 3
Marks given for incorrect answer = – 2
Marks given for not attempting = 0
i) Radhika scored 20 marks. If she has got 12 correct answers, how many questions has she attempted incorrectly?
Solution:
Total marks scored = 20
Number of correct answer = 12
Marks of for correct answer = 12 × 3 = 36
Also
Marks for incorrect answer = (- 2) × Number of incorrect answer
Marks for not attempt answer = 0 × Number of not attempt = 0
Now,
Total marks = marks for correct answer + marks for incorrect answer + marks for not attempt
20 = 36 + (- 2) × No of incorrect answers + 0
20 – 36 = (- 2) × No of incorrect answers
– 16 = (- 2) × No of incorrect answer
\(\frac{-16}{-2}\) = No of incorrect answers
8 = No of incorrect answers
So, Radhika attempted 8 questions incorrectly
ii) Mohini scores -5 marks in this test, though she has got 7 correct answers. How many questions has she attempted incorrectly?
Solution:
Total marks = -5
No of correct answers = 7
Marks for correct answers = 7 × 3 = 21
Also,
Marks for incorrect answer = (-2) × No. of incorrect answers
Marks for not attempt answer = 0 × No of not attempt answers
Now,
Total marks = marks for correct answer + marks for incorrect answer + marks for not attempt
-5 = 21 + (-2) × No. of incorrect answers + 0
-5 – 21 = (-2) × No. of incorrect answers
-26 = -2 × No. of incorrect answers
\(\frac{-26}{-2}\) = No. of incorrect answers
13 = No, of incorrect answers.
∴ Mohini attempted 13 questions incorrectly
Question 7.
An elevator descends into a mine shaft at the rate of 6m/min. If the descent starts from 10m above the ground level, how long will it take to reach – 350 m.
Solution:
Initial position = 10m final position = -350 m
Total distance elevator has to travel = initial position – final position
= 10 – (-350)
= 10 + 350 = 360 m
Now,
Elevator descends at rate 6m/min
∴ Elevator travels 6m in = 1 minute
Elevator travels 1 m in: = \(\frac{1}{6}\)
Elevator travels 360m in = \(\frac{1}{6}\) × 360 minutes
= 60 minutes
= 1 hour
∴ It will take the elevator 1 hour.