7 th maths 1.1

 

Class 7 Maths — Chapter 1: Number System

Exercise 1.1 Solutions

1. Fill in the blanks

1. (-30) + 90 = 60
2. (-5) + -95 = -100
3. (-52) + (-52) = -104
4. 22 + (-22) = 0
5. 140 + (-70) = 70
6. 20 + 80 + -100 = 0
7. 75 + (-25) = 50
8. 171 + -171 = 0
9. [(-3) + (-12)] + (-77) = -3 + [(-12) + (-77)] (Associative Property)
10. (-42) + [15 + (-23)] = [-42 + 15] + -23 (Associative Property)

2. Say True or False

1. The additive inverse of (-32) is (-32)
   Answer: False
   Reason: The additive inverse of (-32) is +32.
2. (-90) + (-30) = 60
   Answer: False
   Reason: (-90) + (-30) = -120.
3. (-125) + 25 = -100
   Answer: True

3. Add the following

1. 8 and -12 using number line:
   Start at 0, move 8 units right to reach +8, then move 12 units left.
   Answer: -4
2. (-3) and (-5) using number line:
   Start at 0, move 3 units left to reach -3, then move 5 more units left.
   Answer: -8
3. (-100) + (-10) = -110
4. 20 + (-72) = -52
5. 82 + (-75) = 7
6. -48 + (-15) = -63
7. -225 + (-63) = -288

4. Word Problem 1

Thenmalar appeared for a competitive exam which has negative scoring of 1 mark for each incorrect answer. In paper I she answered 25 questions incorrectly and in paper II, 13 questions incorrectly. Find the total reduction of marks.

Solution:

• Incorrect answers in Paper I = 25
• Incorrect answers in Paper II = 13
• Total incorrect answers = 25 + 13 = 38
• Marks reduced per wrong answer = -1 mark
• Total reduction of marks = 38 × (-1) = -38 marks

Answer: The total reduction of marks is 38.

5. Word Problem 2

In a quiz competition, Team A scored +30, -20, 0 and Team B scored -20, 0, +30 in three successive rounds. Which team will win? Can we say that we can add integers in any order?

Solution:

• Total score of Team A = 30 + (-20) + 0 = 10 points
• Total score of Team B = (-20) + 0 + 30 = 10 points

Answer:

1. Both teams scored equal points (10 points). Therefore, it is a tie and neither team won.
2. Yes, we can add integers in any order (due to the Commutative and Associative properties of addition).

6. Word Problem 3

Are (11 + 7) + 10 and 11 + (7 + 10) equal? Mention the property.

Solution:

• LHS = (11 + 7) + 10 = 18 + 10 = 28
• RHS = 11 + (7 + 10) = 11 + 17 = 28

Answer: Yes, they are equal. The property shown is the Associative Property of Addition.

7. Find 5 pairs of integers that add up to 2

Find 5 pairs of integers that add up to 2.

Solution:

1. 0 + 2 = 2  →  (0, 2)
2. 1 + 1 = 2  →  (1, 1)
3. (-1) + 3 = 2  →  (-1, 3)
4. (-2) + 4 = 2  →  (-2, 4)
5. (-3) + 5 = 2  →  (-3, 5)