Class 7 Maths Chapter 1 Question Answers - Integers

Q1. Subtract the sum of −1032 and 878 from −34
Ans: 
Step 1: Find the sum of −1032 and 878
(−1032+ 878) = −154
Step 2: Subtract the sum i.e., −154 from −34
-34 - (-154)
= -34 + 154
= 120

Q2. In a quiz, Team A scored −40, 10, 0 and Team B scored 10, 0, − 40 in three successive rounds. Which team scored more? Can we say that we can add integers in any order?
Ans:
Known:
The scores of teams A and B
Unknown:
To find the total score of each team separately.

Steps: 
Scores of Team A =−40, 10, 0
Add the scores,
Total score of Team A = −40 + 10 + 0 = −30
Scores of Team B = 10, 0,− 40
Add the scores,
Total score of Team B = 10 + 0 + (−40)
= 10 + 0 − 40
= −30
We observe that the scores of both the teams are Equal in numbers. Yes. We can add integers in any order even though their order Is different from the above observation.

Q3. In a class test containing 10 questions, 5 marks are awarded for every correct answer and (−2) marks are awarded for every incorrect answer and zero for each question not attempted.
(i)  Ravi gets 4 correct and 6 incorrect answers. What is his score?
(ii)  Reenu gets 5 correct and 5 incorrect answers. What is her score?
(iii)  Heena gets 2 correct and 5 incorrect answers. What is her score?
Ans:
We know that,
Total number of questions in a class test = 10
Marks awarded for every correct answer =+5
Marks awarded for every incorrect answer = (−2)
Marks awarded for questions not attempted = 0

Steps:
(i) To calculate total marks scored by Ravi in the class test:
Marks obtained by Ravi for 4 correct answers = 5 x 4 = 20
Marks obtained by Ravi for 6 incorrect answers = (-2) x  6 = -12
Total marks scored by Ravi = 4 correct answers + 6 incorrect answers
= 20  + (-12
= 20 - 12
= 8
Thus, the total marks scored by Ravi in the class test is 8 marks.
(ii) To calculate total marks scored by Reenu in the class test:
Marks obtained by Reenu for 5 correct answers = 5 x 5 = 25
Marks obtained by Reenu for 5 incorrect answers = (-2) x 5 = -10
Total marks scored by Reenu = 5 correct answers + 5 incorrect answers
= 25 + ( -10)
= 25 - 10
= 15
Thus, the total marks scored by Reenu in the class test is 15 marks.
(iii) To calculate total marks scored by Heena in the class test:
Marks obtained by Heena for 2 correct answers = 5 x 2 = 10
Marks obtained by Heena for 5 incorrect answers = (-2) x 5 = -10
Total marks scored by Heena = 2 correct answers + 5 incorrect answers
= 10 + (-10)
= 10 - 10
= 0
Thus, the total marks scored by Heena in the class test is 0 marks.

Q4. Simplify: (−16) x (-15) + (-16) x (-5)
Ans:
Applying the Distributive Law axb + bxc = ax(b + c) we get,
(-16) x (-15) + (-16) x (-5) = (-16) x (-15 + (-5))
= (-16)x(-15-5)
= (-16)x(-20)
= 320
So, the answer is 320

Q5. Solve 45 - [38 - {60 ÷ 3 — (6 — 9 ÷3) ÷3}]
Ans:
Here, we should apply the BODMAS Rule
45 - [38 -{60÷3 - (6 -9 ÷ 3)÷3}]
First, solve for the inner brackets
= 45 - [38 - (60 ÷3 — (6 — 3) ÷ 3} ]
= 45 - [38 - (60 ÷ 3 — (3) ÷ 3}]
= 45 -[38- (60 ÷ 3- (1)}]
Second, solve for the flower brackets
= 45 - [38 - {20 - 1}]
= 45 - [38 - 19]
Third, solve for the big brackets
= 45 - 19
= 26
Thus, the solution is 26

Q6. Verify that a + {b + c) ≠ {a ÷ b) + {a ÷ c)
(i)    a = 8, b = -4,c = 2
(ii)    a = -15,b = 2,c = 1
Ans: 
We should verify that,
a + {b + c) ≠ {a ÷ b) + {a ÷ c)
Steps:
(i) Given a = 8 b = -4, c = 2 Consider the L.H.S. = a + (b ÷ c)
Substituting the values for a, b and c
L.H.S. = 8 ÷ (-4 + 2)
= 8 ÷ (—2)
= -4
Thus, a ÷ (b + c) = 4
Consider the R.H.S. = (a ÷ b) + (a ÷ c)
Substituting the values for a,b and c
R.H.S. = {(8) ÷ (-4)} + {(8) ÷ 2}
= -2 + 4 = 2
Thus, (a ÷ b) + (a ÷ c) = 2

We observe that L.H.S. and R.H.S. are not same.
Hence, it is verified that a ÷ (b + c) ≠ (a ÷ b) + {a ÷ c)
(ii)    Given a = -15, b = 2, c = 1
Consider the L.H.S. = a ÷ (b + c)
Substituting the values for a,b and c
L.H.S. = -15 ÷ (2 + 1)
= -15 ÷ (3)
= -5
Thus, L.H.S. = a ÷ (b + c) = -5
Consider R.H. S. = {a ÷ b) + {a ÷ c)
Substituting the values for a, b and c
R.H.S. = {(-15) ÷ (2)} + {(-15) ÷ 1}
= -7.5 + (-15)
= -22.5
Thus, R.H.S. = (a ÷ b) + (a ÷ c) = -22.5
We observe that L.H.S. and R.H.S. are not same.
Hence, it is verified that a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c).